The success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease. We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations.The success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease. We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations.

1 aBUONOMO, BRUNO1 aDella Marca, Rossella1 aSHARBAYTA, SILESHI, SINTAYEHU uhttps://doi.org/10.1142/S021833902250008500574nas a2200133 4500008004100000245012300041210006900164300001200233490000700245100002100252700002100273700002100294856012500315 2022 eng d00aA comparison of reduced-order modeling approaches using artificial neural networks for PDEs with bifurcating solutions0 acomparison of reducedorder modeling approaches using artificial a52–650 v561 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/comparison-reduced-order-modeling-approaches-using-artificial-neural-networks-pdes00506nas a2200109 4500008004100000245009600041210006900137100002100206700002100227700002100248856012700269 2022 eng d00aData-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics0 aDataDriven Enhanced Model Reduction for Bifurcating Models in Co1 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/data-driven-enhanced-model-reduction-bifurcating-models-computational-fluid-dynamics00572nas a2200109 4500008004100000245016300041210006900204100002100273700002100294700002100315856012600336 2022 eng d00aA Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation0 aDataDriven Surrogate Modeling Approach for TimeDependent Incompr1 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/data-driven-surrogate-modeling-approach-time-dependent-incompressible-navier-stokes00575nas a2200157 4500008004100000245015100041210006900192260001200261300001600273490000700289100002000296700002200316700001700338700002100355856004100376 2022 eng d00aDriving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier–Stokes equations with model order reduction0 aDriving bifurcating parametrized nonlinear PDEs by optimal contr c2022/// a1361 - 14000 v561 aPichi, Federico1 aStrazzullo, Maria1 aBallarin, F.1 aRozza, Gianluigi uhttps://doi.org/10.1051/m2an/202204402343nas a2200241 4500008004100000020001400041245008300055210006900138260001500207490000800222520159500230653002401825653002601849653002201875653002101897653001901918653002501937100002601962700002901988700002202017700002502039856003702064 2022 eng d a0170-421400aMathematical modelling of oscillating patterns for chronic autoimmune diseases0 aMathematical modelling of oscillating patterns for chronic autoi c2022/04/010 vn/a3 aMany autoimmune diseases are chronic in nature, so that in general, patients experience periods of recurrence and remission of the symptoms characterizing their specific autoimmune ailment. In order to describe this very important feature of autoimmunity, we construct a mathematical model of kinetic type describing the immune system cellular interactions in the context of autoimmunity exhibiting recurrent dynamics. The model equations constitute a nonlinear system of integro-differential equations with quadratic terms that describe the interactions between self-antigen presenting cells, self-reactive T cells, and immunosuppressive cells. We consider a constant input of self-antigen presenting cells, due to external environmental factors that are believed to trigger autoimmunity in people with predisposition for this condition. We also consider the natural death of all cell populations involved in our model, caused by their interaction with cells of the host environment. We derive the macroscopic analogue and show positivity and well-posedness of the solution and then we study the equilibria of the corresponding dynamical system and their stability properties. By applying dynamical system theory, we prove that steady oscillations may arise due to the occurrence of a Hopf bifurcation. We perform some numerical simulations for our model, and we observe a recurrent pattern in the solutions of both the kinetic description and its macroscopic analogue, which leads us to conclude that this model is able to capture the chronic behaviour of many autoimmune diseases.

10aautoimmune diseases10acellular interactions10aDynamical systems10aHopf bifurcation10akinetic theory10amathematical biology1 aDella Marca, Rossella1 aRamos, Maria, da Piedade1 aRibeiro, Carolina1 aSoares, Ana, Jacinta uhttps://doi.org/10.1002/mma.822901740nas a2200253 4500008004100000020001400041245009200055210006900147260001500216490000800231520092600239653002301165653001901188653002401207653001901231653002201250653005301272653003601325653002701361100002001388700002001408700002101428856003701449 2022 eng d a0271-209100aModel order reduction for bifurcating phenomena in fluid-structure interaction problems0 aModel order reduction for bifurcating phenomena in fluidstructur c2022/05/230 vn/a3 aAbstract This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coand? effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper-elastic law delays the bifurcation w.r.t. the standard model, while the same effect is even magnified when considering linear elastic solid.

10aBifurcation theory10aCoandă effect10acontinuum mechanics10afluid dynamics10amonolithic method10aparametrized fluid-structure interaction problem10aProper orthogonal decomposition10areduced order modeling1 aKhamlich, Moaad1 aPichi, Federico1 aRozza, Gianluigi uhttps://doi.org/10.1002/fld.511800480nas a2200097 4500008004100000245010500041210006900146100002100215700002100236856012500257 2022 eng d00aModel Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations0 aModel Reduction Using Sparse Polynomial Interpolation for the In1 aHess, Martin, W.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/model-reduction-using-sparse-polynomial-interpolation-incompressible-navier-stokes02363nas a2200349 4500008004100000245014100041210006900182490000800251520110500259653001401364653002901378653002401407653002501431653002001456653002701476653001501503653003401518653003501552653002401587653001901611653003301630653002701663653002801690653002401718653001601742100002201758700001701780700002301797700002201820700002101842856015001863 2022 eng d00aThe Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations0 aNeural Network shiftedproper orthogonal decomposition A machine 0 v3923 aModels with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N−width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation. © 2022 Elsevier B.V.

10aAdvection10aComputational complexity10aDeep neural network10aDeep neural networks10aLinear subspace10aMultiphase simulations10aNon linear10aNonlinear hyperbolic equation10aPartial differential equations10aPhase space methods10aPre-processing10aPrincipal component analysis10areduced order modeling10aReduced order modelling10aReduced-order model10aShifted-POD1 aPapapicco, Davide1 aDemo, Nicola1 aGirfoglio, Michele1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633&doi=10.1016%2fj.cma.2022.114687&partnerID=40&md5=12f82dcaba04c4a7c44f8e5b2010199701567nas a2200217 4500008004100000020001400041245011400055210007100169260001600240300001100256520078900267653002401056653003001080653003601110653002401146653004201170100002301212700002101235700002101256856007201277 2022 eng d a0045-793000aA POD-Galerkin reduced order model for the Navier–Stokes equations in stream function-vorticity formulation0 aPODGalerkin reduced order model for the Navier–Stokes equations c2022/06/14/ a1055363 aWe develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier–Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parametrization.

10aGalerkin projection10aNavier–Stokes equations10aProper orthogonal decomposition10aReduced order model10aStream function-vorticity formulation1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S004579302200164501169nas a2200133 4500008004100000245014700041210007100188520056100259100001900820700002400839700002100863700001600884856013500900 2022 eng d00aProjection based semi–implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid–Structure Interaction problems0 aProjection based semi–implicit partitioned Reduced Basis Method 3 aThe goal of this manuscript is to present a partitioned Model Order Reduction method that is based on a semi-implicit projection scheme to solve multiphysics problems. We implement a Reduced Order Method based on a Proper Orthogonal Decomposition, with the aim of addressing both time-dependent and time-dependent, parametrized Fluid-Structure Interaction problems, where the fluid is incompressible and the structure is thick and two dimensional.

1 aNonino, Monica1 aBallarin, Francesco1 aRozza, Gianluigi1 aMaday, Yvon uhttps://www.math.sissa.it/publication/projection-based-semi%E2%80%93implicit-partitioned-reduced-basis-method-non-parametrized-and00660nas a2200169 4500008004100000245010500041210006900146653005200215653004300267653002100310653002900331653003300360100002200393700001700415700002100432856003700453 2022 eng d00aA Proper Orthogonal Decomposition approach for parameters reduction of Single Shot Detector networks0 aProper Orthogonal Decomposition approach for parameters reductio10aComputer Vision and Pattern Recognition (cs.CV)10aFOS: Computer and information sciences10aFOS: Mathematics10aMachine Learning (cs.LG)10aNumerical Analysis (math.NA)1 aMeneghetti, Laura1 aDemo, Nicola1 aRozza, Gianluigi uhttps://arxiv.org/abs/2207.1355100455nas a2200121 4500008004100000245006500041210006100106300000600167100002600173700001500199700001800214856010100232 2022 eng d00aAn SIR–like kinetic model tracking individuals' viral load0 aSIR–like kinetic model tracking individuals viral load a-1 aDella Marca, Rossella1 aLoy, Nadia1 aTosin, Andrea uhttps://www.math.sissa.it/publication/sir%E2%80%93-kinetic-model-tracking-individuals-viral-load00546nas a2200121 4500008004100000245009900041210006900140100002000209700002400229700002100253700002200274856012800296 2021 eng d00aAn artificial neural network approach to bifurcating phenomena in computational fluid dynamics0 aartificial neural network approach to bifurcating phenomena in c1 aPichi, Federico1 aBallarin, Francesco1 aRozza, Gianluigi1 aHesthaven, Jan, S uhttps://www.math.sissa.it/publication/artificial-neural-network-approach-bifurcating-phenomena-computational-fluid-dynamics00412nas a2200109 4500008004100000245006200041210006200103300001400165490000800179100002000187856009500207 2021 eng d00aAsymptotic approach to a rotational Taylor swimming sheet0 aAsymptotic approach to a rotational Taylor swimming sheet a103–1160 v3491 aCorsi, Giovanni uhttps://www.math.sissa.it/publication/asymptotic-approach-rotational-taylor-swimming-sheet00553nas a2200133 4500008004100000245010000041210006900141300001100210490000700221100002100228700001900249700002100268856013000289 2021 eng d00aATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis0 aATHENA Advanced Techniques for High dimensional parameter spaces a1001330 v101 aRomor, Francesco1 aTezzele, Marco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/athena-advanced-techniques-high-dimensional-parameter-spaces-enhance-numerical-analysis00537nas a2200109 4500008004100000245012200041210006900163100002200232700002400254700002100278856012800299 2021 eng d00aA CERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC OPTIMAL CONTROL PROBLEMS IN SPACE-TIME FORMULATION0 aCERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC1 aStrazzullo, Maria1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/certified-reduced-basis-method-linear-parametrized-parabolic-optimal-control-problems02606nas a2200265 4500008004100000022001400041245009300055210006900148300001100217490000800228520174600236653003101982653003302013653001902046653002602065653002002091653003602111100002102147700002102168700001902189700002202208700001702230700002102247856007202268 2021 eng d a0045-793000aOn the comparison of LES data-driven reduced order approaches for hydroacoustic analysis0 acomparison of LES datadriven reduced order approaches for hydroa a1048190 v2163 aIn this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

10aDynamic mode decomposition10aFfowcs Williams and Hawkings10aHydroacoustics10aLarge eddy simulation10aModel reduction10aProper orthogonal decomposition1 aGadalla, Mahmoud1 aCianferra, Marta1 aTezzele, Marco1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S004579302030389300623nas a2200133 4500008004100000245014300041210006900184100002200253700002300275700002400298700001600322700002100338856013000359 2021 eng d00aConsistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows0 aConsistency of the full and reduced order models for EvolveFilte1 aStrazzullo, Maria1 aGirfoglio, Michele1 aBallarin, Francesco1 aIliescu, T.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/consistency-full-and-reduced-order-models-evolve-filter-relax-regularization-convection00576nas a2200121 4500008004100000245013300041210006900174100002300243700002200266700001900288700002100307856012600328 2021 eng d00aA data-driven partitioned approach for the resolution of time-dependent optimal control problems with dynamic mode decomposition0 adatadriven partitioned approach for the resolution of timedepend1 aDonadini, Eleonora1 aStrazzullo, Maria1 aTezzele, Marco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/data-driven-partitioned-approach-resolution-time-dependent-optimal-control-problems01404nas a2200157 4500008004100000020001400041245008300055210006900138260001500207300001800222490000700240520091200247100001801159700002201177856004701199 2021 eng d a1559-002X00aA Differential Perspective on Gradient Flows on CAT(K)-Spaces and Applications0 aDifferential Perspective on Gradient Flows on CATKSpaces and App c2021/12/01 a11780 - 118180 v313 aWe review the theory of Gradient Flows in the framework of convex and lower semicontinuous functionals on $$\textsf {CAT} (\kappa )$$-spaces and prove that they can be characterized by the same differential inclusion $$y_t'\in -\partial ^-\textsf {E} (y_t)$$one uses in the smooth setting and more precisely that $$y_t'$$selects the element of minimal norm in $$-\partial ^-\textsf {E} (y_t)$$. This generalizes previous results in this direction where the energy was also assumed to be Lipschitz. We then apply such result to the Korevaar–Schoen energy functional on the space of $$L^2$$and CAT(0) valued maps: we define the Laplacian of such $$L^2$$map as the element of minimal norm in $$-\partial ^-\textsf {E} (u)$$, provided it is not empty. The theory of gradient flows ensures that the set of maps admitting a Laplacian is $$L^2$$-dense. Basic properties of this Laplacian are then studied.

1 aGigli, Nicola1 aNobili, Francesco uhttps://doi.org/10.1007/s12220-021-00701-500460nas a2200109 4500008004100000245007400041210006900115100002200184700001700206700002100223856010600244 2021 eng d00aA Dimensionality Reduction Approach for Convolutional Neural Networks0 aDimensionality Reduction Approach for Convolutional Neural Netwo1 aMeneghetti, Laura1 aDemo, Nicola1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/dimensionality-reduction-approach-convolutional-neural-networks00366nas a2200109 4500008004100000245004200041210003900083100001900122700002200141700001900163856007400182 2021 eng d00aOn Dini derivatives of real functions0 aDini derivatives of real functions1 aKlun, Giuliano1 aFonda, Alessandro1 aSfecci, Andrea uhttps://www.math.sissa.it/publication/dini-derivatives-real-functions01780nas a2200169 4500008004100000020002200041245009500063210006900158260005200227520110800279100001601387700002101403700002101424700002301445700001901468856012301487 2021 eng d a978-3-030-55874-100aDiscontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation0 aDiscontinuous Galerkin Model Order Reduction of Geometrically Pa aChambSpringer International Publishingc2021//3 aThe present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time.

1 aShah, Nirav1 aHess, Martin, W.1 aRozza, Gianluigi1 aVermolen, Fred, J.1 aVuik, Cornelis uhttps://www.math.sissa.it/publication/discontinuous-galerkin-model-order-reduction-geometrically-parametrized-stokes-000487nas a2200133 4500008004100000245008300041210006900124300001400193490001500207100002200222700001800244700002600262856006500288 2021 eng d00aDisplacement convexity of Entropy and the distance cost Optimal Transportation0 aDisplacement convexity of Entropy and the distance cost Optimal a411–4270 vSer. 6, 301 aCavalletti, Fabio1 aGigli, Nicola1 aSantarcangelo, Flavia uhttps://afst.centre-mersenne.org/articles/10.5802/afst.1679/00498nas a2200109 4500008004100000245009500041210006900136100002500205700001700230700002100247856012000268 2021 eng d00aA dynamic mode decomposition extension for the forecasting of parametric dynamical systems0 adynamic mode decomposition extension for the forecasting of para1 aAndreuzzi, Francesco1 aDemo, Nicola1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/dynamic-mode-decomposition-extension-forecasting-parametric-dynamical-systems00587nas a2200145 4500008004100000020001400041245007800055210006900133260001500202300000700217490000700224520014200231100002100373856004700394 2021 eng d a1420-900400aA dynamic model for viscoelasticity in domains with time-dependent cracks0 adynamic model for viscoelasticity in domains with timedependent c2021/10/01 a670 v283 aIn this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracking domains.

1 aSapio, Francesco uhttps://doi.org/10.1007/s00030-021-00729-002134nas a2200157 4500008004100000245011600041210006900157490000700226520151300233100002001746700002001766700002101786700002101807700002001828856012801848 2021 eng d00aEfficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method0 aEfficient computation of bifurcation diagrams with a deflated ap0 v473 aThe majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

1 aPintore, Moreno1 aPichi, Federico1 aHess, Martin, W.1 aRozza, Gianluigi1 aCanuto, Claudio uhttps://www.math.sissa.it/publication/efficient-computation-bifurcation-diagrams-deflated-approach-reduced-basis-spectral-001870nas a2200169 4500008004100000245014800041210006900189300001200258490000700270520119600277100001701473700001901490700002101509700002101530700002201551856012701573 2021 eng d00aAn efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques0 aefficient computational framework for naval shape design and opt a211-2300 v143 aThis contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

1 aDemo, Nicola1 aOrtali, Giulio1 aGustin, Gianluca1 aRozza, Gianluigi1 aLavini, Gianpiero uhttps://www.math.sissa.it/publication/efficient-computational-framework-naval-shape-design-and-optimization-problems-means00935nas a2200133 4500008004100000020001400041245010200055210007100157260001500228520047100243100001900714700002100733856004700754 2021 eng d a1424-320200aAn existence result for the fractional Kelvin–Voigt’s model on time-dependent cracked domains0 aexistence result for the fractional Kelvin–Voigt s model on time c2021/06/043 aWe prove an existence result for the fractional Kelvin–Voigt’s model involving Caputo’s derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin–Voigt’s model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique.

1 aCaponi, Maicol1 aSapio, Francesco uhttps://doi.org/10.1007/s00028-021-00713-200523nas a2200109 4500008004100000245011200041210006900153100001700222700002200239700002100261856013100282 2021 eng d00aAN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS0 aEXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSI1 aDemo, Nicola1 aStrazzullo, Maria1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/extended-physics-informed-neural-network-preliminary-analysis-parametric-optimal-control00414nas a2200097 4500008004100000245007200041210006900113100001800182700002200200856009400222 2021 eng d00aA first-order condition for the independence on p of weak gradients0 afirstorder condition for the independence on p of weak gradients1 aGigli, Nicola1 aNobili, Francesco uhttps://www.math.sissa.it/publication/first-order-condition-independence-p-weak-gradients01265nas a2200157 4500008004100000245008800041210006900129300001200198490000700210520069300217100002200910700001700932700002000949700002100969856011700990 2021 eng d00aHierarchical model reduction techniques for flow modeling in a parametrized setting0 aHierarchical model reduction techniques for flow modeling in a p a267-2930 v193 aIn this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases.

1 aZancanaro, Matteo1 aBallarin, F.1 aPerotto, Simona1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/hierarchical-model-reduction-techniques-flow-modeling-parametrized-setting01664nas a2200169 4500008004100000022001400041245011000055210006900165300000800234490000600242520112900248100001701377700001901394700001701413700002101430856004301451 2021 eng d a2077-131200aHull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing0 aHull Shape Design Optimization with Parameter Space and Model Re a1850 v93 aIn the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.mdpi.com/2077-1312/9/2/18500548nas a2200169 4500008004100000245009600041210006900137260001200206300000800218490000600226100002200232700001900254700002200273700002000295700002100315856004200336 2021 eng d00aHybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters0 aHybrid Neural Network Reduced Order Modelling for Turbulent Flow bMDPI AG a2960 v61 aZancanaro, Matteo1 aMrosek, Markus1 aStabile, Giovanni1 aOthmer, Carsten1 aRozza, Gianluigi uhttps://doi.org/10.3390/fluids608029600554nas a2200169 4500008004100000022001400041245009200055210006900147300001600216490000800232100001900240700002000259700001900279700002200298700002600320856003800346 2021 eng d a0002-994700aIndependence of synthetic curvature dimension conditions on transport distance exponent0 aIndependence of synthetic curvature dimension conditions on tran a5877–59230 v3741 aAkdemir, Afiny1 aColinet, Andrew1 aMcCann, Robert1 aCavalletti, Fabio1 aSantarcangelo, Flavia uhttps://doi.org/10.1090/tran/841300492nas a2200109 4500008004100000245009000041210006900131100002100200700001900221700002100240856012100261 2021 eng d00aA local approach to parameter space reduction for regression and classification tasks0 alocal approach to parameter space reduction for regression and c1 aRomor, Francesco1 aTezzele, Marco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/local-approach-parameter-space-reduction-regression-and-classification-tasks-000401nas a2200109 4500008004100000245005500041210005200096100002200148700002400170700001800194856007900212 2021 eng d00aOn master test plans for the space of BV functions0 amaster test plans for the space of BV functions1 aNobili, Francesco1 aPasqualetto, Enrico1 aSchultz, Timo uhttps://www.math.sissa.it/publication/master-test-plans-space-bv-functions01334nas a2200157 4500008004100000022001400041245010000055210007100155300000800226490000600234520083600240100001901076700001701095700002101112856004301133 2021 eng d a2311-552100aA Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems0 aMonolithic and a Partitioned Reduced Basis Method for Fluid–Stru a2290 v63 aThe aim of this work is to present an overview about the combination of the Reduced Basis Method (RBM) with two different approaches for Fluid–Structure Interaction (FSI) problems, namely a monolithic and a partitioned approach. We provide the details of implementation of two reduction procedures, and we then apply them to the same test case of interest. We first implement a reduction technique that is based on a monolithic procedure where we solve the fluid and the solid problems all at once. We then present another reduction technique that is based on a partitioned (or segregated) procedure: the fluid and the solid problems are solved separately and then coupled using a fixed point strategy. The toy problem that we consider is based on the Turek–Hron benchmark test case, with a fluid Reynolds number Re=100.

1 aNonino, Monica1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.mdpi.com/2311-5521/6/6/22910834nas a2200109 45000080041000002450068000412100065001095201041400174100001810588700002210606856009610628 2021 eng d00aMonotonicity formulas for harmonic functions in RCD(0,N) spaces0 aMonotonicity formulas for harmonic functions in RCD0N spaces3 aWe generalize to the RCD(0,N) setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with non-negative Ricci curvature. Rigidity and almost rigidity statements are also proven, the second appearing to be new even in the smooth setting. Motivated by the recent work in [AFM] we also introduce the notion of electrostatic potential in RCD spaces, which also satisfies our monotonicity formulas. Our arguments are mainly based on new estimates for harmonic functions in RCD(K,N) spaces and on a new functional version of the `(almost) outer volume cone implies (almost) outer metric cone' theorem.

1 aGigli, Nicola1 aViolo, Ivan, Yuri uhttps://www.math.sissa.it/publication/monotonicity-formulas-harmonic-functions-rcd0n-spaces00598nas a2200133 4500008004100000245013200041210006900173260002500242490000700267100002100274700001900295700002100314856012900335 2021 eng d00aMulti-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces0 aMultifidelity data fusion for the approximation of scalar functi bWiley Online Library0 v201 aRomor, Francesco1 aTezzele, Marco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/multi-fidelity-data-fusion-approximation-scalar-functions-low-intrinsic-dimensionality00580nas a2200133 4500008004100000245010900041210006900150100002100219700001900240700001900259700002000278700002100298856012700319 2021 eng d00aMulti-fidelity data fusion through parameter space reduction with applications to automotive engineering0 aMultifidelity data fusion through parameter space reduction with1 aRomor, Francesco1 aTezzele, Marco1 aMrosek, Markus1 aOthmer, Carsten1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/multi-fidelity-data-fusion-through-parameter-space-reduction-applications-automotive00750nas a2200217 4500008004100000245007000041210006800111300001600179490000700195100002300202700002400225700002400249700002400273700002300297700002100320700002100341700002200362700002000384700002400404856010400428 2021 eng d00aNon-intrusive data-driven ROM framework for hemodynamics problems0 aNonintrusive datadriven ROM framework for hemodynamics problems a1183–11910 v371 aGirfoglio, Michele1 aScandurra, Leonardo1 aBallarin, Francesco1 aInfantino, Giuseppe1 aNicolò, Francesca1 aMontalto, Andrea1 aRozza, Gianluigi1 aScrofani, Roberto1 aComisso, Marina1 aMusumeci, Francesco uhttps://www.math.sissa.it/publication/non-intrusive-data-driven-rom-framework-hemodynamics-problems01161nas a2200157 4500008004100000020001400041245007800055210006900133260001500202300001200217520066800229100002200897700001900919700001900938856004600957 2021 eng d a0219-199700aNon-well-ordered lower and upper solutions for semilinear systems of PDEs0 aNonwellordered lower and upper solutions for semilinear systems c2021/08/27 a21500803 aWe prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.

1 aFonda, Alessandro1 aKlun, Giuliano1 aSfecci, Andrea uhttps://doi.org/10.1142/S021919972150080201203nas a2200133 4500008004100000245007700041210006900118490000800187520076200195100002500957700002200982700002201004856004301026 2021 eng d00aNutations in growing plant shoots as a morphoelastic flutter instability0 aNutations in growing plant shoots as a morphoelastic flutter ins0 v3793 aGrowing plant shoots exhibit spontaneous oscillations that Darwin observed, and termed "circumnutations". Recently, they have received renewed attention for the design and optimal actuation of bioinspired robotic devices. We discuss a possible interpretation of these spontaneous oscillations as a Hopf-type bifurcation in a growing morphoelastic rod. Using a three-dimensional model and numerical simulations, we analyse the salient features of this flutter-like phenomenon (e.g. the characteristic period of the oscillations) and their dependence on the model details (in particular, the impact of choosing different growth models) finding that, overall, these features are robust with respect to changes in the details of the growth model adopted.

1 aAgostinelli, Daniele1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://doi.org/10.1098/rsta.2020.011601749nas a2200157 4500008004100000022001400041245010700055210006900162260003400231490000700265520118500272100002501457700002201482700002201504856006501526 2021 eng d a1664-462X00aNutations in plant shoots: Endogenous and exogenous factors in the presence of mechanical deformations0 aNutations in plant shoots Endogenous and exogenous factors in th bCold Spring Harbor Laboratory0 v123 aWe present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots driven by differential growth. We discuss the evolution laws for endogenous oscillators, straightening mechanisms, and reorientations to directional cues, such as gravitropic reactions governed by the avalanche dynamics of statoliths. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of an instability triggered by exogenous factors. When also oscillations due to endogenous cues are present, their weight relative to those associated with the instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the exogenous oscillations becomes dominant.

1 aAgostinelli, Daniele1 aDeSimone, Antonio1 aNoselli, Giovanni uhttps://www.frontiersin.org/article/10.3389/fpls.2021.60800506995nas a2200121 4500008004100000245006500041210005800106520655200164100002106716700001806737700002406755856009406779 2021 eng d00aParallel transport on non-collapsed $\mathsfRCD(K,N)$ spaces0 aParallel transport on noncollapsed mathsfRCDKN spaces3 aWe provide a general theory for parallel transport on non-collapsed RCD spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of curves obtained via the flow of sufficiently regular time dependent vector fields: the price that we pay for this generality is that we cannot study parallel transport along a single such curve, but only along almost all of these (in a sense related to the notions of Sobolev vector calculus and Regular Lagrangian Flow in the nonsmooth setting).

The class of ncRCD spaces contains finite dimensional Alexandrov spaces with curvature bounded from below, thus our construction provides a way of speaking about parallel transport in this latter setting alternative to the one proposed by Petrunin (1998). The precise relation between the two approaches is yet to be understood.

We prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations.

1 aFonda, Alessandro1 aKlun, Giuliano1 aSfecci, Andrea uhttps://doi.org/10.1007/s00009-021-01857-801539nas a2200133 4500008004100000245006800041210006500109490000800174520100800182100002301190700002101213700002101234856015001255 2021 eng d00aA POD-Galerkin reduced order model for a LES filtering approach0 aPODGalerkin reduced order model for a LES filtering approach0 v4363 aWe propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for an implementation of the Leray model that combines a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0≤Re≤100. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented.

1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85102138957&doi=10.1016%2fj.jcp.2021.110260&partnerID=40&md5=73115708267e80754f343561c26f474402164nas a2200157 4500008004100000245011600041210006900157300001200226490000700238520155800245100001701803700002201820700002101842700002001863856012301883 2021 eng d00aA POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step0 aPODGalerkin reduced order model of a turbulent convective buoyan a486-5030 v893 aA Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about 105 times faster than the RANS simulations that are performed on eight cores.

1 aStar, Kelbij1 aStabile, Giovanni1 aRozza, Gianluigi1 aDegroote, Joris uhttps://www.math.sissa.it/publication/pod-galerkin-reduced-order-model-turbulent-convective-buoyant-flow-sodium-over-001345nas a2200169 4500008004100000020001400041245006600055210006500121260001500186300001300201490000600214520084700220100002401067700001901091700001801110856004701128 2021 eng d a2523-368800aQuadratic Life Span of Periodic Gravity-capillary Water Waves0 aQuadratic Life Span of Periodic Gravitycapillary Water Waves c2021/04/01 a85 - 1150 v33 aWe consider the gravity-capillary water waves equations for a bi-dimensional fluid with a periodic one-dimensional free surface. We prove a rigorous reduction of this system to Birkhoff normal form up to cubic degree. Due to the possible presence of three-wave resonances for general values of gravity, surface tension, and depth, such normal form may be not trivial and exhibit a chaotic dynamics (Wilton ripples). Nevertheless, we prove that for all the values of gravity, surface tension, and depth, initial data that are of size $$ \varepsilon $$in a sufficiently smooth Sobolev space leads to a solution that remains in an $$ \varepsilon $$-ball of the same Sobolev space up times of order $$ \varepsilon ^{-2}$$. We exploit that the three-wave resonances are finitely many, and the Hamiltonian nature of the Birkhoff normal form.

1 aBerti, Massimiliano1 aFeola, Roberto1 aFranzoi, Luca uhttps://doi.org/10.1007/s42286-020-00036-800727nas a2200133 4500008004100000020001400041245006600055210006600121260001500187520030200202100002100504700002100525856004700546 2021 eng d a1424-929400aQuasistatic Limit of a Dynamic Viscoelastic Model with Memory0 aQuasistatic Limit of a Dynamic Viscoelastic Model with Memory c2021/11/303 aWe study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the solution of the corresponding stationary problem.

1 aDal Maso, Gianni1 aSapio, Francesco uhttps://doi.org/10.1007/s00032-021-00343-w01746nas a2200217 4500008004100000020001400041245012200055210006900177260001600246520096600262653003001228653003001258653004101288653002501329653001801354100002701372700001901399700001701418700002101435856007201456 2021 eng d a0898-122100aA Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems0 aReduced Order Cut Finite Element method for geometrically parame c2021/08/12/3 aWe focus on steady and unsteady Navier–Stokes flow systems in a reduced-order modeling framework based on Proper Orthogonal Decomposition within a levelset geometry description and discretized by an unfitted mesh Finite Element Method. This work extends the approaches of [1], [2], [3] to nonlinear CutFEM discretization. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.

10aCut Finite Element Method10aNavier–Stokes equations10aParameter–dependent shape geometry10aReduced Order Models10aUnfitted mesh1 aKaratzas, Efthymios, N1 aNonino, Monica1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S089812212100279001664nas a2200181 4500008004100000020002200041245016600063210006900229260005200298520089600350100002201246700001801268700001701286700002101303700002201324700001901346856011701365 2021 eng d a978-3-030-55874-100aReduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences0 aReduced Order Methods for Parametrized Nonlinear and Time Depend aChambSpringer International Publishingc2021//3 aWe introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (1) time dependent Stokes equations and (2) steady non-linear Navier-Stokes equations.

1 aStrazzullo, Maria1 aZainib, Zakia1 aBallarin, F.1 aRozza, Gianluigi1 aVermolen, Fred, J1 aVuik, Cornelis uhttps://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/1912267647999nas a2200097 45000080041000002450072000412100069001135204760600182100002247788856009147810 2021 eng d00aA remark on two notions of flatness for sets in the Euclidean space0 aremark on two notions of flatness for sets in the Euclidean spac3 aIn this note we compare two ways of measuring the n-dimensional "flatness" of a set S⊂Rd, where n∈N and d>n. The first one is to consider the classical Reifenberg-flat numbers α(x,r) (x∈S, r>0), which measure the minimal scaling-invariant Hausdorff distances in Br(x) between S and n-dimensional affine subspaces of Rd. The second is an `intrinsic' approach in which we view the same set S as a metric space (endowed with the induced Euclidean distance). Then we consider numbers a(x,r)'s, that are the scaling-invariant Gromov-Hausdorff distances between balls centered at x of radius r in S and the n-dimensional Euclidean ball of the same radius. As main result of our analysis we make rigorous a phenomenon, first noted by David and Toro, for which the numbers a(x,r)'s behaves as the square of the numbers α(x,r)'s. Moreover we show how this result finds application in extending the Cheeger-Colding intrinsic-Reifenberg theorem to the biLipschitz case. As a by-product of our arguments, we deduce analogous results also for the Jones' numbers β's (i.e. the one-sided version of the numbers α's).

1 aViolo, Ivan, Yuri uhttps://www.math.sissa.it/publication/remark-two-notions-flatness-sets-euclidean-space36575nas a2200109 45000080041000002450109000412100069001505203607300219100002236292700002236314856012936336 2021 eng d00aRigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds0 aRigidity and almost rigidity of Sobolev inequalities on compact 3 a

We prove that if M is a closed n-dimensional Riemannian manifold, n≥3, with Ric≥n−1 and for which the optimal constant in the critical Sobolev inequality equals the one of the n-dimensional sphere Sn, then M is isometric to Sn. An almost-rigidity result is also established, saying that if equality is almost achieved, then M is close in the measure Gromov-Hausdorff sense to a spherical suspension. These statements are obtained in the RCD-setting of (possibly non-smooth) metric measure spaces satisfying synthetic lower Ricci curvature bounds.1 aNobili, Francesco1 aViolo, Ivan, Yuri uhttps://www.math.sissa.it/publication/rigidity-and-almost-rigidity-sobolev-inequalities-compact-spaces-lower-ricci-curvature01083nas a2200205 4500008004100000020002000041245005200061210004800113260000900161300001600170490000700186520039600193653002300589653002900612653002400641100002400665700002000689700002500709856014300734 2021 eng d a02132230 (ISSN)00aThe sharp quantitative isocapacitary inequality0 asharp quantitative isocapacitary inequality c2021 a2191 - 22280 v373 a

An independent result of our analysis is the characterization of the best constant in the Sobolev inequality on any compact CD space, extending to the non-smooth setting a classical result by Aubin. Our arguments are based on a new concentration compactness result for mGH-converging sequences of RCD spaces and on a Polya-Szego inequality of Euclidean-type in CD spaces.

As an application of the technical tools developed we prove both an existence result for the Yamabe equation and the continuity of the generalized Yamabe constant under measure Gromov-Hausdorff convergence, in the RCD-setting.

We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. Analyse Math.'91). © 2021 Real Sociedad Matemática Española

10aFraenkel asymmetry10aisocapacitary inequality10aStability estimates1 aDe Philippis, Guido1 aMarini, Michele1 aMukoseeva, Ekaterina uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff5700877nas a2200145 4500008004100000020002000041245007700061210006900138260000900207520029100216653002900507653002400536100002500560856014600585 2021 eng d a18648258 (ISSN)00aThe sharp quantitative isocapacitary inequality (the case of p-capacity)0 asharp quantitative isocapacitary inequality the case of pcapacit c20213 aWe prove a sharp quantitative form of isocapacitary inequality in the case of a general p. This work is a generalization of the author's paper with Guido De Philippis and Michele Marini, where we treated the case of 2-capacity. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

10aisocapacitary inequality10aStability estimates1 aMukoseeva, Ekaterina uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85106363307&doi=10.1515%2facv-2020-0106&partnerID=40&md5=26dbcad781b68c1d873512e272f0e7f401446nas a2200133 4500008004100000245013900041210006900180490000700249520096200256100001701218700001901235700002101254856003701275 2021 eng d00aA supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems0 asupervised learning approach involving active subspaces for an e0 v433 aIn this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions – Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov – and finally we apply it to an aeronautical shape optimization problem.

1 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://arxiv.org/abs/2006.0728201072nas a2200169 4500008004100000020001400041245006500055210006400120260001500184300001300199490000800212520057200220100002400792700001800816700002100834856004700855 2021 eng d a1432-067300aTraveling Quasi-periodic Water Waves with Constant Vorticity0 aTraveling Quasiperiodic Water Waves with Constant Vorticity c2021/04/01 a99 - 2020 v2403 aWe prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.

1 aBerti, Massimiliano1 aFranzoi, Luca1 aMaspero, Alberto uhttps://doi.org/10.1007/s00205-021-01607-w00999nas a2200157 4500008004100000020001400041245014800055210006900203260001500272300000800287490000700295520045600302100001800758700001800776856004700794 2021 eng d a1432-083500aA vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers0 avanishinginertia analysis for finitedimensional rateindependent c2021/08/03 a1910 v603 aWe study the approximation of finite-dimensional rate-independent quasistatic systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamic solutions to a rate-independent one, employing the variational concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.

1 aGidoni, Paolo1 aRiva, Filippo uhttps://doi.org/10.1007/s00526-021-02067-600698nas a2200157 4500008004100000245015800041210006900199300001200268490000800280100001500288700002200303700002400325700002100349700001800370856015200388 2021 eng d00aA weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences0 aweighted PODreduction approach for parametrized PDEconstrained o a261-2760 v1021 aCarere, G.1 aStrazzullo, Maria1 aBallarin, Francesco1 aRozza, Gianluigi1 aStevenson, R. uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85117948561&doi=10.1016%2fj.camwa.2021.10.020&partnerID=40&md5=cb57d59a6975a35315b2cf5d0e3a600100480nas a2200145 4500008004100000245009200041210006900133260000900202300001400211490000700225100002200232700001900254700001900273856004200292 2021 eng d00aWell-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems0 aWellOrdered and NonWellOrdered Lower and Upper Solutions for Per c2021 a397 - 4190 v211 aFonda, Alessandro1 aKlun, Giuliano1 aSfecci, Andrea uhttps://doi.org/10.1515/ans-2021-211701497nas a2200169 4500008004100000245010500041210006900146520085900215100002101074700001601095700001701111700001901128700002301147700002201170700001701192856011801209 2020 eng d00aAdvances in reduced order methods for parametric industrial problems in computational fluid dynamics0 aAdvances in reduced order methods for parametric industrial prob3 aReduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

1 aRozza, Gianluigi1 aMalik, M.H.1 aDemo, Nicola1 aTezzele, Marco1 aGirfoglio, Michele1 aStabile, Giovanni1 aMola, Andrea uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be67501183nas a2200145 4500008004100000020001400041245012000055210006900175260001500244300001400259490000700273520069200280100001800972856004700990 2020 eng d a1432-146700aOn the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity0 aApproximation of Quasistatic Evolutions for the Debonding of a T c2020/06/01 a903 - 9510 v303 aIn this paper, we contribute to studying the issue of quasistatic limit in the context of Griffith’s theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate and subjected to a vertical loading. Taking viscosity into account and under suitable assumptions on the toughness of the glue, we prove that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time. We then characterise the size of the jump by means of an asymptotic analysis of the debonding front.

1 aRiva, Filippo uhttps://doi.org/10.1007/s00332-019-09595-800632nas a2200169 4500008004100000020001800041245010800059210006900167260003100236300001100267100002100278700002100299700002200320700001900342700001700361856008400378 2020 eng d a978311067149000aBasic ideas and tools for projection-based model reduction of parametric partial differential equations0 aBasic ideas and tools for projectionbased model reduction of par aBerlin, BostonbDe Gruyter a1 - 471 aRozza, Gianluigi1 aHess, Martin, W.1 aStabile, Giovanni1 aTezzele, Marco1 aBallarin, F. uhttps://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml00368nas a2200097 4500008004100000245008900041210006900130260000900199100002000208856004200228 2020 eng d00aOn the blow-up of GSBV functions under suitable geometric properties of the jump set0 ablowup of GSBV functions under suitable geometric properties of c20201 aTasso, Emanuele uhttps://doi.org/10.1515/acv-2019-006801430nas a2200169 4500008004100000245011100041210006900152300001200221490000700233520077800240100001701018700001801035700001701053700001701070700002101087856015201108 2020 eng d00aCertified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height0 aCertified Reduced Basis VMSSmagorinsky model for natural convect a973-9890 v803 aIn this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that lets us obtain an affine decomposition with respect to the parameters. We construct an a posteriori error estimator, based upon the Brezzi–Rappaz–Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for different parameter configuration.

1 aBallarin, F.1 aRebollo, T.C.1 aÁvila, E.D.1 aMarmol, M.G.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85085843368&doi=10.1016%2fj.camwa.2020.05.013&partnerID=40&md5=7c6596865ec89651319c7dd97159dd7700362nas a2200109 4500008004100000245007100041210006000112260001200172490000700184100002000191856004100211 2020 eng d00aOn the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)0 acontinuity of the trace operator in GSBV Ω and GSBD Ω c2020///0 v261 aTasso, Emanuele uhttps://doi.org/10.1051/cocv/201901401178nas a2200157 4500008004100000245006900041210006700110300001100177490000800188520070800196100001900904700002200923700001700945700002100962856003700983 2020 eng d00aData-driven POD-Galerkin reduced order model for turbulent flows0 aDatadriven PODGalerkin reduced order model for turbulent flows a1095130 v4163 aIn this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1907.0990900903nas a2200157 4500008004100000020001400041245007800055210006900133260001500202300001600217490000800233520041700241100001900658700002100677856004700698 2020 eng d a1618-189100aA dynamic model for viscoelastic materials with prescribed growing cracks0 adynamic model for viscoelastic materials with prescribed growing c2020/08/01 a1263 - 12920 v1993 aIn this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions, we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

1 aCaponi, Maicol1 aSapio, Francesco uhttps://doi.org/10.1007/s10231-019-00921-102133nas a2200145 4500008004100000245011600041210006900157520162200226100002001848700002001868700002101888700002101909700002001930856003701950 2020 eng d00aEfficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method0 aEfficient computation of bifurcation diagrams with a deflated ap3 aThe majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work we implemented an elaborated deflated continuation method, that relies on the spectral element method (SEM) and on the reduced basis (RB) one, to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

1 aPintore, Moreno1 aPichi, Federico1 aHess, Martin, W.1 aRozza, Gianluigi1 aCanuto, Claudio uhttps://arxiv.org/abs/1912.0608901597nas a2200145 4500008004100000245008800041210006900129300001400198490000800212520112900220100002201349700002201371700002101393856003701414 2020 eng d00aEfficient Geometrical parametrization for finite-volume based reduced order methods0 aEfficient Geometrical parametrization for finitevolume based red a2655-26820 v1213 aIn this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier–Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

1 aStabile, Giovanni1 aZancanaro, Matteo1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0637301671nas a2200181 4500008004100000020002200041245012000063210006900183260004400252300001400296520095800310100001901268700001701287700002201304700001701326700002101343856012501364 2020 eng d a978-3-030-30705-900aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced aChambSpringer International Publishing a245–2643 aWe present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar-000964nas a2200205 4500008004100000020001400041245005600055210005500111260001600166300001100182490000800193520032700201653003100528653002200559653004400581100001900625700002200644700002000666856007200686 2020 eng d a0022-247X00aEnergy-dissipation balance of a smooth moving crack0 aEnergydissipation balance of a smooth moving crack c2020/03/15/ a1236560 v4833 aIn this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [10] valid for straight fractures.

10aEnergy-dissipation balance10aFracture dynamics10aWave equation in time-dependent domains1 aCaponi, Maicol1 aLucardesi, Ilaria1 aTasso, Emanuele uhttps://www.sciencedirect.com/science/article/pii/S0022247X1930924201480nas a2200157 4500008004100000245009400041210006900135490000600204520097900210100001901189700001701208700002201225700001701247700002101264856003701285 2020 eng d00aEnhancing CFD predictions in shape design problems by model and parameter space reduction0 aEnhancing CFD predictions in shape design problems by model and 0 v73 aIn this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

1 aTezzele, Marco1 aDemo, Nicola1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/2001.0523701243nas a2200145 4500008004100000020001400041245010900055210007100164260001500235300000700250490000700257520076800264100001901032856004601051 2020 eng d a1420-900400aExistence of solutions to a phase–field model of dynamic fracture with a crack–dependent dissipation0 aExistence of solutions to a phase–field model of dynamic fractur c2020/02/11 a140 v273 aWe propose a phase–field model of dynamic fracture based on the Ambrosio–Tortorelli’s approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in Larsen et al. (Math Models Methods Appl Sci 20:1021–1048, 2010), we show the existence of a dynamic crack evolution satisfying an energy–dissipation balance, according to Griffith’s criterion. Finally, we analyze the dynamic phase–field model of Bourdin et al. (Int J Fract 168:133–143, 2011) and Larsen (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, IUTAM Bookseries, vol 21. Springer, Dordrecht, 2010, pp 131–140) with no dissipative terms.

1 aCaponi, Maicol uhttps://doi.org/10.1007/s00030-020-0617-z00784nas a2200121 4500008004100000245004300041210003900084300001200123490000800135520045300143100001900596856004700615 2020 eng d00aOn functions having coincident p-norms0 afunctions having coincident pnorms a955-9680 v1993 aIn a measure space $(X,{\mathcal {A}},\mu )$, we consider two measurable functions $f,g:E\rightarrow {\mathbb {R}}$, for some $E\in {\mathcal {A}}$. We prove that the property of having equal p-norms when p varies in some infinite set $P\subseteq [1,+\infty )$ is equivalent to the following condition: $\begin{aligned} \mu (\{x\in E:|f(x)|>\alpha \})=\mu (\{x\in E:|g(x)|>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$

1 aKlun, Giuliano uhttps://doi.org/10.1007/s10231-019-00907-z01487nas a2200169 4500008004100000245008100041210006900122300001100191490000800202520096400210100002301174700002201197700001701219700002101236700002301257856003701280 2020 eng d00aA hybrid reduced order method for modelling turbulent heat transfer problems0 ahybrid reduced order method for modelling turbulent heat transfe a1046150 v2083 aA parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

1 aGeorgaka, Sokratia1 aStabile, Giovanni1 aStar, Kelbij1 aRozza, Gianluigi1 aBluck, Michael, J. uhttps://arxiv.org/abs/1906.0872500553nam a2200121 4500008004100000245011400041210006900155100002100224700001900245700001800264700002100282856012800303 2020 eng d00aKernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method0 aKernelbased Active Subspaces with application to CFD parametric 1 aRomor, Francesco1 aTezzele, Marco1 aLario, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/kernel-based-active-subspaces-application-cfd-parametric-problems-using-discontinuous02335nas a2200325 4500008004100000022001400041245014400055210006900199300000800268490000600276520131600282653001801598653002401616653001801640653002301658653001601681653002401697653002501721653002501746100002501771700002101796700002301817700002201840700002101862700002501883700002201908700001701930700001901947856004301966 2020 eng d a2640-350100aMicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales0 aMicroMotility State of the art recent accomplishments and perspe a2300 v23 aMathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

10aactive matter10aadhesive locomotion10acell motility10acell sheet folding10aknotted DNA10atopological defects10aunicellular swimmers10aunjamming transition1 aAgostinelli, Daniele1 aCerbino, Roberto1 aDel Alamo, Juan, C1 aDeSimone, Antonio1 aHöhn, Stephanie1 aMicheletti, Cristian1 aNoselli, Giovanni1 aSharon, Eran1 aYeomans, Julia uhttp://dx.doi.org/10.3934/mine.202001100540nas a2200145 4500008004100000245010800041210006900149653002100218653003300239100002100272700002100293700002200314700002100336856003700357 2020 eng d00aMicroROM: An Efficient and Accurate Reduced Order Method to Solve Many-Query Problems in Micro-Motility0 aMicroROM An Efficient and Accurate Reduced Order Method to Solve10aFOS: Mathematics10aNumerical Analysis (math.NA)1 aGiuliani, Nicola1 aHess, Martin, W.1 aDeSimone, Antonio1 aRozza, Gianluigi uhttps://arxiv.org/abs/2006.1383600406nas a2200097 4500008004100000245006600041210006600107100002500173700002000198856009000218 2020 eng d00aMinimality of the ball for a model of charged liquid droplets0 aMinimality of the ball for a model of charged liquid droplets1 aMukoseeva, Ekaterina1 aVescovo, Giulia uhttps://www.math.sissa.it/publication/minimality-ball-model-charged-liquid-droplets-001405nas a2200169 4500008004100000020002200041245014800063210006900211260004400280300001400324520076900338100001901107700002201126700001701148700002101165856004901186 2020 eng d a978-3-030-48721-800aNon-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives0 aNonintrusive Polynomial Chaos Method Applied to FullOrder and Re aChambSpringer International Publishing a217–2403 aIn this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://doi.org/10.1007/978-3-030-48721-8_1000942nas a2200133 4500008004100000022001400041245010700055210006900162520047200231100002200703700001900725700001900744856004500763 2020 eng d a0362-546X00aPeriodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori0 aPeriodic solutions of nearly integrable Hamiltonian systems bifu3 aWe prove the existence of periodic solutions of some infinite-dimensional nearly integrable Hamiltonian systems, bifurcating from infinite-dimensional tori, by the use of a generalization of the Poincaré–Birkhoff Theorem.

1 aFonda, Alessandro1 aKlun, Giuliano1 aSfecci, Andrea uhttps://doi.org/10.1016/j.na.2019.11172001633nas a2200121 4500008004100000245014500041210006900186520106800255100002201323700001701345700002101362856012801383 2020 eng d00aPOD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations0 aPODGalerkin Model Order Reduction for Parametrized Nonlinear Tim3 aIn this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

1 aStrazzullo, Maria1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-model-order-reduction-parametrized-nonlinear-time-dependent-optimal-flow01839nas a2200133 4500008004100000245014300041210007100184490000700255520124500262100002201507700001701529700002101546856013801567 2020 eng d00aPOD–Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation0 aPOD–Galerkin Model Order Reduction for Parametrized Time Depende0 v833 aIn this work we deal with parametrized time dependent optimal control problems governed by partial differential equations. We aim at extending the standard saddle point framework of steady constraints to time dependent cases. We provide an analysis of the well-posedness of this formulation both for parametrized scalar parabolic constraint and Stokes governing equations and we propose reduced order methods as an effective strategy to solve them. Indeed, on one hand, parametrized time dependent optimal control is a very powerful mathematical model which is able to describe several physical phenomena, on the other, it requires a huge computational effort. Reduced order methods are a suitable approach to have rapid and accurate simulations. We rely on POD–Galerkin reduction over the physical and geometrical parameters of the optimality system in a space-time formulation. Our theoretical results and our methodology are tested on two examples: a boundary time dependent optimal control for a Graetz flow and a distributed optimal control governed by time dependent Stokes equations. With these two test cases the convenience of the reduced order modelling is further extended to the field of time dependent optimal control.

1 aStrazzullo, Maria1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-model-order-reduction-parametrized-time-dependent-linear-quadratic-optimal01696nas a2200157 4500008004100000245012100041210007300162300001200235490000700247520104800254100001401302700002201316700002101338700002701359856015201386 2020 eng d00aPOD–Galerkin reduced order methods for combined Navier–Stokes transport equations based on a hybrid FV-FE solver0 aPOD–Galerkin reduced order methods for combined Navier–Stokes tr a256-2730 v793 aThe purpose of this work is to introduce a novel POD–Galerkin strategy for the semi-implicit hybrid high order finite volume/finite element solver introduced in Bermúdez et al. (2014) and Busto et al. (2018). The interest is into the incompressible Navier–Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.

1 aBusto, S.1 aStabile, Giovanni1 aRozza, Gianluigi1 aVázquez-Cendón, M.E. uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85068068567&doi=10.1016%2fj.camwa.2019.06.026&partnerID=40&md5=a8dcce1b53b8ee872d174bbc4c20caa301515nas a2200145 4500008004100000245009800041210006900139300001200208490000700220520092500227100002701152700001701179700002101196856015201217 2020 eng d00aProjection-based reduced order models for a cut finite element method in parametrized domains0 aProjectionbased reduced order models for a cut finite element me a833-8510 v793 aThis work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail.

1 aKaratzas, Efthymios, N1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85070900852&doi=10.1016%2fj.camwa.2019.08.003&partnerID=40&md5=2d222ab9c7832955d155655d3c93e1b101531nas a2200145 4500008004100000245011100041210006900152300001200221490000700233520104500240100002101285700002101306700002101327856003701348 2020 eng d00aReduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature0 aReduced Basis Model Order Reduction for NavierStokes equations i a119-1260 v343 aWe consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

1 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0370801653nas a2200145 4500008004100000245011300041210007100154300001200225490000700237520104600244100002101290700002101311700002101332856015401353 2020 eng d00aReduced basis model order reduction for Navier–Stokes equations in domains with walls of varying curvature0 aReduced basis model order reduction for Navier–Stokes equations a119-1260 v343 aWe consider the Navier–Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced-order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced-order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e. symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

1 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85085233294&doi=10.1080%2f10618562.2019.1645328&partnerID=40&md5=e2ed8f24c66376cdc8b5485aa400efb001868nas a2200181 4500008004100000245012100041210006900162260003800231520122900269100002701498700002201525700001901547700002401566700002101590700001601611700002201627856003701649 2020 eng d00aA Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries0 aReduced Order Approach for the Embedded Shifted Boundary FEM and bSpringer International Publishing3 aA model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.

1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aAtallah, Nabib1 aScovazzi, Guglielmo1 aRozza, Gianluigi1 aFehr, Jörg1 aHaasdonk, Bernard uhttps://arxiv.org/abs/1807.0775301572nas a2200181 4500008004100000245008200041210006900123300001200192490000800204520090200212100002201114700001701136700001901153700002301172700002201195700002101217856015201238 2020 eng d00aReduced order isogeometric analysis approach for pdes in parametrized domains0 aReduced order isogeometric analysis approach for pdes in paramet a153-1700 v1373 aIn this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

1 aGarotta, Fabrizio1 aDemo, Nicola1 aTezzele, Marco1 aCarraturo, Massimo1 aReali, Alessandro1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85089615035&doi=10.1007%2f978-3-030-48721-8_7&partnerID=40&md5=7b15836ae65fa28dcfe8733788d7730c02309nas a2200313 4500008004100000020001400041245013100055210006900186260001500255300001000270490000800280520128800288653003401576653002201610653001701632653002101649653002601670653001701696653003301713653003601746653002601782100001801808700001701826700002401843700002001867700002501887700002101912856006201933 2020 eng d a2040-793900aReduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation0 aReduced order methods for parametric optimal flow control in cor c2020/05/27 ae33670 vn/a3 aAbstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

10acoronary artery bypass grafts10adata assimilation10aflow control10aGalerkin methods10ahemodynamics modeling10aOptimization10apatient-specific simulations10aProper orthogonal decomposition10areduced order methods1 aZainib, Zakia1 aBallarin, F.1 aFremes, Stephen, E.1 aTriverio, Piero1 aJiménez-Juan, Laura1 aRozza, Gianluigi uhttps://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R01537nas a2200121 4500008004100000245011600041210006900157520098400226100002001210700002101230700002101251856014301272 2020 eng d00aA reduced order modeling technique to study bifurcating phenomena: Application to the gross-pitaevskii equation0 areduced order modeling technique to study bifurcating phenomena 3 aWe propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton's method with a reduced order modeling (ROM) technique, suitably supplemented with a hyperreduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schrödinger equation, called the Gross{Pitaevskii equation, as one or two physical parameters are varied. In the two-parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard full order method.

1 aPichi, Federico1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85096768803&doi=10.1137%2f20M1313106&partnerID=40&md5=47d6012d10854c2f9a04b9737f87059201419nas a2200121 4500008004100000245010700041210006900148520098100217100002001198700002101218700002101239856003701260 2020 eng d00aA Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation0 aReduced Order technique to study bifurcating phenomena applicati3 aWe propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton's method with a Reduced Order Modeling (ROM) technique, suitably supplemented with a hyper-reduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schrödinger equation, called Gross-Pitaevskii equation, as one or two physical parameters are varied. In the two parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard Full Order Method.

1 aPichi, Federico1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://arxiv.org/abs/1907.0708201444nas a2200157 4500008004100000245010200041210006900143490000800212520080500220100002701025700002201052700001701074700002401091700002101115856015001136 2020 eng d00aA reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations0 areducedorder shifted boundary method for parametrized incompress0 v3703 aWe investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85087886522&doi=10.1016%2fj.cma.2020.113273&partnerID=40&md5=d864e4808190b682ecb1c8b27cda72d800473nas a2200121 4500008004100000245004900041210004900090300001000139490000700149100002000156700002100176856015400197 2020 eng d00aSpecial Issue on Reduced Order Models in CFD0 aSpecial Issue on Reduced Order Models in CFD a91-920 v341 aPerotto, Simona1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85084258805&doi=10.1080%2f10618562.2020.1756497&partnerID=40&md5=d9316aad9ba95f244e07379318ebbcba01342nas a2200145 4500008004100000245010000041210007100141300001200212490000800224520076800232100002101000700002101021700002101042856013301063 2020 eng d00aA spectral element reduced basis method for navier–stokes equations with geometric variations0 aspectral element reduced basis method for navier–stokes equation a561-5710 v1343 aWe consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

1 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/spectral-element-reduced-basis-method-navier%E2%80%93stokes-equations-geometric-variations01963nas a2200145 4500008004100000245009800041210006900139300001400208490000700222520138100229100001701610700001701627700002101644856015201665 2020 eng d00aStabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations0 aStabilized reduced basis methods for parametrized steady Stokes a2399-24160 v803 aIt is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf–sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf–sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf–sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions. The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi–Pitkaranta, Franca–Hughes, streamline upwind Petrov–Galerkin, Galerkin Least Square. In the spirit of offline–online reduced basis computational splitting, two such options are proposed, namely offline-only stabilization and offline–online stabilization. These approaches are then compared to (and combined with) the state of the art supremizer enrichment approach. Numerical results are discussed, highlighting that the proposed methodology allows to obtain smaller reduced basis spaces (i.e., neglecting supremizer enrichment) for which a modified inf–sup stability is still preserved at the reduced order level.

1 aAli, Shafqat1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85083340115&doi=10.1016%2fj.camwa.2020.03.019&partnerID=40&md5=7ace96eee080701acb04d8155008dd7d02383nas a2200205 4500008004100000022001400041245007400055210006900129300001100198490000800209520174300217653001301960653001801973653002201991653002702013653002002040100002302060700002302083856007102106 2020 eng d a0022-509600aSurface tension controls the onset of gyrification in brain organoids0 aSurface tension controls the onset of gyrification in brain orga a1037450 v1343 aUnderstanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

10aBuckling10aEmbryogenesis10aMorpho-elasticity10aPost-buckling analysis10aSurface tension1 aRiccobelli, Davide1 aBevilacqua, Giulia uhttp://www.sciencedirect.com/science/article/pii/S002250961930406501464nas a2200157 4500008004100000022001400041245007900055210006900134260000700203490000700210520098300217100001901200700002701219700002201246856003801268 2020 eng d a0021-893600aA theoretical study on the transient morphing of linear poroelastic plates0 atheoretical study on the transient morphing of linear poroelasti c120 v883 aBased on their shape-shifting capabilities, soft active materials have enabled new possibilities for the engineering of sensing and actuation devices. While the relation between active strains and emergent equilibrium shapes has been fully characterized, the transient morphing of thin structures is a rather unexplored topic. Here, we focus on polymer gel plates and derive a reduced linear model to study their time-dependent response to changes in the fluid environment. We show that independent control of stretching and bending deformations in stress-free conditions allows to realize spherical shapes with prescribed geometry of the mid-plane. Furthermore, we demonstrate that tensile (compressive) membrane stresses delay (accelerate) swelling-induced shape transitions compared to the stress-free evolution. We believe that these effects should be considered for the accurate design of smart systems and may contribute to explain the complexity of natural shapes.

1 aAndrini, Dario1 aLucantonio, Alessandro1 aNoselli, Giovanni uhttps://doi.org/10.1115/1.404880601145nas a2200145 4500008004100000020001400041245007000055210006900125260001500194300001600209490000800225520069900233100002000932856004700952 2020 eng d a1618-189100aWeak formulation of elastodynamics in domains with growing cracks0 aWeak formulation of elastodynamics in domains with growing crack c2020/08/01 a1571 - 15950 v1993 aIn this paper, we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet–Neumann conditions on the boundary. The only assumptions on the crack sets are to be $$(n-1)$$-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular, they might be dense; hence, the weak formulation must fall outside the usual context of Sobolev spaces and Korn’s inequality. We prove existence of a solution for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.

1 aTasso, Emanuele uhttps://doi.org/10.1007/s10231-019-00932-y00478nas a2200133 4500008004100000245006600041210006600107260001600173300001200189490000700201100002300208700001600231856009700247 2019 eng d00aActivation of a muscle as a mapping of stress–strain curves0 aActivation of a muscle as a mapping of stress–strain curves bElsevier BV a37–420 v281 aRiccobelli, Davide1 aAmbrosi, D. uhttps://www.math.sissa.it/publication/activation-muscle-mapping-stress%E2%80%93strain-curves01451nas a2200133 4500008004100000022001400041245008500055210007100140260000800211520101400219100001801233700001901251856004701270 2019 eng d a1432-206400aBenamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces0 aBenamou–Brenier and duality formulas for the entropic cost on RC cApr3 aIn this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N<\infty$, the entropic cost (i.e. the minimal value of the Schrödinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou–Brenier formula for the Wasserstein distance; A Hamilton–Jacobi–Bellman dual representation, in line with Bobkov–Gentil–Ledoux and Otto–Villani results on the duality between Hamilton–Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf–Lax semigroup is replaced by a suitable `entropic' counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schrödinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.

1 aGigli, Nicola1 aTamanini, Luca uhttps://doi.org/10.1007/s00440-019-00909-102204nas a2200229 4500008004100000022001400041245009200055210006900147300001400216490000800230520153700238653000801775653001801783653000801801653001501809653000801824653002501832653001701857653000801874100002101882856007101903 2019 eng d a0010-465500aBlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D0 aBlackNUFFT Modular customizable black box hybrid parallelization a324 - 3350 v2353 aMany applications benefit from an efficient Discrete Fourier Transform (DFT) between arbitrarily spaced points. The Non Uniform Fast Fourier Transform reduces the computational cost of such operation from O(N2) to O(NlogN) exploiting gridding algorithms and a standard Fast Fourier Transform on an equi-spaced grid. The parallelization of the NUFFT of type 3 (between arbitrary points in space and frequency) still poses some challenges: we present a novel and flexible hybrid parallelization in a MPI-multithreaded environment exploiting existing HPC libraries on modern architectures. To ensure the reliability of the developed library, we exploit continuous integration strategies using Travis CI. We present performance analyses to prove the effectiveness of our implementation, possible extensions to the existing library, and an application of NUFFT type 3 to MRI image processing. Program summary Program Title: BlackNUFFT Program Files doi: http://dx.doi.org/10.17632/vxfj6x2p8x.1 Licensing provisions: LGPL Programming language: C++ External routines/libraries: deal.II , FFTW, PFFT Nature of problem: Provide a modular and extensible implementation of a parallel Non Uniform Fast Fourier Transform of type 3. Solution method: Use of hybrid shared distributed memory paradigm to achieve high level of efficiency. We exploit existing HPC library following best practices in scientific computing (as continuous integration via TravisCI) to reach higher complexities and guarantee the accuracy of the solution proposed.

10aC++10aExtensibility10aFFT10aModularity10aMPI10aMRI image processing10aNUFFT type 310aTBB1 aGiuliani, Nicola uhttp://www.sciencedirect.com/science/article/pii/S001046551830353902116nas a2200133 4500008004100000245013800041210006900179520154200248100001701790700001901807700001701826700002101843856011801864 2019 eng d00aA complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems0 acomplete datadriven framework for the efficient solution of para3 aIn the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry — assuming the topology is inaltered by the deformation —, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565&partnerID=40&md5=d76b8a1290053e7a84fb8801c0e6bb3d02037nas a2200133 4500008004100000245013800041210006900179520154400248100001701792700001901809700001701828700002101845856003701866 2019 eng d00aA complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems0 acomplete datadriven framework for the efficient solution of para3 aIn the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1905.0598200896nas a2200109 4500008004100000245008200041210006900123260001000192520051200202100001800714856005400732 2019 en d00aA continuous dependence result for a dynamic debonding model in dimension one0 acontinuous dependence result for a dynamic debonding model in di bSISSA3 aIn this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3532900784nas a2200157 4500008004100000022001400041245006600055210006600121520024700187653002800434653002100462653003000483100001800513700002400531856007100555 2019 eng d a0723-086900aDifferential structure associated to axiomatic Sobolev spaces0 aDifferential structure associated to axiomatic Sobolev spaces3 aThe aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.

10aAxiomatic Sobolev space10aCotangent module10aLocality of differentials1 aGigli, Nicola1 aPasqualetto, Enrico uhttp://www.sciencedirect.com/science/article/pii/S072308691830097502563nas a2200169 4500008004100000245009100041210006900132520193100201100001702132700001902149700002102168700002502189700001902214700002102233700002102254856011802275 2019 eng d00aEfficient reduction in shape parameter space dimension for ship propeller blade design0 aEfficient reduction in shape parameter space dimension for ship 3 aIn this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

1 aMola, Andrea1 aTezzele, Marco1 aGadalla, Mahmoud1 aValdenazzi, Federica1 aGrassi, Davide1 aPadovan, Roberta1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143&partnerID=40&md5=b6aa0fcedc2f88e78c295d0f437824d001140nas a2200205 4500008004100000022001400041245005800055210005500113520049400168653002800662653002300690653002100713653002500734653002500759100001700784700002400801700001900825700001900844856007100863 2019 eng d a0304-414900aAn entropic interpolation proof of the HWI inequality0 aentropic interpolation proof of the HWI inequality3 aThe HWI inequality is an “interpolation”inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger problem. Our approach consists in making rigorous the Otto–Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

10aEntropic interpolations10aFisher information10aRelative entropy10aSchrödinger problem10aWasserstein distance1 aGentil, Ivan1 aLéonard, Christian1 aRipani, Luigia1 aTamanini, Luca uhttp://www.sciencedirect.com/science/article/pii/S030441491830345401763nas a2200145 4500008004100000245010400041210006900145300001000214490000800224520128300232100002301515700002101538700002101559856003701580 2019 eng d00aA Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization0 aFinite Volume approximation of the NavierStokes equations with n a27-450 v1873 aWe consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation of the model, we adopt the three-step algorithm Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm with a computationally efficient Finite Volume (FV) method. Our approach is validated against numerical data available in the literature for the 2D flow past a cylinder and against experimental measurements for the 3D fluid flow in an idealized medical device, as recommended by the U.S. Food and Drug Administration. We will show that for similar levels of mesh refinement FV and FE methods provide significantly different results. Through our numerical experiments, we are able to provide practical directions to tune the parameters involved in the model. Furthermore, we are able to investigate the impact of mesh features (element type, non-orthogonality, local refinement, and element aspect ratio) and the discretization method for the convective term on the agreement between numerical solutions and experimental data.

1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0525101886nas a2200145 4500008004100000245010400041210006900145300001000214490000800224520128700232100002301519700002101542700002101563856015601584 2019 eng d00aA Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization0 aFinite Volume approximation of the NavierStokes equations with n a27-450 v1873 aWe consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation of the model, we adopt the three-step algorithm Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm with a computationally efficient Finite Volume (FV) method. Our approach is validated against numerical data available in the literature for the 2D flow past a cylinder and against experimental measurements for the 3D fluid flow in an idealized medical device, as recommended by the U.S. Food and Drug Administration. We will show that for similar levels of mesh refinement FV and FE methods provide significantly different results. Through our numerical experiments, we are able to provide practical directions to tune the parameters involved in EFR algorithm. Furthermore, we are able to investigate the impact of mesh features (element type, non-orthogonality, local refinement, and element aspect ratio) and the discretization method for the convective term on the agreement between numerical solutions and experimental data.

1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85065471890&doi=10.1016%2fj.compfluid.2019.05.001&partnerID=40&md5=c982371b5b5d4b5664a676902aaa60f401032nas a2200205 4500008004100000020001400041245006400055210006300119260001600182300001600198490000800214520038000222653002900602653003300631653002200664653002000686100002200706700002600728856007200754 2019 eng d a0022-123600aIsoperimetric inequality under Measure-Contraction property0 aIsoperimetric inequality under MeasureContraction property c2019/11/01/ a2893 - 29170 v2773 aWe prove that if (X,d,m) is an essentially non-branching metric measure space with m(X)=1, having Ricci curvature bounded from below by K and dimension bounded above by N∈(1,∞), understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality à la Lévy-Gromov holds true. Measure theoretic rigidity is also obtained.

10aIsoperimetric inequality10aMeasure-Contraction property10aOptimal transport10aRicci curvature1 aCavalletti, Fabio1 aSantarcangelo, Flavia uhttps://www.sciencedirect.com/science/article/pii/S002212361930228901167nas a2200217 4500008004100000022001400041245008300055210006900138300001400207490000700221520048300228653002500711653001800736653002400754653000800778653003100786653002200817100001900839700002000858856007100878 2019 eng d a0294-144900aLocal well-posedness for quasi-linear NLS with large Cauchy data on the circle0 aLocal wellposedness for quasilinear NLS with large Cauchy data o a119 - 1640 v363 aWe prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

10aDispersive equations10aEnergy method10aLocal wellposedness10aNLS10aPara-differential calculus10aQuasi-linear PDEs1 aFeola, Roberto1 aIandoli, Felice uhttp://www.sciencedirect.com/science/article/pii/S029414491830042802128nas a2200169 4500008004100000245008400041210006900125300001200194490000800206520160300214100002101817700002101838700002101859700002101880700002001901856003701921 2019 eng d00aA Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions0 aLocalized ReducedOrder Modeling Approach for PDEs with Bifurcati a379-4030 v3513 aReduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. In this work, a ROM is developed and tested for the treatment of nonlinear PDEs whose solutions bifurcate as input parameter values change. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does no respect not take advantage of the often large differences in the PDE solutions corresponding to different subregions. Instead, in the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

1 aHess, Martin, W.1 aAlla, Alessandro1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, Max uhttps://arxiv.org/abs/1807.0885102395nas a2200169 4500008004100000245008400041210006900125300001200194490000800206520175700214100002101971700002101992700002102013700002102034700002002055856015002075 2019 eng d00aA localized reduced-order modeling approach for PDEs with bifurcating solutions0 alocalized reducedorder modeling approach for PDEs with bifurcati a379-4030 v3513 aReduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. Although ROMs have been successfully used in many settings, ROMs built specifically for the efficient treatment of PDEs having solutions that bifurcate as the values of input parameters change have not received much attention. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does not respect the often large differences in the PDE solutions corresponding to different subregions. In this work, we develop and test a new ROM approach specifically aimed at bifurcation problems. In the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

1 aHess, Martin, W.1 aAlla, Alessandro1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, Max uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85064313505&doi=10.1016%2fj.cma.2019.03.050&partnerID=40&md5=8b095034b9e539995facc7ce7bafa9e900495nas a2200157 4500008004100000245007500041210006900116260001500185300001300200490000800213100002000221700002200241700001600263700001500279856004300294 2019 eng d00aA neutrally stable shell in a Stokes flow: a rotational Taylor's sheet0 aneutrally stable shell in a Stokes flow a rotational Taylors she c2019/07/26 a201901780 v4751 aCorsi, Giovanni1 aDeSimone, Antonio1 aMaurini, C.1 aVidoli, S. uhttps://doi.org/10.1098/rspa.2019.017801894nas a2200145 4500008004100000245010300041210006900144300001200213490000800225520130700233100001701540700001901557700002101576856015101597 2019 eng d00aA non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces0 anonintrusive approach for the reconstruction of POD modal coeffi a873-8810 v3473 aReduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions—computed for properly chosen parameters, using a full-order model—in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI)—a data-driven reduced order method—with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one.

1 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075379471&doi=10.1016%2fj.crme.2019.11.012&partnerID=40&md5=dcb27af39dc14dc8c3a4a5f681f7d84b00644nas a2200145 4500008004100000245006000041210005800101260003400159300001400193490000700207520015800214100001800372700001900390856008900409 2019 eng d00aA Note About the Strong Maximum Principle on RCD Spaces0 aNote About the Strong Maximum Principle on RCD Spaces bCanadian Mathematical Society a259–2660 v623 aWe give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

1 aGigli, Nicola1 aRigoni, Chiara uhttps://www.math.sissa.it/publication/note-about-strong-maximum-principle-rcd-spaces02026nas a2200205 4500008004100000022001400041245009500055210006900150300001100219520136500230653002001595653002401615653001701639653002101656100002501677700002701702700002201729700002201751856004701773 2019 eng d a0022-509600aNutations in growing plant shoots: The role of elastic deformations due to gravity loading0 aNutations in growing plant shoots The role of elastic deformatio a1037023 aThe effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

10aCircumnutations10aFlutter instability10aGravitropism10aHopf bifurcation1 aAgostinelli, Daniele1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://doi.org/10.1016/j.jmps.2019.10370201425nas a2200169 4500008004100000022001400041245009200055210006900147300001100216490000700227520089500234100002301129700002201152700002101174700002301195856003701218 2019 eng d a1991-712000aParametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems0 aParametric PODGalerkin Model Order Reduction for UnsteadyState H a1–320 v273 aA parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume approximation. Two different paramet- ric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model.

1 aGeorgaka, Sokratia1 aStabile, Giovanni1 aRozza, Gianluigi1 aBluck, Michael, J. uhttps://arxiv.org/abs/1808.0517501658nas a2200157 4500008004100000245009100041210006900132300001200201490000800213520106300221100001701284700001701301700002001318700002101338856014101359 2019 eng d00aA POD-selective inverse distance weighting method for fast parametrized shape morphing0 aPODselective inverse distance weighting method for fast parametr a860-8840 v1173 aEfficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency.

1 aBallarin, F.1 aD'Amario, A.1 aPerotto, Simona1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233&doi=10.1002%2fnme.5982&partnerID=40&md5=6aabcbdc9a0da25e36575a0ebfac034f01079nas a2200133 4500008004100000022001400041245009200055210006900147260000800216520062200224100002900846700002300875856004700898 2019 eng d a1661-826200aPoint-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range0 aPointLike Perturbed Fractional Laplacians Through Shrinking Pote cMay3 aWe construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schrödinger operators formed by a fractional Laplacian and a regular potential.

1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1007/s11785-019-00927-w00394nas a2200109 4500008004100000245004900041210004800090100002000138700001800158700002400176856008400200 2019 eng d00aQuasi-continuous vector fields on RCD spaces0 aQuasicontinuous vector fields on RCD spaces1 aDebin, Clément1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/quasi-continuous-vector-fields-rcd-spaces02191nas a2200169 4500008004100000245015000041210006900191300001200260490000800272520148000280100002701760700002201787700001701809700002401826700002101850856015001871 2019 eng d00aA reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow0 areduced basis approach for PDEs on parametrized geometries based a568-5870 v3473 aWe propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to deal with complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold. First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM. This unfitted boundary method permits to avoid remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary. Second, the computational effort is reduced by the development of a Reduced Order Model (ROM) technique based on a POD-Galerkin approach. Third, the SBM provides a smooth mapping from the true to the surrogate domain, and for this reason, the stability and performance of the reduced order basis are enhanced. This feature is the net result of the combination of the proposed ROM approach and the SBM. Similarly, the combination of the SBM with a projection-based ROM gives the great advantage of an easy and fast to implement algorithm considering geometrical parametrization with large deformations. The transformation of each geometry to a reference geometry (morphing) is in fact not required. These combined advantages will allow the solution of PDE problems more efficiently. We illustrate the performance of this approach on a number of two-dimensional Stokes flow problems.

1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85060107322&doi=10.1016%2fj.cma.2018.12.040&partnerID=40&md5=1a3234f0cb000c91494d946428f8ebef01370nas a2200133 4500008004100000245010900041210006900150300001400219490000700233520091800240100002001158700002101178856003701199 2019 eng d00aReduced basis approaches for parametrized bifurcation problems held by non-linear Von Kármán equations0 aReduced basis approaches for parametrized bifurcation problems h a112–1350 v813 aThis work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity - due to the fourth order derivative terms, the non-linearity and the parameter dependence - provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode. journal = Journal of Scientific Computing

1 aPichi, Federico1 aRozza, Gianluigi uhttps://arxiv.org/abs/1804.0201401440nas a2200133 4500008004100000245010900041210006900150300001200219490000700231520087600238100002001114700002101134856015101155 2019 eng d00aReduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations0 aReduced Basis Approaches for Parametrized Bifurcation Problems h a112-1350 v813 aThis work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity—due to the fourth order derivative terms, the non-linearity and the parameter dependence—provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode.

1 aPichi, Federico1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85068973907&doi=10.1007%2fs10915-019-01003-3&partnerID=40&md5=a09af83ce45183d6965cdb79d87a919b01735nas a2200157 4500008004100000245007200041210006900113300001400182490000700196520114500203100002201348700001701370700001801387700002101405856015101426 2019 eng d00aA reduced order variational multiscale approach for turbulent flows0 areduced order variational multiscale approach for turbulent flow a2349-23680 v453 aThe purpose of this work is to present different reduced order model strategies starting from full order simulations stabilized using a residual-based variational multiscale (VMS) approach. The focus is on flows with moderately high Reynolds numbers. The reduced order models (ROMs) presented in this manuscript are based on a POD-Galerkin approach. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case, the VMS stabilization method is used at both the full order and the reduced order levels. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM, while the latter is named non-consistent ROM, in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark.

1 aStabile, Giovanni1 aBallarin, F.1 aZuccarino, G.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85068076665&doi=10.1007%2fs10444-019-09712-x&partnerID=40&md5=af0142e6d13bbc2e88c6f31750aef6ad01286nas a2200157 4500008004100000020001400041245006600055210006500121260001500186300001600201490000800217520081700225100001801042700002101060856004701081 2019 eng d a1618-189100aReducibility for a fast-driven linear Klein–Gordon equation0 aReducibility for a fastdriven linear Klein–Gordon equation c2019/08/01 a1407 - 14390 v1983 aWe prove a reducibility result for a linear Klein–Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving; however, we require it to be fast oscillating. In particular, provided that the external frequency is sufficiently large and chosen from a Cantor set of large measure, the original equation is conjugated to a time-independent, diagonal one. We achieve this result in two steps. First, we perform a preliminary transformation, adapted to fast oscillating systems, which moves the original equation in a perturbative setting. Then, we show that this new equation can be put to constant coefficients by applying a KAM reducibility scheme, whose convergence requires a new type of Melnikov conditions.

1 aFranzoi, Luca1 aMaspero, Alberto uhttps://doi.org/10.1007/s10231-019-00823-201637nas a2200217 4500008004100000022001400041245007700055210006900132300001400201490000800215520097100223653002001194653001501214653001701229653001701246100001901263700002201282700002301304700002101327856007101348 2019 eng d a0022-123600aReducibility of first order linear operators on tori via Moser's theorem0 aReducibility of first order linear operators on tori via Mosers a932 - 9700 v2763 aIn this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ⋅∂xu+a(ωt,x)⋅∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser's straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

10aHyperbolic PDEs10aKAM theory10aNash–Moser10aReducibility1 aFeola, Roberto1 aGiuliani, Filippo1 aMontalto, Riccardo1 aProcesi, Michela uhttp://www.sciencedirect.com/science/article/pii/S002212361830379300422nas a2200109 4500008004100000245006100041210006100102100002400163700001800187700002000205856008700225 2019 eng d00aRegularity of minimizers for a model of charged droplets0 aRegularity of minimizers for a model of charged droplets1 aDe Philippis, Guido1 aHirsch, Jonas1 aVescovo, Giulia uhttps://www.math.sissa.it/publication/regularity-minimizers-model-charged-droplets01650nas a2200157 4500008004100000022001400041245013600055210006900191260000800260520108900268100002501357700002101382700002201403700002001425856004701445 2019 eng d a1618-189100aOn the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions0 arelaxed area of the graph of discontinuous maps from the plane t cJul3 aIn this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to ``fill the hole'' in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

1 aBellettini, Giovanni1 aElshorbagy, Alaa1 aPaolini, Maurizio1 aScala, Riccardo uhttps://doi.org/10.1007/s10231-019-00887-000411nas a2200145 4500008004100000022001400041245004800055210004400103260000800147300001400155490000700169100001900176700002400195856004600219 2019 eng d a1973-440900aThe Serre–Swan theorem for normed modules0 aSerre–Swan theorem for normed modules cAug a385–4040 v681 aLučić, Danka1 aPasqualetto, Enrico uhttps://doi.org/10.1007/s12215-018-0366-602446nas a2200121 4500008004100000245014200041210006900183520189700252100001902149700001702168700002102185856011802206 2019 eng d00aShape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces0 aShape optimization through proper orthogonal decomposition with 3 aWe propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

1 aTezzele, Marco1 aDemo, Nicola1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244&partnerID=40&md5=3e1f2e9a2539d34594caff13766c94b801397nas a2200193 4500008004100000245006200041210006000103260003800163490000800201520080600209100002101015700002101036700002501057700001801082700001601100700002801116700002201144856003701166 2019 eng d00aA Spectral Element Reduced Basis Method in Parametric CFD0 aSpectral Element Reduced Basis Method in Parametric CFD bSpringer International Publishing0 v1263 aWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

1 aHess, Martin, W.1 aRozza, Gianluigi1 aRadu, Florin, Adrian1 aKumar, Kundan1 aBerre, Inga1 aNordbotten, Jan, Martin1 aPop, Iuliu, Sorin uhttps://arxiv.org/abs/1712.0643201451nas a2200133 4500008004100000245006200041210006000103300001200163490000800175520093900183100002101122700002101143856015301164 2019 eng d00aA spectral element reduced basis method in parametric CFD0 aspectral element reduced basis method in parametric CFD a693-7010 v1263 aWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14,259 degrees of freedom. The steady-state snapshot solutions define a reduced order space, which allows to accurately evaluate the steady-state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation (Karniadakis and Sherwin, Spectral/hp element methods for computational fluid dynamics, 2nd edn. Oxford University Press, Oxford, 2005) in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

1 aHess, Martin, W.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85060005503&doi=10.1007%2f978-3-319-96415-7_64&partnerID=40&md5=d1a900db8ddb92cd818d797ec212a4c600668nas a2200109 4500008004100000245006600041210005900107520027500166100002500441700002100466856007100487 2019 eng d00aOn the square distance function from a manifold with boundary0 asquare distance function from a manifold with boundary3 aWe characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

1 aBellettini, Giovanni1 aElshorbagy, Alaa uhttp://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf01106nas a2200157 4500008004100000022001400041245006700055210006000122260001000182300001200192490000700204520065100211100002200862700001900884856004500903 2019 en d a1230-342900aOn the topological degree of planar maps avoiding normal cones0 atopological degree of planar maps avoiding normal cones bSISSA a825-8450 v533 aThe classical Poincaré-Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones.

We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than $1$.

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems. The algorithm is introduced alongside the weighted greedy method. Our proposed method aims to minimize the error in a L2 norm and, in contrast to the weighted greedy approach, it does not require the availability of an error bound. Moreover, we consider sparse discretization of the input space in the construction of the reduced model; for high-dimensional problems, provided the sampling is done accordingly to the parameters distribution, this enables a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We provide many numerical tests to assess the performance of the proposed method compared to an equivalent reduced order model without weighting, as well as to the weighted greedy approach, in both low and high dimensional problems.

1 a.Venturi, L1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85053798049&doi=10.1007%2fs10915-018-0830-7&partnerID=40&md5=5cad501b6ef1955da55868807079ee5d01267nas a2200145 4500008004100000245010200041210006900143300001000212520067900222100001600901700001400917700001700931700002100948856015200969 2019 eng d00aWeighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs0 aWeighted Reduced Order Methods for Parametrized Partial Differen a27-403 aIn this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.

1 aVenturi, L.1 aTorlo, D.1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379&doi=10.1007%2f978-3-030-04870-9_2&partnerID=40&md5=446bcc1f331167bbba67bc00fb17015000374nas a2200085 4500008004100000245011800041210006900159100002300228856003700251 2019 eng d00aZero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions0 aZero modes and lowenergy resolvent expansion for three dimension1 aScandone, Raffaele uhttps://arxiv.org/abs/1901.0244901047nas a2200133 4500008004100000245007000041210006900111300001400180490000700194520062800201100002400829700002100853856003900874 2018 eng d00aAnalysis of a Dynamic Peeling Test with Speed-Dependent Toughness0 aAnalysis of a Dynamic Peeling Test with SpeedDependent Toughness a1206-12270 v783 aWe analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttps://doi.org/10.1137/17M114735400682nas a2200121 4500008004100000245007400041210006600115260001000181520028100191100002100472700001900493856004800512 2018 en d00aOn the Cauchy problem for the wave equation on time-dependent domains0 aCauchy problem for the wave equation on timedependent domains bSISSA3 aWe introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness.1 aDal Maso, Gianni1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3531400586nas a2200133 4500008004100000245010800041210006900149300001200218490000700230100002200237700002200259700002100281856015000302 2018 eng d00aCertified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models0 aCertified Reduced Basis Approximation for the Coupling of Viscou a197-2190 v741 aMartini, Immanuel1 aHaasdonk, Bernard1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a96401398nas a2200121 4500008004100000245014300041210006900184260001000253520092300263100002301186700001901209856004801228 2018 en d00aCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations0 aCharacteristic boundary layers for mixed hyperbolic systems in o bSISSA3 aWe provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://preprints.sissa.it/handle/1963/3532501651nas a2200145 4500008004100000245009700041210006900138300001400207490000700221520116600228100001901394700002401413700002201437856004601459 2018 eng d00aCohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue0 aCohesive fracture with irreversibility Quasistatic evolution for a1371-14120 v283 aIn this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

1 aCrismale, Vito1 aLazzaroni, Giuliano1 aOrlando, Gianluca uhttps://doi.org/10.1142/S021820251850037900540nas a2200145 4500008004100000245007700041210006900118300001400187490000600201100002100207700002100228700002200249700001700271856010600288 2018 eng d00adeal2lkit: A toolkit library for high performance programming in deal.II0 adeal2lkit A toolkit library for high performance programming in a318–3270 v71 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttps://www.math.sissa.it/publication/deal2lkit-toolkit-library-high-performance-programming-dealii-000395nas a2200109 4500008004100000245004700041210004700088100001800135700002400153700002600177856008200203 2018 eng d00aDifferential of metric valued Sobolev maps0 aDifferential of metric valued Sobolev maps1 aGigli, Nicola1 aPasqualetto, Enrico1 aSoultanis, Elefterios uhttps://www.math.sissa.it/publication/differential-metric-valued-sobolev-maps00493nas a2200097 4500008004100000245012200041210006900163100001900232700001900251856012500270 2018 eng d00aDimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case0 aDimension reduction for thin films with transversally varying pr1 aLewicka, Marta1 aLučić, Danka uhttps://www.math.sissa.it/publication/dimension-reduction-thin-films-transversally-varying-prestrain-oscillatory-and-non00945nas a2200109 4500008004100000245010200041210006900143520053000212100002100742700001800763856005400781 2018 en d00aExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping0 aExistence and uniqueness of dynamic evolutions for a one dimensi3 aIn this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

1 aNardini, Lorenzo1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3531900762nas a2200121 4500008004100000245009200041210006900133520032400202100002100526700002600547700001900573856004800592 2018 en d00aExistence for elastodynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for elastodynamic Griffith fracture with a weak maxima3 aWe consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3530800528nas a2200145 4500008004100000020002200041245007200063210006900135260004400204300001200248100002300260700002100283700003000304856004800334 2018 eng d a978-3-319-89800-100aFailure of the Chain Rule in the Non Steady Two-Dimensional Setting0 aFailure of the Chain Rule in the Non Steady TwoDimensional Setti aChambSpringer International Publishing a33–601 aBianchini, Stefano1 aBonicatto, Paolo1 aRassias, Themistocles, M. uhttps://doi.org/10.1007/978-3-319-89800-1_201151nas a2200133 4500008004100000245012600041210006900167300001200236490000800248520056200256100002200818700002100840856015600861 2018 eng d00aFinite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations0 aFinite volume PODGalerkin stabilised reduced order methods for t a273-2840 v1733 aIn this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier–Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a finite volumes approximation. The reduced basis spaces are constructed with a POD approach. Two different pressure stabilisation strategies are proposed and compared: the former one is based on the supremizer enrichment of the velocity space, and the latter one is based on a pressure Poisson equation approach.

1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85043366603&doi=10.1016%2fj.compfluid.2018.01.035&partnerID=40&md5=c15435ea3b632e55450da19ba2bb612500442nas a2200121 4500008004100000245005000041210005000091100002600141700002200167700002700189700001900216856008500235 2018 eng d00aFoldable structures made of hydrogel bilayers0 aFoldable structures made of hydrogel bilayers1 aAgostiniani, Virginia1 aDeSimone, Antonio1 aLucantonio, Alessandro1 aLučić, Danka uhttps://www.math.sissa.it/publication/foldable-structures-made-hydrogel-bilayers00971nas a2200145 4500008004100000245008600041210006900127300001100196490000700207520050000214100002900714700002100743700002300764856003800787 2018 eng d00aFractional powers and singular perturbations of quantum differential Hamiltonians0 aFractional powers and singular perturbations of quantum differen a0721060 v593 aWe consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

1 aMichelangeli, Alessandro1 aOttolini, Andrea1 aScandone, Raffaele uhttps://doi.org/10.1063/1.503385601226nas a2200193 4500008004100000022001400041245006800055210006500123300001600188490000800204520054000212653002300752653006700775653004400842100002300886700002900909700002300938856007100961 2018 eng d a0022-123600aOn fractional powers of singular perturbations of the Laplacian0 afractional powers of singular perturbations of the Laplacian a1551 - 16020 v2753 aWe qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

10aPoint interactions10aRegular and singular component of a point-interaction operator10aSingular perturbations of the Laplacian1 aGeorgiev, Vladimir1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttp://www.sciencedirect.com/science/article/pii/S002212361830104601283nas a2200169 4500008004100000022001400041245010100055210006900156260000800225300000700233490000700240520074700247100002100994700002901015700002301044856004601067 2018 eng d a1420-903900aGlobal, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials0 aGlobal finite energy weak solutions for the NLS with rough timed cMar a460 v693 aWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

1 aAntonelli, Paolo1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1007/s00033-018-0938-500570nas a2200121 4500008004100000245011800041210006900159260001700228100002600245700002700271700001900298856013100317 2018 eng d00aHeterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets0 aHeterogeneous elastic plates with inplane modulation of the targ bEDP Sciences1 aAgostiniani, Virginia1 aLucantonio, Alessandro1 aLučić, Danka uhttps://www.math.sissa.it/publication/heterogeneous-elastic-plates-plane-modulation-target-curvature-and-applications-thin-gel00439nas a2200097 4500008004100000245008500041210006900126100001900195700002000214856010700234 2018 eng d00aLong time existence for fully nonlinear NLS with small Cauchy data on the circle0 aLong time existence for fully nonlinear NLS with small Cauchy da1 aRoberto, Feola1 aIandoli, Felice uhttps://www.math.sissa.it/publication/long-time-existence-fully-nonlinear-nls-small-cauchy-data-circle00806nas a2200181 4500008004100000022001400041245009400055210006900149260000800218300001400226490000700240520023200247100002900479700002900508700002300537700001800560856004600578 2018 eng d a1424-066100aLp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction0 aLpBoundedness of Wave Operators for the ThreeDimensional MultiCe cJan a283–3220 v193 aWe prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro1 aScandone, Raffaele1 aYajima, Kenji uhttps://doi.org/10.1007/s00023-017-0628-400694nas a2200121 4500008004100000245007500041210006900116260001000185520028900195100002100484700001900505856004800524 2018 en d00aA minimization approach to the wave equation on time-dependent domains0 aminimization approach to the wave equation on timedependent doma bSISSA3 aWe prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.1 aDal Maso, Gianni1 aDe Luca, Lucia uhttp://preprints.sissa.it/handle/1963/3531801671nas a2200205 4500008004100000022001400041245009100055210006900146300001100215490000800226520095800234653002501192653005401217653002501271653002901296100002501325700001901350700002501369856007101394 2018 eng d a0021-782400aMinimizing movements for mean curvature flow of droplets with prescribed contact angle0 aMinimizing movements for mean curvature flow of droplets with pr a1 - 580 v1173 aWe study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the solutions constructed as a limit of an approximation algorithm of Almgren–Taylor–Wang and Luckhaus–Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. Résumé Nous étudions le mouvement par courbure moyenne d'une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit éventuellement non constant. En utilisant les solutions construites comme limites d'un algorithme d'approximation dû à Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l'existence d'une évolution faible, et sa compatibilité avec une solution au sens des distributions. Nous démontrons également plusieurs résultats de comparaison.

10aCapillary functional10aMean curvature flow with prescribed contact angle10aMinimizing movements10aSets of finite perimeter1 aBellettini, Giovanni1 aNovaga, Matteo1 aKholmatov, Shokhrukh uhttp://www.sciencedirect.com/science/article/pii/S002178241830082501065nas a2200133 4500008004100000245006300041210006300104300001400167490000700181520065400188100002500842700002500867856003900892 2018 eng d00aMinimizing Movements for Mean Curvature Flow of Partitions0 aMinimizing Movements for Mean Curvature Flow of Partitions a4117-41480 v503 aWe prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.

1 aBellettini, Giovanni1 aKholmatov, Shokhrukh uhttps://doi.org/10.1137/17M115929400730nas a2200109 4500008004100000245008900041210006900130520032300199100002900522700002100551856004800572 2018 en d00aNon-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis0 aNonlinear GrossPitaevskii dynamics of a 2D binary condensate a n3 aWe present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://preprints.sissa.it/handle/1963/3532300361nas a2200097 4500008004100000245005400041210004700095100001800142700002400160856007900184 2018 eng d00aOn the notion of parallel transport on RCD spaces0 anotion of parallel transport on RCD spaces1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/notion-parallel-transport-rcd-spaces00508nas a2200145 4500008004100000245008900041210006900130260002300199300001400222490000800236100002200244700002600266700001900292856005100311 2018 eng d00aA novel reduced order model for vortex induced vibrations of long flexible cylinders0 anovel reduced order model for vortex induced vibrations of long bElsevier {BV}cmay a191–2070 v1561 aStabile, Giovanni1 aMatthies, Hermann, G.1 aBorri, Claudio uhttps://doi.org/10.1016/j.oceaneng.2018.02.06401177nas a2200145 4500008004100000245008600041210006900127300001300196490000800209520068400217100001800901700002100919700002100940856007000961 2018 eng d00aNumerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves0 aNumerical study of the KadomtsevPetviashvili equation and disper a201704580 v4743 aA detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

1 aGrava, Tamara1 aKlein, Christian1 aPitton, Giuseppe uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.045802205nas a2200253 4500008004100000022001400041245007200055210006900127260001200196490000600208520146100214653002201675653002201697653002501719653002101744653001701765653001601782653002001798653001801818100002501836700002301861700002201884856004501906 2018 eng d a2296-914400aPeristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots0 aPeristaltic Waves as Optimal Gaits in Metameric BioInspired Robo c09/20180 v53 a*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

We study the periodic boundary value problem associated with the second order nonlinear equation u''+(λa+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m−1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526401233nas a2200133 4500008004100000245007600041210006900117300001200186490000700198520080200205100002301007700002301030856004601053 2018 eng d00aPositive subharmonic solutions to nonlinear ODEs with indefinite weight0 aPositive subharmonic solutions to nonlinear ODEs with indefinite a17500210 v203 aWe prove that the superlinear indefinite equation u″ + a(t)up = 0, where p > 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt < 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo uhttps://doi.org/10.1142/S021919971750021300509nas a2200133 4500008004100000245012700041210006900168300001400237490000600251100002100257700001700278700002200295856005800317 2018 eng d00aPredicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions0 aPredicting and Optimizing Microswimmer Performance from the Hydr a410–4240 v51 aGiuliani, Nicola1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/01019nas a2200157 4500008004100000022001400041245008700055210006900142260000800211300001400219490000700233520053000240100002400770700002100794856004600815 2018 eng d a1432-146700aOn the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One0 aQuasistatic Limit of Dynamic Evolutions for a Peeling Test in Di cFeb a269–3040 v283 aThe aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith's criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttps://doi.org/10.1007/s00332-017-9407-000448nas a2200097 4500008004100000245008100041210006900122100002900191700002300220856010700243 2018 eng d00aOn real resonances for the three-dimensional, multi-centre point interaction0 areal resonances for the threedimensional multicentre point inter1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://www.math.sissa.it/publication/real-resonances-three-dimensional-multi-centre-point-interaction00849nas a2200157 4500008004100000022001400041245009800055210006900153260000800222300000800230490000700238520036300245100001800608700001900626856004600645 2018 eng d a1432-083500aRecognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group0 aRecognizing the flat torus among RCD0N spaces via the study of t cJun a1040 v573 aWe prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

1 aGigli, Nicola1 aRigoni, Chiara uhttps://doi.org/10.1007/s00526-018-1377-z00501nas a2200121 4500008004100000245013400041210006900175490000700244100002100251700002000272700002100292856006600313 2018 eng d00aReduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings0 aReduced Basis Approximation and A Posteriori Error Estimation Ap0 v151 aHuynh, D., B. P.1 aPichi, Federico1 aRozza, Gianluigi uhttps://link.springer.com/chapter/10.1007/978-3-319-94676-4_802258nas a2200145 4500008004100000245013400041210006900175300001200244490000700256520163800263100001801901700002001919700002101939856015201960 2018 eng d00aReduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings0 aReduced Basis Approximation and A Posteriori Error Estimation Ap a203-2470 v153 aIn this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinely parametrized geometries. The essential ingredients of the methodology are: a Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold”—dimension reduction; an efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations—rapid convergence; an a posteriori error estimation procedures—rigorous and sharp bounds for the functional outputs related with the underlying solution or related quantities of interest, like stress intensity factor; and Offline-Online computational decomposition strategies—minimum marginal cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present several illustrative results for linear elasticity problem in parametrized geometries representing 2D Cartesian or 3D axisymmetric configurations like an arc-cantilever beam, a center crack problem, a composite unit cell or a woven composite beam, a multi-material plate, and a closed vessel. We consider different parametrization for the systems: either physical quantities—to model the materials and loads—and geometrical parameters—to model different geometrical configurations—with isotropic and orthotropic materials working in plane stress and plane strain approximation. We would like to underline the versatility of the methodology in very different problems. As last example we provide a nonlinear setting with increased complexity.

1 aHuynh, D.B.P.1 aPichi, Federico1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85055036627&doi=10.1007%2f978-3-319-94676-4_8&partnerID=40&md5=e9c07038e7bcc6668ec702c0653410dc00517nas a2200109 4500008004100000245011200041210006900153100001900222700002200241700002100263856012300284 2018 eng d00aReducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation0 aReducibility for a class of weakly dispersive linear operators a1 aFeola, Roberto1 aGiuliani, Filippo1 aProcesi, Michela uhttps://www.math.sissa.it/publication/reducibility-class-weakly-dispersive-linear-operators-arising-degasperis-procesi01236nas a2200121 4500008004100000245007700041210006900118300001200187490000700199520084400206100001801050856004601068 2018 eng d00aRegularity estimates for scalar conservation laws in one space dimension0 aRegularity estimates for scalar conservation laws in one space d a623-6910 v153 aWe deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function f has on the entropy solution. More precisely, if the set w : f″(w)≠0 is dense, the regularity of the solution can be expressed in terms of BVΦ spaces, where Φ depends on the nonlinearity of f. If moreover the set w : f″(w) = 0 is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that f′∘ u(t) ∈BV loc(ℝ) for every t > 0 and that this can be improved to SBVloc(ℝ) regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.

1 aMarconi, Elio uhttps://doi.org/10.1142/S021989161850020000433nas a2200121 4500008004100000245006100041210005800102300001400160490000700174100001800181700001900199856009300218 2018 eng d00aSecond order differentiation formula on RCD(K, N) spaces0 aSecond order differentiation formula on RCDK N spaces a377–3860 v291 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-rcdk-n-spaces00386nas a2200097 4500008004100000245006100041210005700102100001800159700001900177856009200196 2018 eng d00aSecond order differentiation formula on RCD*(K,N) spaces0 aSecond order differentiation formula on RCDKN spaces1 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-rcdkn-spaces01292nas a2200157 4500008004100000245006900041210006900110260002100179300001200200490000700212520078900219100002901008700002401037700002301061856005001084 2018 eng d00aSingular Hartree equation in fractional perturbed Sobolev spaces0 aSingular Hartree equation in fractional perturbed Sobolev spaces bTaylor & Francis a558-5880 v253 aWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1080/14029251.2018.150342301712nas a2200229 4500008004100000022001400041245010200055210006900157300001200226490000800238520097600246653001601222653002001238653001601258653002201274100001601296700002701312700002701339700002201366700002201388856007201410 2018 eng d a0020-740300aSpontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry0 aSpontaneous morphing of equibiaxially prestretched elastic bilay a481-4860 v1493 aAn elastic bilayer, consisting of an equibiaxially pre-stretched sheet bonded to a stress-free one, spontaneously morphs into curved shapes in the absence of external loads or constraints. Using experiments and numerical simulations, we explore the role of geometry for square and rectangular samples in determining the equilibrium shape of the system, for a fixed pre-stretch. We classify the observed shapes over a wide range of aspect ratios according to their curvatures and compare measured and computed values, which show good agreement. In particular, as the bilayer becomes thinner, a bifurcation of the principal curvatures occurs, which separates two scaling regimes for the energy of the system. We characterize the transition between these two regimes and show the peculiar features that distinguish square from rectangular samples. The results for our model bilayer system may help explaining morphing in more complex systems made of active materials.

10aBifurcation10aElastic bilayer10aPre-stretch10aShape programming1 aCaruso, Noe1 aCvetković, Aleksandar1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://www.sciencedirect.com/science/article/pii/S002074031731176101774nas a2200169 4500008004100000245006400041210006100105520122900166100001801395700001801413700001401431700001701445700001701462700001901479700002101498856008501519 2018 eng d00aSRTP 2.0 - The evolution of the safe return to port concept0 aSRTP 20 The evolution of the safe return to port concept3 aIn 2010 IMO (International Maritime Organisation) introduced new rules in SOLAS with the aim of intrinsically increase the safety of passenger ships. This requirement is achieved by providing safe areas for passengers and essential services for allowing ship to Safely Return to Port (SRtP). The entry into force of these rules has changed the way to design passenger ships. In this respect big effort in the research has been done by industry to address design issues related to the impact on failure analysis of the complex interactions among systems. Today the research activity is working to bring operational matters in the design stage. This change of research focus was necessary because human factor and the way to operate the ship itself after a casualty on board may have a big impact in the design of the ship/systems. Also the management of the passengers after a casualty is becoming a major topic for safety. This paper presents the state of the art of Italian knowledge in the field of system engineering applied to passenger ship address to safety improvement and design reliability. An overview of present tools and methodologies will be offered together with future focuses in the research activity.

1 aCangelosi, D.1 aBonvicini, A.1 aNardo, M.1 aMola, Andrea1 aMarchese, A.1 aTezzele, Marco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/srtp-20-evolution-safe-return-port-concept01436nas a2200145 4500008004100000245011100041210006900152300001400221490000600235520085400241100001401095700001701109700002101126856014301147 2018 eng d00aStabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs0 aStabilized weighted reduced basis methods for parametrized advec a1475-15020 v63 aIn this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.

1 aTorlo, D.1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502&doi=10.1137%2f17M1163517&partnerID=40&md5=6c54e2f0eb727cb85060e988486b8ac801002nas a2200133 4500008004100000245006100041210006000102520056900162100002200731700002100753700001900774700002700793856004800820 2018 en d00aStochastic homogenisation of free-discontinuity problems0 aStochastic homogenisation of freediscontinuity problems3 aIn this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida uhttp://preprints.sissa.it/handle/1963/3530901022nas a2200121 4500008004100000245005500041210005500096520063900151100002100790700002300811700001800834856004800852 2018 en d00aTransmission conditions obtained by homogenisation0 aTransmission conditions obtained by homogenisation3 aWe study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems.1 aDal Maso, Gianni1 aFranzina, Giovanni1 aZucco, Davide uhttp://preprints.sissa.it/handle/1963/3531000568nas a2200145 4500008004100000020002200041245008900063210006900152260004400221300001400265100002100279700002700300700002800327856006700355 2018 eng d a978-3-319-91545-600aOn Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field0 aUniqueness of Weak Solutions to Transport Equation with Nonsmoot aChambSpringer International Publishing a191–2031 aBonicatto, Paolo1 aKlingenberg, Christian1 aWestdickenberg, Michael uhttps://link.springer.com/chapter/10.1007/978-3-319-91545-6_1500574nas a2200133 4500008004100000245012000041210007000161300001200231490000800243100002100251700001700272700001700289856013400306 2018 eng d00aπ-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods0 aπBEM A flexible parallel implementation for adaptive geometry aw a39–580 v1211 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca uhttps://www.math.sissa.it/publication/%CF%80-bem-flexible-parallel-implementation-adaptive-geometry-aware-and-high-order-boundary00999nas a2200121 4500008004100000245009100041210006900132260001000201520057300211100002400784700002100808856004800829 2017 en d00aOn the 1D wave equation in time-dependent domains and the problem of debond initiation0 a1D wave equation in timedependent domains and the problem of deb bSISSA3 aMotivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://preprints.sissa.it/handle/1963/3530202169nas a2200109 4500008004100000245012900041210006900170520172600239100002401965700002201989856004802011 2017 en d00aAlmost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions0 aAlmost global existence of solutions for capillaritygravity wate3 aThe goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.1 aBerti, Massimiliano1 aDelort, Jean-Marc uhttp://preprints.sissa.it/handle/1963/3528500564nas a2200133 4500008004100000245012900041210006900170260008500239300001400324490000700338100002300345700001900368856004300387 2017 eng d00aAn application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators0 aapplication of coincidence degree theory to cyclic feedback type bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a683–7260 v501 aFeltrin, Guglielmo1 aZanolin, Fabio uhttps://doi.org/10.12775/TMNA.2017.03801212nas a2200109 4500008004100000245010500041210006900146520071800215100002100933700002100954856012700975 2017 eng d00aOn the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics0 aApplication of Reduced Basis Methods to Bifurcation Problems in 3 aIn this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

1 aPitton, Giuseppe1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/application-reduced-basis-methods-bifurcation-problems-incompressible-fluid-dynamics00875nas a2200193 4500008004100000022001400041245006900055210006600124300001600190490000800206520024700214653002900461653002400490653002300514653003300537100002200570700001800592856007100610 2017 eng d a0022-039600aAn avoiding cones condition for the Poincaré–Birkhoff Theorem0 aavoiding cones condition for the Poincaré–Birkhoff Theorem a1064 - 10840 v2623 aWe provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincaré–Birkhoff fixed point Theorem for Poincaré maps of Hamiltonian systems.

10aAvoiding cones condition10aHamiltonian systems10aPeriodic solutions10aPoincaré–Birkhoff theorem1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S002203961630327802454nas a2200169 4500008004100000020002200041024003400063245010200097210006900199250004300268260002500311490000900336520177800345100001802123700002102141856012202162 2017 eng d a978-3-319-65869-8 aDOI 10.1007/978-3-319-65870-400aCertified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation0 aCerti fied Reduced Basis Method for Affinely Parametric Isogeome aBittencourt, Dumont, Hesthaven. (Eds). aHeildebergbSpringer0 v 1193 aIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization

of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis

(IGA) is a growing research theme in scientic computing and computational mechanics, as well as reduced

basis methods for parametric PDEs. Their combination enhances the solution of some class of problems,

especially the ones characterized by parametrized geometries we introduced in this work. For a general

overview on Reduced Basis (RB) methods we recall [7, 15] and on IGA [3]. This work wants to demonstrate

that it is also possible for some class of problems to deal with ane geometrical parametrization combined

with a NURBS IGA formulation. This is what this work brings as original ingredients with respect to other

works dealing with reduced order methods and IGA (set in a non-affine formulation, and using a POD [2]

sampling without certication: see for example for potential flows [12] and for Stokes flows [17]). In this work

we show a certication of accuracy and a complete integration between IGA formulation and parametric

certified greedy RB formulation. Section 2 recalls the abstract setting for parametrized PDEs, Section 3

recalls IGA setting, Section 4 deals with RB formulation, and Section 5 illustrates two numerical examples in heat transfer with different parametrization.

1 aDevaud, Denis1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/certi-fied-reduced-basis-method-affinely-parametric-isogeometric-analysis-nurbs00572nas a2200157 4500008004100000245006200041210005700103300001400160490000700174100001800181700001700199700001700216700001700233700002100250856014300271 2017 eng d00aOn a certified smagorinsky reduced basis turbulence model0 acertified smagorinsky reduced basis turbulence model a3047-30670 v551 aRebollo, T.C.1 aÁvila, E.D.1 aMarmol, M.G.1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c01188nas a2200181 4500008004100000022001400041245007200055210007100127300001600198490000800214520059300222653002900815653001900844653003300863653002100896100001800917856007100935 2017 eng d a0022-039600aClifford Tori and the singularly perturbed Cahn–Hilliard equation0 aClifford Tori and the singularly perturbed Cahn–Hilliard equatio a5306 - 53620 v2623 aIn this paper we construct entire solutions uε to the Cahn–Hilliard equation −ε2Δ(−ε2Δu+W′(u))+W″(u)(−ε2Δu+W′(u))=ε4λε(1−uε), under the volume constraint ∫R3(1−uε)2dx=82π2cε, with cε→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov–Schmidt reduction and on careful geometric expansions of the Laplacian.

10aCahn–Hilliard equation10aClifford Torus10aLyapunov–Schmidt reduction10aWillmore surface1 aRizzi, Matteo uhttp://www.sciencedirect.com/science/article/pii/S002203961730053002413nas a2200205 4500008004100000245015800041210006900199260001200268300000800280490000800288520159500296653004301891653002501934653002301959653003401982100002102016700002102037700002102058856012802079 2017 eng d00aComputational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology0 aComputational reduction strategies for the detection of steady b c09/2017 a5570 v3443 aWe focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

10aMultigrid10aPhase field10aQuasi-Newton10aSuper-hydrophobicity1 aFedeli, Livio uhttp://www.sciencedirect.com/science/article/pii/S002199911730356X01069nas a2200181 4500008004100000022001400041245011100055210006900166300001400235490000800249520044900257653001400706653003100720653002700751100002100778700001700799856007100816 2017 eng d a0362-546X00aCurvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators0 aCurvature terms in small time heat kernel expansion for a model a118 - 1340 v1643 aWe consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

10aCurvature10aHypoelliptic heat equation10aSmall time asymptotics1 aBarilari, Davide1 aPaoli, Elisa uhttp://www.sciencedirect.com/science/article/pii/S0362546X1730229800906nas a2200121 4500008004100000245009600041210006900137520045600206100002300662700002400685700002400709856005100733 2017 en d00aDerivation of a rod theory from lattice systems with interactions beyond nearest neighbours0 aDerivation of a rod theory from lattice systems with interaction3 aWe study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526901416nas a2200169 4500008004100000020002200041245008400063210007000147260004400217300001400261520082100275100002001096700002301116700002901139700002901168856004901197 2017 eng d a978-3-319-58904-600aDispersive Estimates for Schrödinger Operators with Point Interactions in ℝ30 aDispersive Estimates for Schrödinger Operators with Point Intera aChambSpringer International Publishing a187–1993 aThe study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

1 aIandoli, Felice1 aScandone, Raffaele1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_1101090nas a2200121 4500008004100000245009000041210006900131520064600200100002300846700002400869700002400893856005100917 2017 en d00aOn the effect of interactions beyond nearest neighbours on non-convex lattice systems0 aeffect of interactions beyond nearest neighbours on nonconvex la3 aWe analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526800962nas a2200133 4500008004100000245012600041210006900167260002600236300001400262490000700276520044200283100001800725856008500743 2017 eng d00aEnergy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening0 aEnergy release rate and quasistatic evolution via vanishing visc bEDP Sciencesc05/2017 a791–8260 v233 aIn the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

1 aAlmi, Stefano uhttps://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/201601401393nas a2200145 4500008004100000245005300041210005100094260001000145520095500155100002201110700002101132700001901153700002701172856004801199 2017 en d00aGamma-Convergence of Free-discontinuity problems0 aGammaConvergence of Freediscontinuity problems bSISSA3 aWe study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida uhttp://preprints.sissa.it/handle/1963/3527601320nas a2200133 4500008004100000245008300041210006900124300001400193490000700207520089100214100001801105700002201123856004101145 2017 eng d00aOn the genesis of directional friction through bristle-like mediating elements0 agenesis of directional friction through bristlelike mediating el a1023-10460 v233 aWe propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

1 aGidoni, Paolo1 aDeSimone, Antonio uhttps://doi.org/10.1051/cocv/201703001385nas a2200145 4500008004100000022001400041245009300055210006900148260000800217300001400225490000800239520092700247100001901174856004601193 2017 eng d a1618-189100aGlobally stable quasistatic evolution for strain gradient plasticity coupled with damage0 aGlobally stable quasistatic evolution for strain gradient plasti cApr a641–6850 v1963 aWe consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin–Anand formulation (J Mech Phys Solids 53:1624–1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material's degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).

1 aCrismale, Vito uhttps://doi.org/10.1007/s10231-016-0590-700440nas a2200157 4500008004100000022001400041245004400055210004400099260000800143300000800151490000700159100002500166700002400191700002100215856004600236 2017 eng d a1432-083500aHomotopically invisible singular curves0 aHomotopically invisible singular curves cJul a1050 v561 aAgrachev, Andrei, A.1 aBoarotto, Francesco1 aLerario, Antonio uhttps://doi.org/10.1007/s00526-017-1203-z00569nas a2200133 4500008004100000245009900041210006900140260003400209300001400243490000700257100002400264700002100288856012600309 2017 eng d00aHomotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry0 aHomotopy properties of horizontal path spaces and a theorem of S bInternational Press of Boston a269–3010 v251 aBoarotto, Francesco1 aLerario, Antonio uhttps://www.math.sissa.it/publication/homotopy-properties-horizontal-path-spaces-and-theorem-serre-subriemannian-geometry00713nas a2200157 4500008004100000245004400041210004000085520026500125653001200390653001000402653004000412100002000452700002400472700001800496856004100514 2017 eng d00aThe injectivity radius of Lie manifolds0 ainjectivity radius of Lie manifolds3 aWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

10a(58J40)10a53C2110aMathematics - Differential Geometry1 aAntonini, Paolo1 aDe Philippis, Guido1 aGigli, Nicola uhttps://arxiv.org/pdf/1707.07595.pdf00384nas a2200109 4500008004100000245006300041210006000104100002300164700002100187700001800208856004800226 2017 en d00aA Lagrangian approach for scalar multi-d conservation laws0 aLagrangian approach for scalar multid conservation laws1 aBianchini, Stefano1 aBonicatto, Paolo1 aMarconi, Elio uhttp://preprints.sissa.it/handle/1963/3529001119nas a2200157 4500008004100000245006600041210006600107260004500173300001400218490000700232520056500239100002300804700002100827700001800848856009500866 2017 eng d00aLagrangian representations for linear and nonlinear transport0 aLagrangian representations for linear and nonlinear transport bPeoples' Friendship University of Russia a418–4360 v633 aIn this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

1 aBianchini, Stefano1 aBonicatto, Paolo1 aMarconi, Elio uhttp://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cmfd&paperid=327&option_lang=eng01179nas a2200121 4500008004100000245009100041210006900132300001200201490000700213520077600220100002000996856004101016 2017 eng d00aLimit of viscous dynamic processes in delamination as the viscosity and inertia vanish0 aLimit of viscous dynamic processes in delamination as the viscos a593-6250 v233 aWe introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.

1 aScala, Riccardo uhttps://doi.org/10.1051/cocv/201600601454nas a2200145 4500008004100000020001400041245006100055210006100116260001500177300001400192490000700206520103000213100001901243856004601262 2017 eng d a1424-929400aLinear Hyperbolic Systems in Domains with Growing Cracks0 aLinear Hyperbolic Systems in Domains with Growing Cracks c2017/06/01 a149 - 1850 v853 aWe consider the hyperbolic system ü$${ - {\rm div} (\mathbb{A} \nabla u) = f}$$in the time varying cracked domain $${\Omega \backslash \Gamma_t}$$, where the set $${\Omega \subset \mathbb{R}^d}$$is open, bounded, and with Lipschitz boundary, the cracks $${\Gamma_t, t \in [0, T]}$$, are closed subsets of $${\bar{\Omega}}$$, increasing with respect to inclusion, and $${u(t) : \Omega \backslash \Gamma_t \rightarrow \mathbb{R}^d}$$for every $${t \in [0, T]}$$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system v̈$${ - {\rm div} (\mathbb{B}\nabla v) + a\nabla v - 2 \nabla \dot{v}b = g}$$on the fixed domain $${\Omega \backslash \Gamma_0}$$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions v, which allows us to prove a continuous dependence result for both systems. The same study has already been carried out in [3, 7] in the scalar case.

1 aCaponi, Maicol uhttps://doi.org/10.1007/s00032-017-0268-701406nas a2200133 4500008004100000245004000041210004000081520101100121100002301132700002101155700002401176700002401200856004801224 2017 en d00aLinearisation of multiwell energies0 aLinearisation of multiwell energies3 aLinear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours.1 aAlicandro, Roberto1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://preprints.sissa.it/handle/1963/3528800988nas a2200157 4500008004100000245010900041210006900150260001500219300001400234490000700248520038700255100002100642700002200663700001900685856012600704 2017 eng d00aLower semicontinuity of a class of integral functionals on the space of functions of bounded deformation0 aLower semicontinuity of a class of integral functionals on the s bDe Gruyter a183–2070 v103 aWe study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttps://www.math.sissa.it/publication/lower-semicontinuity-class-integral-functionals-space-functions-bounded-deformation01104nas a2200145 4500008004100000245009100041210006900132300001200201490000800213520063400221100001800855700002100873700001900894856004500913 2017 en d00aA lower semicontinuity result for a free discontinuity functional with a boundary term0 alower semicontinuity result for a free discontinuity functional a952-9900 v1083 aWe study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1597901160nas a2200205 4500008004100000022001400041245006400055210006400119300000900183490000700192520049200199653003500691653001800726653003600744653002900780100002500809700001900834700002500853856007600878 2017 eng d a1534-039200aMinimizers of anisotropic perimeters with cylindrical norms0 aMinimizers of anisotropic perimeters with cylindrical norms a14270 v163 aWe study various regularity properties of minimizers of the Φ–perimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

10aanisotropic Bernstein problem;10aminimal cones10aNon parametric minimal surfaces10aSets of finite perimeter1 aBellettini, Giovanni1 aNovaga, Matteo1 aKholmatov, Shokhrukh uhttp://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d01736nas a2200181 4500008004100000022001400041245010800055210006900163300000900232490000700241520106900248653003901317653002301356653004001379653003601419100002301455856007601478 2017 eng d a1534-039200aMultiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities0 aMultiple positive solutions of a sturmliouville boundary value p a10830 v163 aWe study the second order nonlinear differential equation

\begindocument $ u'' + \sum\limits_i = 1^m α_ia_i(x)g_i(u) - \sum\limits_j = 1^m + 1 β_jb_j(x)k_j(u) = 0,\rm $ \enddocument

where $\alpha_i, \beta_j>0$, $a_i(x), b_j(x)$ are non-negative Lebesgue integrable functions defined in $\mathopen[0, L\mathclose]$, and the nonlinearities $g_i(s), k_j(s)$ are continuous, positive and satisfy suitable growth conditions, as to cover the classical superlinear equation $u"+a(x)u.p = 0$, with $p>1$.When the positive parameters $\beta_j$ are sufficiently large, we prove the existence of at least $2.m-1$positive solutions for the Sturm-Liouville boundary value problems associated with the equation.The proof is based on the Leray-Schauder topological degree for locally compact operators on open and possibly unbounded sets.Finally, we deal with radially symmetric positive solutions for the Dirichlet problems associated with elliptic PDEs.

10aLeray-Schauder topological degree;10apositive solutions10aSturm-Liouville boundary conditions10aSuperlinear indefinite problems1 aFeltrin, Guglielmo uhttp://aimsciences.org//article/id/1163b042-0c64-4597-b25c-3494b268e5a101598nas a2200217 4500008004100000022001400041245010600055210006900161300001600230490000800246520083500254653002301089653002501112653003601137653003201173653002601205653003601231100002301267700001901290856007101309 2017 eng d a0022-039600aMultiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree0 aMultiplicity of positive periodic solutions in the superlinear i a4255 - 42910 v2623 aWe study the periodic boundary value problem associated with the second order nonlinear differential equationu″+cu′+(a+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill's equation. We prove the existence of 2m−1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin's coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.

10aCoincidence degree10aMultiplicity results10aNeumann boundary value problems10aPositive periodic solutions10asubharmonic solutions10aSuperlinear indefinite problems1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961730021900849nas a2200109 4500008004100000245006100041210005900102260002000161520048400181100002300665856005100688 2017 en d00aA note on a fixed point theorem on topological cylinders0 anote on a fixed point theorem on topological cylinders bSpringer Verlag3 aWe present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skii ones.

1 aFeltrin, Guglielmo uhttp://urania.sissa.it/xmlui/handle/1963/3526300446nas a2200133 4500008004100000022001400041245009200055210006900147260000800216300001400224490000700238100002100245856004600266 2017 eng d a1572-922200aA Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations0 aNote on the Convergence of Singularly Perturbed Second Order Pot cJun a783–7970 v291 aNardini, Lorenzo uhttps://doi.org/10.1007/s10884-015-9461-y00704nas a2200181 4500008004100000245009900041210006900140300001400209490000700223100001700230700002000247700002000267700002200287700002100309700002000330700002200350856015000372 2017 eng d00aNumerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts0 aNumerical modeling of hemodynamics scenarios of patientspecific a1373-13990 v161 aBallarin, F.1 aFaggiano, Elena1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aIppolito, Sonia1 aScrofani, Roberto uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd001724nas a2200169 4500008004100000245012600041210006900167300001200236490000600248520107700254100002201331700001901353700001701372700002101389700002101410856012301431 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di a210-2360 v83 aVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

1 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-reduced-order-methods-cfd-using-finite-volume-discretisation-vortex01350nas a2200193 4500008004100000022001400041245007200055210006900127300001600196490000800212520074100220653001800961653000800979653002400987653002301011653002901034100002201063856007101085 2017 eng d a0022-039600aQuasi-periodic solutions for quasi-linear generalized KdV equations0 aQuasiperiodic solutions for quasilinear generalized KdV equation a5052 - 51320 v2623 aWe prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash–Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iteration is achieved by pseudo-differential techniques, linear Birkhoff normal form algorithms and a linear KAM reducibility scheme.

10aKAM for PDE's10aKdV10aNash–Moser theory10aQuasi-linear PDE's10aQuasi-periodic solutions1 aGiuliani, Filippo uhttp://www.sciencedirect.com/science/article/pii/S002203961730048700824nas a2200157 4500008004100000022001400041245009600055210006900151260000800220300000600228490000700234520033600241100001900577700002400596856004600620 2017 eng d a1420-900400aQuasistatic crack growth based on viscous approximation: a model with branching and kinking0 aQuasistatic crack growth based on viscous approximation a model cJan a70 v243 aEmploying the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.

1 aCrismale, Vito1 aLazzaroni, Giuliano uhttps://doi.org/10.1007/s00030-016-0426-602504nas a2200157 4500008004100000245005700041210005700098260001200155300000800167490000600175520201600181100001502197700002202212700002102234856009102255 2017 eng d00aReduced Basis Methods for Uncertainty Quantification0 aReduced Basis Methods for Uncertainty Quantification c08/2017 a8690 v53 aIn this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

Read More: http://epubs.siam.org/doi/abs/10.1137/151004550

POD–Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

1 aBallarin, F.1 aRozza, Gianluigi1 aMaday, Yvon1 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aUrban, Karsten uhttps://www.math.sissa.it/node/1294801221nas a2200097 4500008004100000245007700041210006900118520087000187100001801057856004801075 2017 en d00aRegularity estimates for scalar conservation laws in one space dimension0 aRegularity estimates for scalar conservation laws in one space d3 aIn this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.1 aMarconi, Elio uhttp://preprints.sissa.it/handle/1963/3529100410nas a2200097 4500008004100000245006900041210006500110100001800175700001900193856010000212 2017 eng d00aSecond order differentiation formula on compact RCD*(K,N) spaces0 aSecond order differentiation formula on compact RCDKN spaces1 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-compact-rcdkn-spaces01212nas a2200145 4500008004100000022001400041245008800055210007000143260000800213300001400221490000700235520076100242100001701003856004601020 2017 eng d a1573-869800aSmall Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators0 aSmall Time Asymptotics on the Diagonal for Hörmanders Type Hypoe cJan a111–1430 v233 aWe compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

1 aPaoli, Elisa uhttps://doi.org/10.1007/s10883-016-9321-z01538nas a2200157 4500008004100000022001400041245009300055210006900148260000800217300001400225490000700239520104800246100001801294700002201312856004601334 2017 eng d a1572-964800aStasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler0 aStasis domains and slip surfaces in the locomotion of a bioinspi cFeb a587–6010 v523 aWe formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

1 aGidoni, Paolo1 aDeSimone, Antonio uhttps://doi.org/10.1007/s11012-016-0408-001540nas a2200133 4500008004100000245006000041210005900101520111900160100001301279700002401292700001901316700002301335856004801358 2017 en d00aTime quasi-periodic gravity water waves in finite depth0 aTime quasiperiodic gravity water waves in finite depth3 aWe prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.1 aBaldi, P1 aBerti, Massimiliano1 aHaus, Emanuele1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3529601449nas a2200121 4500008004100000245006900041210006700110260001000177520104800187100002301235700002101258856004801279 2017 en d00aA uniqueness result for the decomposition of vector fields in Rd0 auniqueness result for the decomposition of vector fields in Rd bSISSA3 aGiven a vector field $\rho (1,\b) \in L^1_\loc(\R^+\times \R^{d},\R^{d+1})$ such that $\dive_{t,x} (\rho (1,\b))$ is a measure, we consider the problem of uniqueness of the representation $\eta$ of $\rho (1,\b) \mathcal L^{d+1}$ as a superposition of characteristics $\gamma : (t^-_\gamma,t^+_\gamma) \to \R^d$, $\dot \gamma (t)= \b(t,\gamma(t))$. We give conditions in terms of a local structure of the representation $\eta$ on suitable sets in order to prove that there is a partition of $\R^{d+1}$ into disjoint trajectories $\wp_\a$, $\a \in \A$, such that the PDE \begin{equation*} \dive_{t,x} \big( u \rho (1,\b) \big) \in \mathcal M(\R^{d+1}), \qquad u \in L^\infty(\R^+\times \R^{d}), \end{equation*} can be disintegrated into a family of ODEs along $\wp_\a$ with measure r.h.s.. The decomposition $\wp_\a$ is essentially unique. We finally show that $\b \in L^1_t(\BV_x)_\loc$ satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible $\BV$ vector fields.

1 aBianchini, Stefano1 aBonicatto, Paolo uhttp://preprints.sissa.it/handle/1963/3527402562nas a2200145 4500008004100000245012400041210006900165300001100234490000700245520198000252100001702232700001702249700002202266856012802288 2017 eng d00aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations0 aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear P a1–140 v613 aWe present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/wet-and-dry-transom-stern-treatment-unsteady-and-nonlinear-potential-flow-model-naval02105nas a2200217 4500008004100000245018600041210006900227260003600296520123100332100002501563700001701588700002001605700001701625700001901642700002101661700002101682700002101703700001701724700001601741856013001757 2016 en d00aAdvances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives0 aAdvances in geometrical parametrization and reduced order models aCrete, GreecebECCOMASc06/20163 aSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

1 aSalmoiraghi, Filippo1 aBallarin, F.1 aCorsi, Giovanni1 aMola, Andrea1 aTezzele, Marco1 aRozza, Gianluigi1 aPapadrakakis, M.1 aPapadopoulos, V.1 aStefanou, G.1 aPlevris, V. uhttps://www.math.sissa.it/publication/advances-geometrical-parametrization-and-reduced-order-models-and-methods-computational01524nas a2200157 4500008004100000245011100041210006900152300001000221490000700231520095900238653002001197100002501217700001801242700002201260856008401282 2016 en d00aOn the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity0 aarea of the graph of a piecewise smooth map from the plane to th a29-630 v223 aIn this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

10aArea functional1 aBellettini, Giovanni1 aTealdi, Lucia1 aPaolini, Maurizio uhttps://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html00407nas a2200097 4500008004100000245006600041210006600107100001800173700002400191856009400215 2016 eng d00aBehaviour of the reference measure on RCD spaces under charts0 aBehaviour of the reference measure on RCD spaces under charts1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/behaviour-reference-measure-rcd-spaces-under-charts00926nas a2200205 4500008004100000022001400041245006500055210005800120300000700178490000600185520030900191653001800500653002200518653002200540653003000562653001100592100002300603700001800626856007600644 2016 eng d a1937-163200aOn the concentration of entropy for scalar conservation laws0 aconcentration of entropy for scalar conservation laws a730 v93 aWe prove that the entropy for an $L^∞$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

10aconcentration10aConservation laws10aentropy solutions10aLagrangian representation10ashocks1 aBianchini, Stefano1 aMarconi, Elio uhttp://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae01304nas a2200133 4500008004100000245008300041210006900124520084400193100002201037700002201059700002001081700001801101856005101119 2016 en d00aConfinement of dislocations inside a crystal with a prescribed external strain0 aConfinement of dislocations inside a crystal with a prescribed e3 aWe study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.1 aLucardesi, Ilaria1 aMorandotti, Marco1 aScala, Riccardo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3524700867nas a2200145 4500008004100000022001400041245006500055210006500120260000800185300001400193490000700207520043700214100002400651856004600675 2016 eng d a1573-869800aConformal Equivalence of 3D Contact Structures on Lie Groups0 aConformal Equivalence of 3D Contact Structures on Lie Groups cApr a251–2830 v223 aIn this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

1 aBoarotto, Francesco uhttps://doi.org/10.1007/s10883-015-9273-800357nas a2200085 4500008004100000245006000041210005900101100001800160856009300178 2016 eng d00aCritical points of a perturbed Otha-Kawasaki functional0 aCritical points of a perturbed OthaKawasaki functional1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/critical-points-perturbed-otha-kawasaki-functional01884nas a2200145 4500008004100000245005300041210005300094260003400147300001100181490000700192520140800199100002001607700002501627856008601652 2016 eng d00aCurrents and dislocations at the continuum scale0 aCurrents and dislocations at the continuum scale bInternational Press of Boston a1–340 v233 aA striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

1 aScala, Riccardo1 aVan Goethem, Nicolas uhttps://www.math.sissa.it/publication/currents-and-dislocations-continuum-scale-000471nas a2200097 4500008004100000245009600041210006900137100001800206700002400224856012500248 2016 eng d00aEquivalence of two different notions of tangent bundle on rectifiable metric measure spaces0 aEquivalence of two different notions of tangent bundle on rectif1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/equivalence-two-different-notions-tangent-bundle-rectifiable-metric-measure-spaces00458nas a2200121 4500008004100000245009600041210006900137260001300206100002200219700002300241700002100264856005100285 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I0 aEulerian Lagrangian and Broad continuous solutions to a balance bElsevier1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3520700434nas a2200109 4500008004100000245009700041210006900138100002200207700002300229700002100252856005100273 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II0 aEulerian Lagrangian and Broad continuous solutions to a balance 1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3519701307nas a2200193 4500008004100000022001400041245009500055210006900150300001600219490000800235520066200243653002900905653002400934653002600958653001600984100002001000700002201020856007101042 2016 eng d a0022-123600aExistence and non-existence results for the SU(3) singular Toda system on compact surfaces0 aExistence and nonexistence results for the SU3 singular Toda sys a3750 - 38070 v2703 aWe consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

10aLiouville-type equations10aMin–max solutions10aNon-existence results10aToda system1 aBattaglia, Luca1 aMalchiodi, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002212361500494201120nas a2200229 4500008004100000022001400041245008700055210006900142300001600211490000800227520034000235653002200575653003200597653002100629653002500650653003400675653004400709100002100753700002400774700002100798856007100819 2016 eng d a0022-039600aExistence and uniqueness of dynamic evolutions for a peeling test in dimension one0 aExistence and uniqueness of dynamic evolutions for a peeling tes a4897 - 49230 v2613 aIn this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

10aDynamic debonding10aDynamic energy release rate10aDynamic fracture10aGriffith's criterion10aMaximum dissipation principle10aWave equation in time-dependent domains1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://www.sciencedirect.com/science/article/pii/S002203961630177201710nas a2200193 4500008004100000245011900041210006900160260001400229520106200243100001701305700002001322700002001342700002101362700002201383700002001405700002201425700001801447856005101465 2016 en d00aA fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts0 afast virtual surgery platform for many scenarios haemodynamics o bSubmitted3 aA fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.1 aBallarin, F.1 aFaggiano, Elena1 aManzoni, Andrea1 aRozza, Gianluigi1 aQuarteroni, Alfio1 aIppolito, Sonia1 aScrofani, Roberto1 aAntona, Carlo uhttp://urania.sissa.it/xmlui/handle/1963/3524000965nas a2200169 4500008004100000022001400041245012900055210006900184260000800253300000700261490000700268520041200275100002100687700002200708700001900730856004600749 2016 eng d a1432-083500aFracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case0 aFracture models for elastoplastic materials as limits of gradien cApr a450 v553 aWe study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttps://doi.org/10.1007/s00526-016-0981-z00945nas a2200157 4500008004100000022001400041245007900055210007200134260000800206300001600214490000800230520046300238100002200701700001800723856004600741 2016 eng d a1618-189100aGeneralizing the Poincaré–Miranda theorem: the avoiding cones condition0 aGeneralizing the Poincaré–Miranda theorem the avoiding cones con cAug a1347–13710 v1953 aAfter proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

1 aFonda, Alessandro1 aGidoni, Paolo uhttps://doi.org/10.1007/s10231-015-0519-600947nas a2200133 4500008004100000245008500041210006900126260001700195300001400212490000700226520047700233100001900710856008400729 2016 eng d00aGlobally stable quasistatic evolution for a coupled elastoplastic–damage model0 aGlobally stable quasistatic evolution for a coupled elastoplasti bEDP Sciences a883–9120 v223 aWe show the existence of globally stable quasistatic evolutions for a rate-independent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

1 aCrismale, Vito uhttps://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html00539nas a2200109 4500008004100000245007800041210006900119260001000188520009700198100002400295856011000319 2016 en d00aIntegrability of continuous bundles and applications to dynamical systems0 aIntegrability of continuous bundles and applications to dynamica bSISSA3 aIn this dissertation we study the problem of integrability of bundles with low regularities.1 aWar, Khadim, Mbacke uhttps://www.math.sissa.it/publication/integrability-continuous-bundles-and-applications-dynamical-systems01402nas a2200145 4500008004100000245011900041210006900160260007700229520081900306100002501125700001701150700001701167700002101184856005101205 2016 en d00aIsogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes0 aIsogeometric analysisbased reduced order modelling for incompres bSpringer, AMOS Advanced Modelling and Simulation in Engineering Sciences3 aIn this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.1 aSalmoiraghi, Filippo1 aBallarin, F.1 aHeltai, Luca1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519901362nas a2200121 4500008004100000245005800041210005800099520096700157100002401124700002101148700002301169856004801192 2016 en d00aLarge KAM tori for perturbations of the dNLS equation0 aLarge KAM tori for perturbations of the dNLS equation3 aWe prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2×2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues.1 aBerti, Massimiliano1 aKappeler, Thomas1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3528400690nas a2200109 4500008004100000245007500041210006900116520030100185100002100486700002200507856005100529 2016 en d00aA model for the quasistatic growth of cracks with fractional dimension0 amodel for the quasistatic growth of cracks with fractional dimen3 aWe study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated.1 aDal Maso, Gianni1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3517500391nas a2200133 4500008004100000245003600041210003500077260001000112100002400122700002000146700002100166700001900187856005100206 2016 en d00aModel Order Reduction: a survey0 aModel Order Reduction a survey bWiley1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttp://urania.sissa.it/xmlui/handle/1963/3519401034nas a2200145 4500008004100000022001400041245006600055210006600121260000800187300001600195490000800211520060300219100002000822856004600842 2016 eng d a1432-182300aMoser–Trudinger inequalities for singular Liouville systems0 aMoser–Trudinger inequalities for singular Liouville systems cApr a1169–11900 v2823 aIn this paper we prove a Moser–Trudinger inequality for the Euler–Lagrange functional of general singular Liouville systems on a compact surface. We characterize the values of the parameters which yield coercivity for the functional, hence the existence of energy-minimizing solutions for the system, and we give necessary conditions for boundedness from below. We also provide a sharp inequality under assuming the coefficients of the system to be non-positive outside the diagonal. The proofs use a concentration-compactness alternative, Pohožaev-type identities and blow-up analysis.

1 aBattaglia, Luca uhttps://doi.org/10.1007/s00209-015-1584-701781nas a2200157 4500008004100000022001400041245006600055210006600121260000800187300000700195490000700202520131900209100002601528700002201554856004701576 2016 eng d a1292-895X00aMotion planning and motility maps for flagellar microswimmers0 aMotion planning and motility maps for flagellar microswimmers cJul a720 v393 aWe study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttps://doi.org/10.1140/epje/i2016-16072-y01951nas a2200169 4500008004100000245009300041210006900134260001300203300000800216490000700224520142100231100002101652700001901673700001701692700002101709856005101730 2016 en d00aA multi-physics reduced order model for the analysis of Lead Fast Reactor single channel0 amultiphysics reduced order model for the analysis of Lead Fast R bElsevier a2080 v873 aIn this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519100467nas a2200109 4500008004100000245009200041210006900133300001200202490000800214100002000222856011500242 2016 eng d00aNew existence results for the mean field equation on compact surfaces via degree theory0 aNew existence results for the mean field equation on compact sur a11–170 v1361 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/new-existence-results-mean-field-equation-compact-surfaces-degree-theory01002nas a2200109 4500008004100000245009900041210007000140520058100210100002900791700002100820856005100841 2016 en d00aNon-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics0 aNonlinear Schrödinger system for the dynamics of a binary conden3 aWe present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/3526600476nas a2200121 4500008004100000245008400041210006900125260001500194300001400209490000700223100002000230856010400250 2016 eng d00aA note on a multiplicity result for the mean field equation on compact surfaces0 anote on a multiplicity result for the mean field equation on com bDe Gruyter a221–2290 v161 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/note-multiplicity-result-mean-field-equation-compact-surfaces00961nas a2200133 4500008004100000245014200041210006900183260003100252520042800283100002300711700002300734700001900757856005100776 2016 en d00aPairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case0 aPairs of positive periodic solutions of nonlinear ODEs with inde bCambridge University Press3 aWe study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526200883nas a2200157 4500008004100000245005000041210005000091260001500141300001400156490000600170520040100176100002200577700002300599700001800622856008500640 2016 eng d00aPeriodic perturbations of Hamiltonian systems0 aPeriodic perturbations of Hamiltonian systems bDe Gruyter a367–3820 v53 aWe prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

1 aFonda, Alessandro1 aGarrione, Maurizio1 aGidoni, Paolo uhttps://www.math.sissa.it/publication/periodic-perturbations-hamiltonian-systems02275nas a2200145 4500008004100000245009200041210006900133260006800202520165800270100002101928700001901949700001701968700002101985856012302006 2016 en d00aPOD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations0 aPODGalerkin Method for Finite Volume Approximation of NavierStok bComputer Methods in Applied Mechanics and Engineering, Elsevier3 aNumerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.1 aLorenzi, Stefano1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-method-finite-volume-approximation-navier-stokes-and-rans-equations01495nas a2200121 4500008004100000245010500041210007100146260001000217520097200227100001701199700002101216856013601237 2016 en d00aPOD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems0 aPOD–Galerkin monolithic reduced order models for parametrized fl bWiley3 aIn this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-monolithic-reduced-order-models-parametrized-fluid-structure-interaction02865nas a2200121 4500008004100000245007000041210006900111260001000180520240500190653002302595100002302618856010202641 2016 en d00aPositive solutions to indefinite problems: a topological approach0 aPositive solutions to indefinite problems a topological approach bSISSA3 aThe present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.10apositive solutions1 aFeltrin, Guglielmo uhttps://www.math.sissa.it/publication/positive-solutions-indefinite-problems-topological-approach00997nas a2200145 4500008004100000022001400041245010200055210006900157260000800226300001400234490000700248520053000255100002000785856004600805 2016 eng d a1678-771400aA quadratic interaction estimate for conservation laws: motivations, techniques and open problems0 aquadratic interaction estimate for conservation laws motivations cJun a589–6040 v473 aIn a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

1 aModena, Stefano uhttps://doi.org/10.1007/s00574-016-0171-900510nas a2200121 4500008004100000245008100041210006900122260004500191300001400236490000700250100002000257856011100277 2016 eng d00aQuadratic interaction estimate for hyperbolic conservation laws, an overview0 aQuadratic interaction estimate for hyperbolic conservation laws bPeoples' Friendship University of Russia a148–1720 v591 aModena, Stefano uhttps://www.math.sissa.it/publication/quadratic-interaction-estimate-hyperbolic-conservation-laws-overview00972nas a2200121 4500008004100000245009000041210006900131260001000200520038100210653011700591100001800708856012400726 2016 en d00aQualitative properties and construction of solutions to some semilinear elliptic PDEs0 aQualitative properties and construction of solutions to some sem bSISSA3 aThis thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction.10amoving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/qualitative-properties-and-construction-solutions-some-semilinear-elliptic-pdes-001110nas a2200097 4500008004100000245006200041210006000103520078000163100001800943856005100961 2016 en d00aQuasi-static hydraulic crack growth driven by Darcy's law0 aQuasistatic hydraulic crack growth driven by Darcys law3 aIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

1 aAlmi, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3519801691nas a2200169 4500008004100000245008700041210006900128260001800197300000600215490000600221520116500227100002101392700001901413700001701432700002101449856005101470 2016 en d00aA Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods0 aReduced Basis Approach for Modeling the Movement of Nuclear Reac bASMEc02/2016 a80 v23 aThis work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519201905nas a2200157 4500008004100000245012000041210006900161260002200230300000800252490000700260520128900267100002101556700002201577700002101599856012701620 2016 en d00aReduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries0 aReduced basis method and domain decomposition for elliptic probl bElsevierc01/2016 a4300 v713 aThe aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.1 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-method-and-domain-decomposition-elliptic-problems-networks-and-complex01365nas a2200145 4500008004100000245009200041210006900133300000900202490000700211520090200218100002301120700002101143700001601164856003901180 2016 eng d00aRenormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions0 aRenormalization for Autonomous Nearly Incompressible BV Vector F a1-330 v483 aGiven a bounded autonomous vector field $b \colon \mathbb{R}^d \to \mathbb{R}^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio's superposition principle [4].

1 aBianchini, Stefano1 aBonicatto, Paolo1 aGusev, N.A. uhttps://doi.org/10.1137/15M100738000431nas a2200133 4500008004100000245004100041210004000082260001000122100002700132700001700159700002200176700002000198856007900218 2016 en d00aSecond-order structured deformations0 aSecondorder structured deformations bSISSA1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttps://www.math.sissa.it/publication/second-order-structured-deformations00651nas a2200157 4500008004100000245009600041210006900137260005800206300001400264490000600278100001700284700001700301700002200318700002400340856012900364 2016 eng d00aShip Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model0 aShip Sinkage and Trim Predictions Based on a CAD Interfaced Full bInternational Society of Offshore and Polar Engineers a511–5180 v31 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/ship-sinkage-and-trim-predictions-based-cad-interfaced-fully-nonlinear-potential-model00428nas a2200097 4500008004100000245008000041210006900121260001000190100001900200856011100219 2016 en d00aSome results on quasistatic evolution problems for unidirectional processes0 aSome results on quasistatic evolution problems for unidirectiona bSISSA1 aCrismale, Vito uhttps://www.math.sissa.it/publication/some-results-quasistatic-evolution-problems-unidirectional-processes01439nas a2200121 4500008004100000245010500041210006900146260001000215520093000225653002301155100001801178856012101196 2016 en d00aSome results on the mathematical analysis of crack problems with forces applied on the fracture lips0 aSome results on the mathematical analysis of crack problems with bSISSA3 aThis thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.10aFracture mechanics1 aAlmi, Stefano uhttps://www.math.sissa.it/publication/some-results-mathematical-analysis-crack-problems-forces-applied-fracture-lips01230nas a2200157 4500008004100000245009000041210006900131260002100200300001000221490000700231520073600238100001700974700001800991700001301009856005001022 2016 eng d00aSpectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds0 aSpectral analysis and the AharonovBohm effect on certain almostR bTaylor & Francis a32-500 v413 aWe study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

1 aBoscain, Ugo1 aPrandi, Dario1 aSeri, M. uhttps://doi.org/10.1080/03605302.2015.109576601093nas a2200121 4500008004100000245010400041210006900145260001000214520065500224100002300879700001800902856005100920 2016 en d00aOn the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension0 astructure of Linftyentropy solutions to scalar conservation laws bSISSA3 aWe prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

1 aBianchini, Stefano1 aMarconi, Elio uhttp://urania.sissa.it/xmlui/handle/1963/3520900553nas a2200145 4500008004100000245008000041210006900121260002200190300001600212490000700228100002000235700002200255700001800277856011200295 2016 eng d00aSymmetry properties of some solutions to some semilinear elliptic equations0 aSymmetry properties of some solutions to some semilinear ellipti bClasse di Scienze a1209–12340 v161 aFarina, Alberto1 aMalchiodi, Andrea1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/symmetry-properties-some-solutions-some-semilinear-elliptic-equations00745nas a2200121 4500008004100000245005600041210005600097260001000153520032000163653003100483100001800514856009100532 2016 en d00aTwo explorations in Dynamical Systems and Mechanics0 aTwo explorations in Dynamical Systems and Mechanics bSISSA3 aThis thesis contains the work done by Paolo Gidoni during the doctorate programme in Matematical Analysis at SISSA, under the supervision of A. Fonda and A. DeSimone. The thesis is composed of two parts: "Avoiding cones conditions and higher dimensional twist" and "Directional friction in bio-inspired locomotion".10aPoincaré-Birkhoff Theorem1 aGidoni, Paolo uhttps://www.math.sissa.it/publication/two-explorations-dynamical-systems-and-mechanics00786nas a2200157 4500008004100000022001400041245009300055210006900148260000800217300000700225490000700232520030000239100001900539700002400558856004600582 2016 eng d a1432-083500aViscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model0 aViscous approximation of quasistatic evolutions for a coupled el cJan a170 v553 aEmploying the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

1 aCrismale, Vito1 aLazzaroni, Giuliano uhttps://doi.org/10.1007/s00526-015-0947-600469nas a2200109 4500008004100000245007600041210006900117100002500186700002100211700001700232856011000249 2016 eng d00aVolume geodesic distortion and Ricci curvature for Hamiltonian dynamics0 aVolume geodesic distortion and Ricci curvature for Hamiltonian d1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aPaoli, Elisa uhttps://www.math.sissa.it/publication/volume-geodesic-distortion-and-ricci-curvature-hamiltonian-dynamics00968nas a2200145 4500008004100000022001400041245003700055210003700092300000900129490000700138520055900145100002200704700002000726856007600746 2016 eng d a1078-094700aYoung towers for product systems0 aYoung towers for product systems a14650 v363 aWe show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, Hénon maps and partially hyperbolic systems.

1 aLuzzatto, Stefano1 aRuziboev, Marks uhttp://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c64201380nas a2200133 4500008004300000245007200043210006900115260001500184520093400199100001901133700001801152700002501170856005101195 2015 en_Ud 00aAnisotropic mean curvature on facets and relations with capillarity0 aAnisotropic mean curvature on facets and relations with capillar bde Gruyter3 aWe discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

1 aAmato, Stefano1 aTealdi, Lucia1 aBellettini, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3448101510nas a2200121 4500008004100000245009300041210006900134520100200203100001701205700001701222700002401239856012501263 2015 en d00aBenchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems0 aBenchmarking the Immersed Finite Element Method for FluidStructu3 aWe present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks.1 aSaswati, Roy1 aHeltai, Luca1 aCostanzo, Francesco uhttps://www.math.sissa.it/publication/benchmarking-immersed-finite-element-method-fluid-structure-interaction-problems-000903nas a2200133 4500008004100000245009000041210006900131260001000200520043700210100002100647700002400668700002700692856005000719 2015 en d00aA bridging mechanism in the homogenisation of brittle composites with soft inclusions0 abridging mechanism in the homogenisation of brittle composites w bSISSA3 aWe provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.1 aBarchiesi, Marco1 aLazzaroni, Giuliano1 aZeppieri, Caterina Ida uhttp://urania.sissa.it/xmlui/handle/1963/749201368nam a2200229 4500008004100000020002200041022001400063245008400077210006900161250000600230260002600236300000800262520053600270653003000806653002800836653004800864653004500912100002200957700002100979700002001000856011801020 2015 eng d a978-3-319-22469-5 a2191-820100aCertified Reduced Basis Methods for Parametrized Partial Differential Equations0 aCertified Reduced Basis Methods for Parametrized Partial Differe a1 aSwitzerlandbSpringer a1353 aThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

10aa posteriori error bounds10aempirical interpolation10aparametrized partial differential equations10areduced basis methods, greedy algorithms1 aHesthaven, Jan, S1 aRozza, Gianluigi1 aStamm, Benjamin uhttps://www.math.sissa.it/publication/certified-reduced-basis-methods-parametrized-partial-differential-equations01802nas a2200229 4500008004100000245010400041210006900145300001400214490000700228520107100235653001001306653001001316653002901326653001501355653002001370653002501390653001801415100003301433700002001466700002501486856006101511 2015 eng d00aA compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity0 acompatibleincompatible decomposition of symmetric tensors in Lp a5217-52300 v383 aIn this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

10a35J5810a35Q7410acompatibility conditions10aelasticity10aKorn inequality10astrain decomposition10asubclass74B051 aMaggiani, Giovanni, Battista1 aScala, Riccardo1 aVan Goethem, Nicolas uhttps://onlinelibrary.wiley.com/doi/abs/10.1002/mma.345001202nas a2200133 4500008004100000245004900041210004800090300001200138490000700150520084200157100001300999700001801012856003801030 2015 eng d00aComplexity of Control-Affine Motion Planning0 aComplexity of ControlAffine Motion Planning a816-8440 v533 aIn this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

1 aJean, F.1 aPrandi, Dario uhttps://doi.org/10.1137/13095079301209nas a2200121 4500008004300000245007700043210006900120520072500189100001900914700002500933700002200958856010700980 2015 en_Ud 00aConstrained BV functions on double coverings for Plateau's type problems0 aConstrained BV functions on double coverings for Plateaus type p3 aWe link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttps://www.math.sissa.it/publication/constrained-bv-functions-double-coverings-plateaus-type-problems00336nas a2200097 4500008004100000245004100041210004100082100002000123700002300143856007200166 2015 eng d00aConvergence rate of the Glimm scheme0 aConvergence rate of the Glimm scheme1 aModena, Stefano1 aBianchini, Stefano uhttps://www.math.sissa.it/publication/convergence-rate-glimm-scheme01185nas a2200121 4500008004100000245008500041210006900126260001000195520076800205100002100973700001800994856005101012 2015 en d00aConvex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets0 aConvex combinations of low eigenvalues Fraenkel asymmetries and bSISSA3 aWe consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure.1 aMazzoleni, Dario1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514001640nas a2200145 4500008004100000245007700041210006900118260001000187520116500197100002101362700002101383700002201404700001701426856005101443 2015 en d00aDeal2lkit: a Toolkit Library for High Performance Programming in deal.II0 aDeal2lkit a Toolkit Library for High Performance Programming in bSISSA3 aWe present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit.1 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttp://urania.sissa.it/xmlui/handle/1963/3500600605nas a2200181 4500008004100000245003700041210003000078520010700108100002300215700001800238700001700256700001700273700002400290700002000314700002000334700001800354856005100372 2015 en d00aThe deal.II Library, Version 8.20 adealII Library Version 823 aThis paper provides an overview of the new features of the finite element library deal.II version 8.21 aBangerth, Wolfgang1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, Bruno1 aYoung, T., D. uhttp://urania.sissa.it/xmlui/handle/1963/3446400709nas a2200133 4500008004100000245007500041210007000116260002100186300001200207490000700219520027900226100002000505856005000525 2015 eng d00aDecay of correlations for invertible maps with non-Hölder observables0 aDecay of correlations for invertible maps with nonHölder observa bTaylor & Francis a341-3520 v303 aAn invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain Hénon maps and Solenoid maps with intermittency.

1 aRuziboev, Marks uhttps://doi.org/10.1080/14689367.2015.104681601384nas a2200133 4500008004100000245008700041210006900128260001000197520092000207100002701127700002301154700002201177856005101199 2015 en d00aDynamics of screw dislocations: a generalised minimising-movements scheme approach0 aDynamics of screw dislocations a generalised minimisingmovements bSISSA3 aThe gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric.1 aBonaschi, Giovanni, A.1 aVan Meurs, Patrick1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3449501187nas a2200193 4500008004100000022001400041245006700055210006700122300001200189490000800201520057400209653002100783653002900804653002400833653002900857653001600886100002000902856007100922 2015 eng d a0022-247X00aExistence and multiplicity result for the singular Toda system0 aExistence and multiplicity result for the singular Toda system a49 - 850 v4243 aWe consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

10aExistence result10aLiouville-type equations10aMultiplicity result10aPDEs on compact surfaces10aToda system1 aBattaglia, Luca uhttp://www.sciencedirect.com/science/article/pii/S0022247X1401019101267nas a2200121 4500008004100000245009800041210006900139520082000208100002101028700002601049700001901075856005101094 2015 en d00aExistence for constrained dynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for constrained dynamic Griffith fracture with a weak 3 aThere are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/3504501084nas a2200121 4500008004100000245013700041210006900178260002300247520059900270100002300869700001900892856005100911 2015 en d00aExistence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems0 aExistence of positive solutions in the superlinear case via coin bKhayyam Publishing3 aWe prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://projecteuclid.org/euclid.ade/143506451801364nas a2200181 4500008004100000022001400041245009900055210006900154300000800223490000900231520072700240653002700967653002300994653004101017653002501058100002301083856007601106 2015 eng d a0133-018900aExistence of positive solutions of a superlinear boundary value problem with indefinite weight0 aExistence of positive solutions of a superlinear boundary value a4360 v20153 aWe deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

10aboundary value problem10aindefinite weight10aPositive solution; existence result.10asuperlinear equation1 aFeltrin, Guglielmo uhttp://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc4847802602252nas a2200145 4500008004100000245009600041210006900137260001000206520175300216100002701969700001701996700002202013700002002035856005102055 2015 en d00aExplicit formulas for relaxed disarrangement densities arising from structured deformations0 aExplicit formulas for relaxed disarrangement densities arising f bSISSA3 aStructured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements.1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttp://urania.sissa.it/xmlui/handle/1963/3449201813nas a2200169 4500008004100000245015600041210006900197520118400266100001701450700002001467700002001487700002001507700002201527700002101549700002201570856005101592 2015 en d00aFast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization0 aFast simulations of patientspecific haemodynamics of coronary ar3 aIn this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.1 aBallarin, F.1 aFaggiano, Elena1 aIppolito, Sonia1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aScrofani, Roberto uhttp://urania.sissa.it/xmlui/handle/1963/3462301899nas a2200133 4500008004300000245010100043210006900144520142800213100002101641700001701662700001701679700001801696856005101714 2015 en_Ud 00aFEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows0 aFEM SUPG stabilisation of mixed isoparametric BEMs application t3 aIn finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

1 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca1 aFormaggia, L. uhttp://urania.sissa.it/xmlui/handle/1963/3446601381nas a2200205 4500008004100000022001400041245007100055210006900126300001400195490000800209520074400217653001900961653002200980653002401002100002001026700002001046700002201066700001601088856007101104 2015 eng d a0001-870800aA general existence result for the Toda system on compact surfaces0 ageneral existence result for the Toda system on compact surfaces a937 - 9790 v2853 aIn this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

10aGeometric PDEs10aMin–max schemes10aVariational methods1 aBattaglia, Luca1 aJevnikar, Aleks1 aMalchiodi, Andrea1 aRuiz, David uhttp://www.sciencedirect.com/science/article/pii/S000187081500307201188nas a2200157 4500008004100000245005800041210005700099260003700156300001600193490000700209520065100216100002500867700002400892700002100916856009300937 2015 eng d00aGeodesics and horizontal-path spaces in Carnot groups0 aGeodesics and horizontalpath spaces in Carnot groups bMathematical Sciences Publishers a1569–16300 v193 aWe study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families (compact critical manifolds) with controlled topology. We study the asymptotic of the number of critical manifolds as the energy grows. The topology of the horizontal-path space is also investigated, and we find asymptotic results for the total Betti number of the sublevels of the energy as it goes to infinity. We interpret these results as local invariants of the sub-Riemannian structure.

1 aAgrachev, Andrei, A.1 aGentile, Alessandro1 aLerario, Antonio uhttps://www.math.sissa.it/publication/geodesics-and-horizontal-path-spaces-carnot-groups01836nas a2200121 4500008004100000245006000041210005800101260001000159520139100169653003901560100002001599856009501619 2015 en d00aGibbs-Markov-Young Structures and Decay of Correlations0 aGibbsMarkovYoung Structures and Decay of Correlations bSISSA3 aIn this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity.10aDecay of Correlations, GMY-towers1 aRuziboev, Marks uhttps://www.math.sissa.it/publication/gibbs-markov-young-structures-and-decay-correlations00685nas a2200121 4500008004100000245007200041210006900113260001000182520028100192100001700473700002200490856005100512 2015 en d00aHomogenization problems in the Calculus of Variations: an overview0 aHomogenization problems in the Calculus of Variations an overvie bSISSA3 aIn this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.1 aMatias, Jose1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3445503404nas a2200121 4500008004100000245013600041210006900177260001000246520292200256653003303178100002003211856005103231 2015 en d00aInteraction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws0 aInteraction functionals Glimm approximations and Lagrangian stru bSISSA3 aThis thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate.10aHyperbolic conservation laws1 aModena, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3454201765nas a2200217 4500008004100000022001400041245005300055210005300108300001400161490000700175520110000182653002201282653002501304653002801329653003001357653002701387100002201414700001801436700002201454856007101476 2015 eng d a0022-509600aLiquid crystal elastomer strips as soft crawlers0 aLiquid crystal elastomer strips as soft crawlers a254 - 2720 v843 aIn this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

10aCrawling motility10aDirectional surfaces10aFrictional interactions10aLiquid crystal elastomers10aSoft biomimetic robots1 aDeSimone, Antonio1 aGidoni, Paolo1 aNoselli, Giovanni uhttp://www.sciencedirect.com/science/article/pii/S002250961530043000496nas a2200109 4500008004100000245010000041210006900141260001000210653001300220100002600233856012700259 2015 en d00aMathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming0 aMathematical Models of Locomotion Legged Crawling Snakelike Moti bSISSA10aMotility1 aCicconofri, Giancarlo uhttps://www.math.sissa.it/publication/mathematical-models-locomotion-legged-crawling-snake-motility-and-flagellar-swimming01569nas a2200181 4500008004100000022001400041245006000055210005800115300001400173490000700187520100500194653001901199653002201218653002801240100002601268700002201294856007101316 2015 eng d a0020-746200aMotility of a model bristle-bot: A theoretical analysis0 aMotility of a model bristlebot A theoretical analysis a233 - 2390 v763 aBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

10aBristle-robots10aCrawling motility10aFrictional interactions1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002074621500002501516nas a2200133 4500008004100000245012100041210006900162260001300231520102900244100002101273700001501294700002201309856005101331 2015 en d00aMultilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations0 aMultilevel and weighted reduced basis method for stochastic opti bSpringer3 aIn this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems.1 aRozza, Gianluigi1 aChen, Peng1 aQuarteroni, Alfio uhttp://urania.sissa.it/xmlui/handle/1963/3449101194nas a2200121 4500008004100000245008200041210006900123260001300192520077400205100002300979700001901002856005101021 2015 en d00aMultiple positive solutions for a superlinear problem: a topological approach0 aMultiple positive solutions for a superlinear problem a topologi bElsevier3 aWe study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s→0^+ and above λ_1 as s→+∞. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u'' + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large.

1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3514700775nas a2200133 4500008004100000245006500041210006300106300001200169490000700181520032000188100002000508700002200528856009100550 2015 en d00aA note on compactness properties of the singular Toda system0 anote on compactness properties of the singular Toda system a299-3070 v263 aIn this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

1 aBattaglia, Luca1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/note-compactness-properties-singular-toda-system00769nas a2200109 4500008004100000245006200041210006100103260001600164520036100180100002200541856009600563 2015 en d00aOnofri-Type Inequalities for Singular Liouville Equations0 aOnofriType Inequalities for Singular Liouville Equations bSpringer US3 aWe study the blow-up behavior of minimizing sequences for the singular Moser–Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/onofri-type-inequalities-singular-liouville-equations00827nas a2200193 4500008004100000022001400041245005300055210005100108300001200159490000800171520026300179653002100442653001500463653002000478653002400498100002200522700001800544856007100562 2015 eng d a0362-546X00aA permanence theorem for local dynamical systems0 apermanence theorem for local dynamical systems a73 - 810 v1213 aWe provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka–Volterra predator–prey model with intraspecific competition.

10aLotka–Volterra10apermanence10aPredator–prey10aUniform persistence1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S0362546X1400333200719nas a2200217 4500008004100000245009200041210006900133260003300202100002200235700002400257700001600281700002300297700001500320700001400335700002200349700002600371700002100397700001300418700001900431856005100450 2015 en d00aThe phototransduction machinery in the rod outer segment has a strong efficacy gradient0 aphototransduction machinery in the rod outer segment has a stron bNational Academy of Sciences1 aMazzolini, Monica1 aFacchetti, Giuseppe1 aAndolfi, L.1 aZaccaria, Proietti1 aTuccio, S.1 aTreud, J.1 aAltafini, Claudio1 aDi Fabrizio, Enzo, M.1 aLazzarino, Marco1 aRapp, G.1 aTorre, Vincent uhttp://urania.sissa.it/xmlui/handle/1963/3515701121nas a2200133 4500008004100000245007800041210006900119300001600188490000800204520062100212100002300833700002000856856011100876 2015 eng d00aQuadratic Interaction Functional for General Systems of Conservation Laws0 aQuadratic Interaction Functional for General Systems of Conserva a1075–11520 v3383 aFor the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

1 aBianchini, Stefano1 aModena, Stefano uhttps://www.math.sissa.it/publication/quadratic-interaction-functional-general-systems-conservation-laws-002042nas a2200217 4500008004100000022001400041245010200055210006900157490003500226520122900261653002501490653002101515653002501536653002701561653002501588653001601613100002201629700002101651700002201672856013001694 2015 eng d a1019-716800aReduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system0 aReduced basis approximation and aposteriori error estimation for0 vspecial issue for MoRePaS 20123 aThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

10aDomain decomposition10aError estimation10aNon-coercive problem10aPorous medium equation10aReduced basis method10aStokes flow1 aMartini, Immanuel1 aRozza, Gianluigi1 aHaasdonk, Bernard uhttps://www.math.sissa.it/publication/reduced-basis-approximation-and-posteriori-error-estimation-coupled-stokes-darcy-system01235nas a2200145 4500008004100000245010300041210006900144300001400213490000700227520066400234100002000898700002000918700002100938856013000959 2015 eng d00aReduced basis approximation of parametrized optimal flow control problems for the Stokes equations0 aReduced basis approximation of parametrized optimal flow control a319–3360 v693 aThis paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

1 aNegri, Federico1 aManzoni, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-parametrized-optimal-flow-control-problems-stokes-equations02449nas a2200121 4500008004100000245012900041210006900170520189900239100002002138700002502158700001702183856012702200 2015 en d00aReduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils0 aReduced Basis Isogeometric Methods RBIGA for the realtime simula3 aWe present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.1 aManzoni, Andrea1 aSalmoiraghi, Filippo1 aHeltai, Luca uhttps://www.math.sissa.it/publication/reduced-basis-isogeometric-methods-rb-iga-real-time-simulation-potential-flows-about01509nas a2200121 4500008004100000245012400041210006900165260001000234520098200244653002001226100001801246856012301264 2015 en d00aThe relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces.0 arelaxed area of maps from the plane to the plane with a line dis bSISSA3 aIn this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided.10aArea functional1 aTealdi, Lucia uhttps://www.math.sissa.it/publication/relaxed-area-maps-plane-plane-line-discontinuity-and-role-semicartesian-surfaces00953nas a2200121 4500008004100000245009700041210006900138520050800207100001800715700002500733700002200758856005100780 2015 en d00aResults on the minimization of the Dirichlet functional among semicartesian parametrizations0 aResults on the minimization of the Dirichlet functional among se3 aWe start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

1 aTealdi, Lucia1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://urania.sissa.it/xmlui/handle/1963/3448801420nas a2200133 4500008004100000245009400041210006900135260001000204520094900214100002401163700002401187700002501211856005001236 2015 en d00aRigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires0 aRigidity of threedimensional lattices and dimension reduction in bSISSA3 aIn the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large1 aLazzaroni, Giuliano1 aPalombaro, Mariapia1 aSchlomerkemper, Anja uhttp://urania.sissa.it/xmlui/handle/1963/749401475nas a2200121 4500008004100000245011300041210006900154520101400223100001801237700002501255700002201280856005101302 2015 en d00aSemicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity0 aSemicartesian surfaces and the relaxed area of maps from the pla3 aWe address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

1 aTealdi, Lucia1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://urania.sissa.it/xmlui/handle/1963/3448301019nas a2200121 4500008004100000245008500041210006900126260001000195520053500205653002000740100002200760856011500782 2015 en d00aSharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.0 aSharp Inequalities and Blowup Analysis for Singular MoserTruding bSISSA3 aWe investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.10aMoser-Trudinger1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/sharp-inequalities-and-blow-analysis-singular-moser-trudinger-embeddings00685nas a2200097 4500008004100000245008200041210006900123520032200192100002200514856005100536 2015 en d00aSingular Liouville Equations on S^2: Sharp Inequalities and Existence Results0 aSingular Liouville Equations on S2 Sharp Inequalities and Existe3 aWe prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

1 aMancini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3448900981nas a2200121 4500008004100000245008300041210006900124260001000193520048800203653003100691100001900722856011800741 2015 en d00aSome results on anisotropic mean curvature and other phase-transition problems0 aSome results on anisotropic mean curvature and other phasetransi bSISSA3 aThe present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions.10aAnisotropic mean curvature1 aAmato, Stefano uhttps://www.math.sissa.it/publication/some-results-anisotropic-mean-curvature-and-other-phase-transition-problems02147nas a2200157 4500008004100000245008700041210006900128260001000197300001200207490000700219520161800226653002801844100002001872700002501892856007201917 2015 en d00aStable regular critical points of the Mumford-Shah functional are local minimizers0 aStable regular critical points of the MumfordShah functional are bSISSA a533-5700 v323 aIn this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

-topology. A global minimality result in small tubular neighborhoods of the discontinuity set is also established.

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.005400682nas a2200145 4500008004100000245009900041210006900140260001000209520018600219100001700405700002000422700002200442700002100464856005100485 2015 en d00aSupremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations0 aSupremizer stabilization of PODGalerkin approximation of paramet bWiley3 aIn this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number.1 aBallarin, F.1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3470101401nas a2200121 4500008004100000245007200041210006900113260001300182520098700195100002401182700002201206856005101228 2015 en d00aThree-sphere low-Reynolds-number swimmer with a passive elastic arm0 aThreesphere lowReynoldsnumber swimmer with a passive elastic arm bSpringer3 aOne of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.1 aMontino, Alessandro1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3453000591nas a2200145 4500008004100000245009500041210006900136260003700205300001600242490000600258100002000264700001800284700002200302856012100324 2015 eng d00aA topological join construction and the Toda system on compact surfaces of arbitrary genus0 atopological join construction and the Toda system on compact sur bMathematical Sciences Publishers a1963–20270 v81 aJevnikar, Aleks1 aKallel, Sadok1 aMalchiodi, Andrea uhttps://www.math.sissa.it/publication/topological-join-construction-and-toda-system-compact-surfaces-arbitrary-genus00409nas a2200109 4500008004100000245005900041210005900100260001000159653001600169100002000185856009400205 2015 en d00aVariational aspects of Liouville equations and systems0 aVariational aspects of Liouville equations and systems bSISSA10aToda system1 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/variational-aspects-liouville-equations-and-systems00779nas a2200121 4500008004100000245005400041210005400095260001000149520029900159653009000458100002000548856008900568 2015 en d00aVariational aspects of singular Liouville systems0 aVariational aspects of singular Liouville systems bSISSA3 aI studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.10aVariational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods1 aBattaglia, Luca uhttps://www.math.sissa.it/publication/variational-aspects-singular-liouville-systems02046nas a2200121 4500008004100000245006500041210006500106260001000171520159900181653002801780100001701808856009901825 2015 en d00aVolume variation and heat kernel for affine control problems0 aVolume variation and heat kernel for affine control problems bSISSA3 aIn this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak Hörmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume.10aHeat kernel asymptotics1 aPaoli, Elisa uhttps://www.math.sissa.it/publication/volume-variation-and-heat-kernel-affine-control-problems01514nas a2200109 4500008004100000245013600041210006900177520106400246100002101310700002201331856005101353 2015 en d00aThe wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data0 awave equation on domains with cracks growing on a prescribed pat3 aGiven a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks.1 aDal Maso, Gianni1 aLucardesi, Ilaria uhttp://urania.sissa.it/xmlui/handle/1963/3462901482nas a2200133 4500008004100000245013000041210007100171260001300242520098000255100002401235700001701259700002101276856005101297 2014 en d00aAn Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds0 aAbstract Nash–Moser Theorem and QuasiPeriodic Solutions for NLW bSpringer3 aWe prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups.1 aBerti, Massimiliano1 aCorsi, Livia1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3465101483nas a2200121 4500008004100000245005900041210005900100260005900159520105100218100002201269700001901291856005101310 2014 en d00aAchieving unanimous opinions in signed social networks0 aAchieving unanimous opinions in signed social networks bInstitute of Electrical and Electronics Engineers Inc.3 aBeing able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n.1 aAltafini, Claudio1 aLini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3493501081nas a2200145 4500008004100000245007400041210006900115260003100184520057600215100002700791700002100818700002300839700002200862856005100884 2014 en d00aBuckling dynamics of a solvent-stimulated stretched elastomeric sheet0 aBuckling dynamics of a solventstimulated stretched elastomeric s bRoyal Society of Chemistry3 aWhen stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet.1 aLucantonio, Alessandro1 aRoché, Matthieu1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3496702162nas a2200133 4500008004100000245009400041210006900135260001300204520170200217100001501919700002201934700002101956856005101977 2014 en d00aComparison between reduced basis and stochastic collocation methods for elliptic problems0 aComparison between reduced basis and stochastic collocation meth bSpringer3 aThe stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3472701580nas a2200157 4500008004100000245009300041210006900134260002800203520103900231100001901270700001901289700002101308700002001329700002201349856005101371 2014 en d00aConformal invariants from nodal sets. I. negative eigenvalues and curvature prescription0 aConformal invariants from nodal sets I negative eigenvalues and bOxford University Press3 aIn this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.1 aGover, Rod, R.1 aCanzani, Yaiza1 aJakobson, Dmitry1 aPonge, Raphaël1 aMalchiodi, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3512800720nas a2200109 4500008004100000245007700041210006900118260003100187520031700218100002400535856005100559 2014 en d00aA correction and an extension of Stampacchia's work on the geometric BVP0 acorrection and an extension of Stampacchias work on the geometri bAdvanced Nonlinear Studies3 aG. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results.1 aVidossich, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3502301733nas a2200217 4500008004100000022001400041245003700055210003700092300001200129490000700141520111900148653002901267653001901296653002201315653002501337653002001362100001801382700002201400700002201422856007101444 2014 eng d a0020-746200aCrawling on directional surfaces0 aCrawling on directional surfaces a65 - 730 v613 aIn this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

10aBio-mimetic micro-robots10aCell migration10aCrawling motility10aDirectional surfaces10aSelf-propulsion1 aGidoni, Paolo1 aNoselli, Giovanni1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002074621400021301111nas a2200121 4500008004100000245006400041210006300105260003400168520070800202100002200910700002100932856003600953 2014 en d00aCritical points of the Moser-Trudinger functional on a disk0 aCritical points of the MoserTrudinger functional on a disk bEuropean Mathematical Society3 aOn the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/656001482nas a2200157 4500008004100000245004800041210004700089260001300136300001400149490000700163520105700170100001801227700001701245700001301262856004901275 2014 en d00aCurvature-adapted remeshing of CAD surfaces0 aCurvatureadapted remeshing of CAD surfaces bElsevier a253–2650 v823 aA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

1 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1016/j.proeng.2014.10.38800403nas a2200109 4500008004100000245007400041210006900115260001000184653002700194100002200221856005000243 2014 en d00aThe decomposition of optimal transportation problems with convex cost0 adecomposition of optimal transportation problems with convex cos bSISSA10aOptimal Transportation1 aBardelloni, Mauro uhttp://urania.sissa.it/xmlui/handle/1963/747500387nas a2200109 4500008004300000245007400043210006900117260001000186100002300196700002200219856003600241 2014 en_Ud 00aThe decomposition of optimal transportation problems with convex cost0 adecomposition of optimal transportation problems with convex cos bSISSA1 aBianchini, Stefano1 aBardelloni, Mauro uhttp://hdl.handle.net/1963/743300921nas a2200109 4500008004100000245010000041210006900141260001300210520051500223100002200738856005100760 2014 en d00aA density result for GSBD and its application to the approximation of brittle fracture energies0 adensity result for GSBD and its application to the approximation bSpringer3 aWe present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

1 aIurlano, Flaviana uhttp://urania.sissa.it/xmlui/handle/1963/3464701213nas a2200145 4500008004100000245011200041210006900153260001300222520069800235653001900933100002200952700002000974700002200994856005101016 2014 en d00aDiscrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost0 aDiscrete onedimensional crawlers on viscous substrates achievabl bElsevier3 aWe study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility.10aCell migration1 aNoselli, Giovanni1 aTatone, Amabile1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3444900376nas a2200097 4500008004100000245008700041210006900128100002000197700002500217856003600242 2014 eng d00aDislocations at the continuum scale: functional setting and variational properties0 aDislocations at the continuum scale functional setting and varia1 aScala, Riccardo1 aVan Goethem, Nicolas uhttp://cvgmt.sns.it/paper/2294/00316nas a2200121 4500008004100000245001400041210001400055260001300069100002000082700002100102700002000123856005100143 2014 en d00aEditorial0 aEditorial bSpringer1 aCiliberto, Ciro1 aDal Maso, Gianni1 aVetro, Pasquale uhttp://urania.sissa.it/xmlui/handle/1963/3471201955nas a2200145 4500008004100000245009100041210006900132260006400201520139800265100002701663700002201690700002101712700002501733856005101758 2014 en d00aAn effective model for nematic liquid crystal composites with ferromagnetic inclusions0 aeffective model for nematic liquid crystal composites with ferro bSociety for Industrial and Applied Mathematics Publications3 aMolecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.1 aCalderer, Maria, Carme1 aDeSimone, Antonio1 aGolovaty, Dmitry1 aPanchenko, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3494001997nas a2200109 4500008004100000245014300041210006900184520134000253653014901593100002001742856012501762 2014 en d00aAn efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows0 aefficient computational framework for reduced basis approximatio3 aWe present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy & Patera, Quarteroni & Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework.10aReduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability1 aManzoni, Andrea uhttps://www.math.sissa.it/publication/efficient-computational-framework-reduced-basis-approximation-and-posteriori-error00833nas a2200121 4500008004100000245010200041210006900143260003900212520036100251100002300612700002500635856005100660 2014 en d00aExistence and uniqueness of the gradient flow of the Entropy in the space of probability measures0 aExistence and uniqueness of the gradient flow of the Entropy in bEUT Edizioni Universita di Trieste3 aAfter a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below.1 aBianchini, Stefano1 aDabrowski, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3469303135nas a2200205 4500008004100000022001400041245009400055210006900149300001400218490000700232520242200239653004902661653002302710653002902733653002802762653002402790100002002814700002402834856007102858 2014 eng d a0294-144900aExistence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds0 aExistence of immersed spheres minimizing curvature functionals i a707 - 7240 v313 aWe study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

10aDirect methods in the calculus of variations10aGeneral Relativity10aGeometric measure theory10asecond fundamental form10aWillmore functional1 aMondino, Andrea1 aSchygulla, Johannes uhttp://www.sciencedirect.com/science/article/pii/S029414491300085101126nas a2200169 4500008004100000022001400041245009000055210006900145260000800214300001400222490000800236520060400244100001800848700002000866700002400886856004600910 2014 eng d a1432-180700aExistence of immersed spheres minimizing curvature functionals in compact 3-manifolds0 aExistence of immersed spheres minimizing curvature functionals i cJun a379–4250 v3593 aWe study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

1 aKuwert, Ernst1 aMondino, Andrea1 aSchygulla, Johannes uhttps://doi.org/10.1007/s00208-013-1005-301095nas a2200145 4500008004100000022001400041245011100055210006900166260000800235300001400243490000700257520061900264100002000883856004600903 2014 eng d a1432-083500aExistence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds0 aExistence of integral mvarifolds minimizing int Ap and int Hp pm cJan a431–4700 v493 aWe prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int |H|^p$to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

1 aMondino, Andrea uhttps://doi.org/10.1007/s00526-012-0588-y01202nas a2200145 4500008004100000245010600041210006900147260001000216520062900226653002300855100001700878700001700895700002200912856012200934 2014 en d00aA fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures0 afully nonlinear potential model for ship hydrodynamics directly bSISSA3 aWe present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.10aship hydrodynamics1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/fully-nonlinear-potential-model-ship-hydrodynamics-directly-interfaced-cad-data01604nas a2200133 4500008004100000245010100041210006900142260001900211490000800230520099000238653009201228100002101320856012901341 2014 eng d00aFundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications0 aFundamentals of Reduced Basis Method for problems governed by pa aWienbSpringer0 v5543 aIn this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

10areduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/fundamentals-reduced-basis-method-problems-governed-parametrized-pdes-and-applications01517nas a2200121 4500008004100000245010200041210006900143260001000212520108600222653001901308100001801327856005001345 2014 en d00aGeometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution0 aGeometry and analysis of controlaffine systems motion planning h bSISSA3 aThis thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation.10acontrol theory1 aPrandi, Dario uhttp://urania.sissa.it/xmlui/handle/1963/747401332nas a2200121 4500008004100000245014300041210006900184260002100253520085000274100002301124700001201147856005101159 2014 en d00aGlobal Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension0 aGlobal Structure of Admissible BV Solutions to Piecewise Genuine bTaylor & Francis3 aThe paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

1 aBianchini, Stefano1 aYu, Lei uhttp://urania.sissa.it/xmlui/handle/1963/3469400468nas a2200121 4500008004100000245007300041210007000114260001700184300001600201490000700217100001800224856010400242 2014 eng d00aHölder equivalence of the value function for control-affine systems0 aHölder equivalence of the value function for controlaffine syste bEDP Sciences a1224–12480 v201 aPrandi, Dario uhttps://www.math.sissa.it/publication/h%C3%B6lder-equivalence-value-function-control-affine-systems00862nas a2200133 4500008004100000245008700041210006900128260001000197520041000207100001700617700002200634700002200656856005000678 2014 en d00aHomogenization of functional with linear growth in the context of A-quasiconvexity0 aHomogenization of functional with linear growth in the context o bSISSA3 aThis work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.1 aMatias, Jose1 aMorandotti, Marco1 aSantos, Pedro, M. uhttp://urania.sissa.it/xmlui/handle/1963/743600620nas a2200121 4500008004100000245006500041210006500106260001300171520022300184100001800407700002200425856005100447 2014 en d00aHomology computation for a class of contact structures on T30 aHomology computation for a class of contact structures on T3 bSpringer3 aWe consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability.1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3464900376nas a2200097 4500008004100000245008500041210006900126260001000195100002300205856005000228 2014 en d00aKAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations0 aKAM for quasilinear and fully nonlinear perturbations of Airy an bSISSA1 aMontalto, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/747600573nas a2200157 4500008004100000245002900041210002800070260001300098300001200111490000800123520017300131100001300304700002400317700002300341856005100364 2014 en d00aKAM for quasi-linear KdV0 aKAM for quasilinear KdV bElsevier a603-6070 v3523 aWe prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/3506700608nas a2200157 4500008004100000245004900041210004900090260001300139300001200152490000800164520016500172100002400337700001700361700002100378856005100399 2014 en d00aKAM for Reversible Derivative Wave Equations0 aKAM for Reversible Derivative Wave Equations bSpringer a905-9550 v2123 aWe prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3464601118nas a2200145 4500008004100000245013100041210006900172260001000241520052100251653010200772100002100874700002200895700001900917856003600936 2014 en d00aLaplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length0 aLaplace equation in a domain with a rectilinear crack higher ord bSISSA3 aWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

10acracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttp://hdl.handle.net/1963/727100830nas a2200121 4500008004100000245005800041210005800099260003100157520043000188100001700618700002200635856005100657 2014 en d00aLecture notes on gradient flows and optimal transport0 aLecture notes on gradient flows and optimal transport bCambridge University Press3 aWe present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/3509300818nas a2200109 4500008004100000245005900041210005900100260003000159520044600189100002200635856005100657 2014 en d00aLegendre duality on hypersurfaces in Kähler manifolds0 aLegendre duality on hypersurfaces in Kähler manifolds bWalter de Gruyter and Co.3 aWe give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional Kähler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3477701077nas a2200133 4500008004100000245007900041210007000120260001700190300001400207490000700221520058200228100001800810856011500828 2014 eng d00aLinearized plastic plate models as Γ-limits of 3D finite elastoplasticity0 aLinearized plastic plate models as Γlimits of 3D finite elastopl bEDP Sciences a725–7470 v203 aThe subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/linearized-plastic-plate-models-%CE%B3-limits-3d-finite-elastoplasticity00762nas a2200121 4500008004100000245010000041210006900141260001300210520031900223100002200542700002500564856005100589 2014 en d00aLipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups0 aLipschitz continuous viscosity solutions for a class of fully no bSpringer3 aIn this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.1 aMartino, Vittorio1 aMontanari, Annamaria uhttp://urania.sissa.it/xmlui/handle/1963/3469901060nas a2200157 4500008004100000245008400041210006900125260002200194300001400216490000700230520054900237653003500786100002000821700002500841856003600866 2014 en d00aLocal and global minimality results for a nonlocal isoperimetric problem on R^N0 aLocal and global minimality results for a nonlocal isoperimetric bSIAM Publications a2310-23490 v463 aWe consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

10aNonlocal isoperimetric problem1 aBonacini, Marco1 aCristoferi, Riccardo uhttp://hdl.handle.net/1963/698400578nas a2200145 4500008004100000245004600041210004500087260001000132520011500142653003000257100002200287700001700309700002500326856008100351 2014 en d00aLocal behavior of fractional p-minimizers0 aLocal behavior of fractional pminimizers bSISSA3 aWe extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

10afractional Sobolev spaces1 aDi Castro, Agnese1 aKuusi, Tuomo1 aPalatucci, Giampiero uhttps://www.math.sissa.it/publication/local-behavior-fractional-p-minimizers00800nas a2200133 4500008004100000245006400041210005600105260003400161520035400195100002200549700002300571700002100594856005100615 2014 en d00aOn the Lp-differentiability of certain classes of functions0 aLpdifferentiability of certain classes of functions bEuropean Mathematical Society3 aWe prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469500683nas a2200109 4500008004100000245005300041210005300094260001300147520034200160100002000502856005100522 2014 en d00aMaximal generalized solution of eikonal equation0 aMaximal generalized solution of eikonal equation bElsevier3 aWe study the Dirichlet problem for the eikonal equation: 1/2 |∇u(x)|^2-a(x)=0 in Ω u(x)=(x) on Ω, without continuity assumptions on the map a(.). We find a class of maps a(.) contained in the space L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.1 aZagatti, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3464201687nas a2200145 4500008004100000245005600041210005400097260001000151300001100161490000700172520119700179653007701376100001801453856007001471 2014 en d00aA model for crack growth with branching and kinking0 amodel for crack growth with branching and kinking bSISSA a63-1100 v893 aWe study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith's theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

10aquasistatic crack evolution, branching, kinking, Griffith\\\'s criterion1 aRacca, Simone uhttps://content.iospress.com/articles/asymptotic-analysis/asy123301650nas a2200145 4500008004100000245007300041210006900114260001300183520112000196100001801316700002001334700002201354700002101376856010701397 2014 en d00aModel Order Reduction in Fluid Dynamics: Challenges and Perspectives0 aModel Order Reduction in Fluid Dynamics Challenges and Perspecti bSpringer3 aThis chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/model-order-reduction-fluid-dynamics-challenges-and-perspectives00433nas a2200121 4500008004100000245006200041210005900103300001100162490000600173100002000179700002200199856009000221 2014 eng d00aA Moser-Trudinger inequality for the singular Toda system0 aMoserTrudinger inequality for the singular Toda system a1–230 v91 aBattaglia, Luca1 aMalchiodi, Andrea uhttps://www.math.sissa.it/publication/moser-trudinger-inequality-singular-toda-system00423nas a2200133 4500008004100000245005600041210005500097260001300152653002200165100001800187700002100205700002700226856003600253 2014 en d00aNew results on Gamma-limits of integral functionals0 aNew results on Gammalimits of integral functionals bElsevier10aGamma-convergence1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/588002051nas a2200145 4500008004100000245007600041210006900117260001300186520158600199653002601785100001701811700001901828700002201847856003601869 2014 en d00aNonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D0 aNonsingular Isogeometric Boundary Element Method for Stokes Flow bElsevier3 aIsogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.10aIsogeometric Analysis1 aHeltai, Luca1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/632600713nas a2200145 4500008004100000245005900041210005400100260003200154300001200186490000700198520028400205100002300489700002000512856003500532 2014 en d00aOn a quadratic functional for scalar conservation laws0 aquadratic functional for scalar conservation laws bWorld Scientific Publishing a355-4350 v113 aWe prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.

1 aBianchini, Stefano1 aModena, Stefano uhttp://arxiv.org/abs/1311.292900441nas a2200121 4500008004100000245008400041210006900125300001200194490000600206100002300212700002000235856006400255 2014 eng d00aQuadratic interaction functional for systems of conservation laws: a case study0 aQuadratic interaction functional for systems of conservation law a487-5460 v91 aBianchini, Stefano1 aModena, Stefano uhttps://w3.math.sinica.edu.tw/bulletin_ns/20143/2014308.pdf00712nas a2200157 4500008004100000245005200041210005100093260001300144300001200157490000800169520027400177100001800451700002100469700001900490856004500509 2014 en d00aQuasi-static crack growth in hydraulic fracture0 aQuasistatic crack growth in hydraulic fracture bElsevier a301-3180 v1093 aWe present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1735000819nas a2200157 4500008004100000022001400041245007800055210006900133260000800202300001400210490000700224520034300231100002100574700002000595856004600615 2014 eng d a1572-922200aQuasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes0 aQuasistatic Evolution in Perfect Plasticity as Limit of Dynamic cDec a915–9540 v263 aWe introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

1 aDal Maso, Gianni1 aScala, Riccardo uhttps://doi.org/10.1007/s10884-014-9409-701155nas a2200121 4500008004100000245010200041210006900143300001400212490000700226520073600233100001800969856004600987 2014 eng d00aQuasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity0 aQuasistatic evolution models for thin plates arising as low ener a2085-21530 v243 aIn this paper we deduce by $\Gamma$-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we study the case where the scaling factor of the elasto-plastic energy is of order $\epsilon^{2 \alpha -2}$, with $\alpha\geq 3$. These scalings of the energy lead, in the absence of plastic dissipation, to the Von Kármán and linearized Von Kármán functionals for thin plates. We show that solutions to the three-dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on $\alpha$.

1 aDavoli, Elisa uhttps://doi.org/10.1142/S021820251450016X01353nas a2200145 4500008004100000245007400041210006900115260001000184520088100194100002401075700002001099700001901119700001901138856005001157 2014 en d00aRate-independent damage in thermo-viscoelastic materials with inertia0 aRateindependent damage in thermoviscoelastic materials with iner bSISSA3 aWe present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/744400566nas a2200133 4500008004100000245010000041210006900141300001000210100002100220700002200241700002100263700002100284856012700305 2014 eng d00aReduced basis method for the Stokes equations in decomposable domains using greedy optimization0 aReduced basis method for the Stokes equations in decomposable do a1–71 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aVolkwein, Stefan uhttps://www.math.sissa.it/publication/reduced-basis-method-stokes-equations-decomposable-domains-using-greedy-optimization01878nam a2200181 4500008004100000022002200041245006700063210006700130250000600197260002100203300000800224490000600232520123600238653007801474100002201552700002101574856010101595 2014 eng d a978-3-319-02089-100aReduced Order Methods for Modeling and Computational Reduction0 aReduced Order Methods for Modeling and Computational Reduction a1 aMilanobSpringer a3340 v93 aThis monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

10areduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-order-methods-modeling-and-computational-reduction00458nas a2200133 4500008004100000245007200041210006900113260001000182653003000192100002200222700002300244700002100267856003600288 2014 en d00aReduction on characteristics for continuous of a scalar balance law0 aReduction on characteristics for continuous of a scalar balance bSISSA10aMethod of characteristics1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/656201083nas a2200121 4500008004100000245012700041210006900168260002900237520052100266100002200787700002200809856013000831 2014 en d00aA robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model0 arobotic crawler exploiting directional frictional interactions e bRoyal Society Publishing3 aWe present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/robotic-crawler-exploiting-directional-frictional-interactions-experiments-numerics-and00632nas a2200109 4500008004100000245008300041210007100124260001300195520024000208100002300448856005100471 2014 en d00aSBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations0 aSBV Regularity of Systems of Conservation Laws and Hamilton–Jaco bSpringer3 aWe review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper.1 aBianchini, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3469101169nas a2200145 4500008004100000245008500041210006900126260001000195520065500205653006700860100002100927700001900948700002000967856003600987 2014 en d00aSecond Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional0 aSecond Order Asymptotic Development for the Anisotropic CahnHill bSISSA3 aThe asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.10aGamma-convergence, Cahn-Hilliard functional, phase transitions1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/739001649nas a2200121 4500008004100000245007500041210006900116260001300185520123700198100001901435700002201454856005101476 2014 en d00aShape control of active surfaces inspired by the movement of euglenids0 aShape control of active surfaces inspired by the movement of eug bElsevier3 aWe examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3511801619nas a2200145 4500008004100000245010700041210006900148260001300217520111600230100001701346700002001363700002101383700001801404856005101422 2014 en d00aShape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows0 aShape Optimization by FreeForm Deformation Existence Results and bSpringer3 aShape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.1 aBallarin, F.1 aManzoni, Andrea1 aRozza, Gianluigi1 aSalsa, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3469800707nas a2200145 4500008004100000022001400041245007900055210006900134300001400203490000700217520023000224100001700454700001900471856007100490 2014 eng d a0294-144900aSmooth approximation of bi-Lipschitz orientation-preserving homeomorphisms0 aSmooth approximation of biLipschitz orientationpreserving homeom a567 - 5890 v313 a

We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

1 aDaneri, Sara1 aPratelli, Aldo uhttp://www.sciencedirect.com/science/article/pii/S029414491300071100987nas a2200145 4500008004100000245008700041210006900128260001000197520050200207100002400709700002000733700001900753700001900772856005000791 2014 en d00aSome remarks on a model for rate-independent damage in thermo-visco-elastodynamics0 aSome remarks on a model for rateindependent damage in thermovisc bSISSA3 aThis note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/746301769nas a2200133 4500008004100000245008300041210006900124260001900193520130400212100002001516700002101536700002701557856005101584 2014 en d00aSome remarks on the seismic behaviour of embedded cantilevered retaining walls0 aSome remarks on the seismic behaviour of embedded cantilevered r bThomas Telford3 aThis paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls.1 aConti, Riccardo1 aD'Arezzo, Burali1 aViggiani, Giulia, M.B. uhttp://urania.sissa.it/xmlui/handle/1963/3507300993nas a2200121 4500008004100000245006500041210006500106260003000171520058100201100001600782700002200798856005100820 2014 en d00aSpontaneous division and motility in active nematic droplets0 aSpontaneous division and motility in active nematic droplets bAmerican Physical Society3 aWe investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.1 aGiomi, Luca1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3490200979nas a2200157 4500008004100000022004000041245009000081210006900171260001900240300001200259490000600271520039700277653003900674100002000713856008800733 2014 en d aOnline: 1864-8266; Print: 1864-825800aStability of equilibrium configurations for elastic films in two and three dimensions0 aStability of equilibrium configurations for elastic films in two bSISSAc01/2014 a117-1530 v83 aWe establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

10aEpitaxially strained elastic films1 aBonacini, Marco uhttps://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml01201nas a2200133 4500008004100000245007800041210006900119300001100188490000800199520070800207100001900915700002100934856011200955 2014 eng d00aStabilized reduced basis method for parametrized advection-diffusion PDEs0 aStabilized reduced basis method for parametrized advectiondiffus a1–180 v2743 aIn this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/stabilized-reduced-basis-method-parametrized-advection-diffusion-pdes01104nas a2200121 4500008004100000245016100041210006900202300001600271520058500287100001900872700002100891856007000912 2014 eng d00aStabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts0 aStabilized reduced basis method for parametrized scalar advectio a5614–56243 aAdvection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf00470nas a2200109 4500008004100000245008400041210006900125260001000194100002300204700001600227856011700243 2014 en d00aSteady nearly incompressible vector elds in 2D: chain rule and renormalization0 aSteady nearly incompressible vector elds in 2D chain rule and re bSISSA1 aBianchini, Stefano1 aGusev, N.A. uhttps://www.math.sissa.it/publication/steady-nearly-incompressible-vector-elds-2d-chain-rule-and-renormalization00484nas a2200133 4500008004100000245009400041210006900135260001900204300001200223490000800235100002300243700001200266856007200278 2014 en d00aStructure of entropy solutions to general scalar conservation laws in one space dimension0 aStructure of entropy solutions to general scalar conservation la bSISSAc08/2015 a356-3860 v4281 aBianchini, Stefano1 aYu, Lei uhttps://www.sciencedirect.com/science/article/pii/S0022247X1500221801169nas a2200133 4500008004100000245007700041210006900118260003400187520069100221100002700912700002300939700002200962856005100984 2014 en d00aSwelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch0 aSwelling dynamics of a thin elastomeric sheet under uniaxial pre bAmerican Institute of Physics3 aIt has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3511301394nas a2200133 4500008004100000245006500041210006400106260002800170520094000198100002701138700002301165700002101188856005101209 2014 en d00aSwelling-induced and controlled curving in layered gel beams0 aSwellinginduced and controlled curving in layered gel beams bRoyal Society of London3 aWe describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aPezzulla, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/3498700781nas a2200121 4500008004100000245008700041210006900128260003100197520034000228100001800568700002200586856005100608 2014 en d00aThe topology of a subspace of the Legendrian curves on a closed contact 3-manifold0 atopology of a subspace of the Legendrian curves on a closed cont bAdvanced Nonlinear Studies3 aIn this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry.1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3501601084nas a2200133 4500008004100000245014200041210006900183260005100252520053000303100002200833700002300855700002100878856005100899 2014 en d00aA uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday0 auniqueness result for the continuity equation in two dimensions bEuropean Mathematical Society; Springer Verlag3 aWe characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469200850nas a2200121 4500008004300000245007700043210006900120260001000189520044200199653001700641100002000658856005000678 2014 en_Ud 00aA variational approach to statics and dynamics of elasto-plastic systems0 avariational approach to statics and dynamics of elastoplastic sy bSISSA3 aWe prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers.10adelamination1 aScala, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/747100848nas a2200133 4500008004100000245009600041210006900137260003400206520037800240653002300618100001800641700001900659856003600678 2014 en d00aA variational model for the quasi-static growth of fractional dimensional brittle fractures0 avariational model for the quasistatic growth of fractional dimen bEuropean Mathematical Society3 aWe propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

10aVariational models1 aRacca, Simone1 aToader, Rodica uhttp://hdl.handle.net/1963/698301557nas a2200133 4500008004100000245009400041210006900135260001700204520109300221100001501314700002201329700002101351856005101372 2014 en d00aA weighted empirical interpolation method: A priori convergence analysis and applications0 aweighted empirical interpolation method A priori convergence ana bEDP Sciences3 aWe extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3502100995nas a2200121 4500008004300000245007400043210006900117260001000186520059200196100001700788700001800805856005000823 2014 en_Ud 00aWhere best to place a Dirichlet condition in an anisotropic membrane?0 aWhere best to place a Dirichlet condition in an anisotropic memb bSISSA3 aWe study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure). We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed length tends to infinity, via $\Gamma$-convergence.1 aTilli, Paolo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/748101521nas a2200133 4500008004100000245009100041210006900132260001000201520106100211653003701272100002001309700002201329856003601351 2013 en d00aAmbrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity0 aAmbrosioTortorelli approximation of cohesive fracture models in bSISSA3 aWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

10aFunctions of bounded deformation1 aFocardi, Matteo1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/661501048nas a2200145 4500008004100000245010400041210006900145260001300214520050500227653007400732100002100806700001900827700002000846856003600866 2013 en d00aAnalytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces0 aAnalytical validation of a continuum model for epitaxial growth bSpringer3 aIn this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].10asingular nonlinear parabolic equations, Hilbert transform, thin films1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/724500531nas a2200109 4500008004100000245011300041210006900154260001000223653003700233100002200270856012900292 2013 en d00aAn Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems0 aApproximation Result for Generalised Functions of Bounded Deform bSISSA10aFunctions of bounded deformation1 aIurlano, Flaviana uhttps://www.math.sissa.it/publication/approximation-result-generalised-functions-bounded-deformation-and-applications-damage01539nas a2200121 4500008004100000245009200041210006900133260005100202520107800253100001701331700001801348856005101366 2013 en d00aAsymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length0 aAsymptotics of the first Laplace eigenvalue with Dirichlet regio bSociety for Industrial and Applied Mathematics3 aWe consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian.1 aTilli, Paolo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514100882nas a2200133 4500008004100000245004600041210004600087260001000133520050000143100002600643700002100669700002200690856003600712 2013 en d00aAttainment results for nematic elastomers0 aAttainment results for nematic elastomers bSISSA3 aWe consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/717401890nas a2200145 4500008004100000245011800041210006900159260001300228520137300241653003501614100001801649700002001667700002101687856003601708 2013 en d00aA combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices0 acombination between the reduced basis method and the ANOVA expan bElsevier3 aWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

10aPartial differential equations1 aDevaud, Denis1 aManzoni, Andrea1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/738901565nas a2200169 4500008004100000245010100041210006900142260001000211520092400221100002201145700002401167700002201191700001701213700001901230700002201249856012401271 2013 en d00aCommon dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.0 aCommon dynamical features of sensory adaptation in photoreceptor bSISSA3 aSensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

1 aDe Palo, Giovanna1 aFacchetti, Giuseppe1 aMazzolini, Monica1 aMenini, Anna1 aTorre, Vincent1 aAltafini, Claudio uhttps://www.math.sissa.it/publication/common-dynamical-features-sensory-adaptation-photoreceptors-and-olfactory-sensory01080nas a2200169 4500008004100000022001400041245009400055210006900149300001200218490000800230520048300238653003400721653002000755653004300775100002100818856007100839 2013 eng d a0022-039600aConcentration of solutions for a singularly perturbed mixed problem in non-smooth domains0 aConcentration of solutions for a singularly perturbed mixed prob a30 - 660 v2543 aWe consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

10aFinite-dimensional reductions10aLocal inversion10aSingularly perturbed elliptic problems1 aDipierro, Serena uhttp://www.sciencedirect.com/science/article/pii/S002203961200331200887nas a2200145 4500008004100000022001400041245006300055210005800118260000800176300001400184490000700198520047000205100002000675856004600695 2013 eng d a1559-002X00aThe Conformal Willmore Functional: A Perturbative Approach0 aConformal Willmore Functional A Perturbative Approach cApr a764–8110 v233 aThe conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ – where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

1 aMondino, Andrea uhttps://doi.org/10.1007/s12220-011-9263-300784nas a2200121 4500008004100000245005400041210005300095260001300148520042200161100002100583700002200604856003600626 2013 en d00aConnected Sum Construction for σk-Yamabe Metrics0 aConnected Sum Construction for σkYamabe Metrics bSpringer3 aIn this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.1 aCatino, Giovanni1 aMazzieri, Lorenzo uhttp://hdl.handle.net/1963/644101071nas a2200145 4500008004100000245006700041210006600108260001300174520054900187100002200736700002400758700002200782700002000804856010100824 2013 en d00aCrawlers in viscous environments: linear vs nonlinear rheology0 aCrawlers in viscous environments linear vs nonlinear rheology bElsevier3 aWe study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.1 aDeSimone, Antonio1 aGuarnieri, Federica1 aNoselli, Giovanni1 aTatone, Amabile uhttps://www.math.sissa.it/publication/crawlers-viscous-environments-linear-vs-nonlinear-rheology01043nas a2200145 4500008004100000245004200041210003700083260001000120520060700130653006200737100002500799700002100824700001600845856003600861 2013 en d00aThe curvature: a variational approach0 acurvature a variational approach bSISSA3 aThe curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.10aCrurvature, subriemannian metric, optimal control problem1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aRizzi, Luca uhttp://hdl.handle.net/1963/722600613nas a2200193 4500008004100000245003700041210003000078260001000108520010800118100002300226700001800249700001700267700001700284700002400301700002000325700002000345700001800365856003600383 2013 en d00aThe deal.II Library, Version 8.10 adealII Library Version 81 bSISSA3 aThis paper provides an overview of the new features of the finite element library deal.II version 8.0.1 aBangerth, Wolfgang1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, Bruno1 aYoung, T., D. uhttp://hdl.handle.net/1963/723601298nas a2200145 4500008004100000245006100041210006100102260001000163520087100173100001601044700002101060700001101081700002401092856003601116 2013 en d00aDefect annihilation and proliferation in active nematics0 aDefect annihilation and proliferation in active nematics bSISSA3 aLiquid crystals inevitably possess topological defect excitations generated\r\nthrough boundary conditions, applied fields or in quenches to the ordered\r\nphase. In equilibrium pairs of defects coarsen and annihilate as the uniform\r\nground state is approached. Here we show that defects in active liquid crystals\r\nexhibit profoundly different behavior, depending on the degree of activity and\r\nits contractile or extensile character. While contractile systems enhance the\r\nannihilation dynamics of passive systems, extensile systems act to drive\r\ndefects apart so that they swarm around in the manner of topologically\r\nwell-characterized self-propelled particles. We develop a simple analytical\r\nmodel for the defect dynamics which reproduces the key features of both the\r\nnumerical solutions and recent experiments on microtuble-kinesin assemblies.1 aGiomi, Luca1 aBowick, Mark, J.1 aMa, Xu1 aMarchetti, Cristina uhttp://hdl.handle.net/1963/656600951nas a2200145 4500008004100000245009100041210006900132260001000201520045700211653003300668100002100701700002500722700002200747856003600769 2013 en d00aDislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting0 aDislocation dynamics in crystals a macroscopic theory in a fract bSISSA3 aWe consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential.10anonlocal Allen-Cahn equation1 aDipierro, Serena1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttp://hdl.handle.net/1963/712401988nas a2200133 4500008004100000245010500041210006900146260003000215520151100245100002101756700002201777700001901799856003601818 2013 en d00aEarly phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus0 aEarly phase of plasticityrelated gene regulation and SRF depende bPublic Library of Science3 aHippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.1 aIacono, Giovanni1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/728701025nas a2200109 4500008004100000245008100041210006900122260001700191520065100208100002000859856003600879 2013 en d00aEpitaxially strained elastic films: the case of anisotropic surface energies0 aEpitaxially strained elastic films the case of anisotropic surfa bEDP Sciences3 aIn the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

1 aBonacini, Marco uhttp://hdl.handle.net/1963/426800989nas a2200133 4500008004100000245010200041210006900143260002600212520042000238100002100658700002500679700002200704856012900726 2013 en d00aExistence and symmetry results for a Schrodinger type problem involving the fractional Laplacian0 aExistence and symmetry results for a Schrodinger type problem in bUniversity of Catania3 aThis paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

1 aDipierro, Serena1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/existence-and-symmetry-results-schrodinger-type-problem-involving-fractional-laplacian00556nas a2200121 4500008004100000245010500041210006900146260005100215300001600266490000800282100002000290856012400310 2013 eng d00aAn existence result for the mean-field equation on compact surfaces in a doubly supercritical regime0 aexistence result for the meanfield equation on compact surfaces bRoyal Society of Edinburgh Scotland Foundation a1021–10450 v1431 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/existence-result-mean-field-equation-compact-surfaces-doubly-supercritical-regime01391nas a2200109 4500008004100000245006200041210006200103260001000165520104500175100002501220856003601245 2013 en d00aFields of bounded deformation for mesoscopic dislocations0 aFields of bounded deformation for mesoscopic dislocations bSISSA3 aIn this paper we discuss the consequences of the distributional approach to dislocations in terms of the mathematical properties\\r\\nof the auxiliary model fields such as displacement and displacement gradient which are obtained directly from \\r\\nthe main model field here considered as the linear strain. We show that these fields cannot be introduced rigourously without \\r\\nthe introduction of gauge fields, or equivalently, without cuts in the Riemann foliation associated to the dislocated crystal.\\r\\nIn a second step we show that the space of bounded deformations follows from the distributional approach in a natural way and \\r\\ndiscuss the reasons why it is adequate to model dislocations. The case of dislocation clusters is also addressed, as it represents an important issue in industrial crystal growth while from a mathematical point of view, peculiar phenomena might appear at the set of accumulation points. \\r\\nThe elastic-plastic decomposition of the strain within this approach is also given a precise meaning.1 aVan Goethem, Nicolas uhttp://hdl.handle.net/1963/637800902nas a2200121 4500008004100000245005300041210005200094260004800146520050700194100002100701700002200722856003600744 2013 en d00aFracture models as Gamma-limits of damage models0 aFracture models as Gammalimits of damage models bAmerican Institute of Mathematical Sciences3 aWe analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

1 aDal Maso, Gianni1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/422501258nas a2200145 4500008004100000245010200041210006900143260008500212300001400297490000700311520069200318100002201010700002301032856005701055 2013 eng d00aGeneralized Sturm-Liouville boundary conditions for first order differential systems in the plane0 aGeneralized SturmLiouville boundary conditions for first order d bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a293–3250 v423 aWe study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fučík spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

1 aFonda, Alessandro1 aGarrione, Maurizio uhttps://projecteuclid.org:443/euclid.tmna/146124898100420nas a2200109 4500008004100000245011000041210006900151260001000220100002200230700002200252856003600274 2013 en d00aAn improved geometric inequality via vanishing moments, with applications to singular Liouville equations0 aimproved geometric inequality via vanishing moments with applica bSISSA1 aBardelloni, Mauro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/656100759nas a2200157 4500008004100000022001300041245006000054210006000114300001200174490000700186520025600193100002400449700001700473700002100490856009000511 2013 eng d a0012959300aKAM theory for the Hamiltonian derivative wave equation0 aKAM theory for the Hamiltonian derivative wave equation a301-3730 v463 aWe prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. © 2013 Société Mathématique de France.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttps://www.math.sissa.it/publication/kam-theory-hamiltonian-derivative-wave-equation01360nas a2200181 4500008004100000022001400041245008900055210006900144260000800213300001400221490000700235520080900242100001701051700002301068700002001091700002101111856004601132 2013 eng d a1559-002X00aLipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces0 aLipschitz Classification of AlmostRiemannian Distances on Compac cJan a438–4550 v233 aTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot–Carathéodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttps://doi.org/10.1007/s12220-011-9262-400625nas a2200157 4500008004100000245011600041210006900157260001700226300001400243490000700257100001500264700002300279700002200302700001800324856012500342 2013 eng d00aMacroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations0 aMacroscopic contact angle and liquid drops on rough solid surfac bEDP Sciences a837–8580 v471 aCacace, S.1 aChambolle, Antonin1 aDeSimone, Antonio1 aFedeli, Livio uhttps://www.math.sissa.it/publication/macroscopic-contact-angle-and-liquid-drops-rough-solid-surfaces-homogenization-and01676nas a2200145 4500008004100000245009400041210006900135260001000204520112400214653008201338100002001420700002501440700002901465856003601494 2013 en d00aMinimal partitions and image classification using a gradient-free perimeter approximation0 aMinimal partitions and image classification using a gradientfree bSISSA3 aIn this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring.10aImage classification, deblurring, optimal partitions, perimeter approximation1 aAmstutz, Samuel1 aVan Goethem, Nicolas1 aNovotny, Antonio, André uhttp://hdl.handle.net/1963/697600516nas a2200109 4500008004100000245010700041210006900148260001000217653003200227100002000259856012700279 2013 en d00aMinimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems0 aMinimality and stability results for a class of freediscontinuit bSISSA10afree-discontinuity problems1 aBonacini, Marco uhttps://www.math.sissa.it/publication/minimality-and-stability-results-class-free-discontinuity-and-nonlocal-isoperimetric01330nas a2200157 4500008004100000022001400041245005900055210005500114260000800169300001400177490000800191520088200199100002301081700002201104856004601126 2013 eng d a1432-091600aThe Monge Problem for Distance Cost in Geodesic Spaces0 aMonge Problem for Distance Cost in Geodesic Spaces cMar a615–6730 v3183 aWe address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dLis a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting dL-cyclical monotonicity is not sufficient for optimality.

1 aBianchini, Stefano1 aCavalletti, Fabio uhttps://doi.org/10.1007/s00220-013-1663-800430nas a2200121 4500008004100000245009500041210006900136260001300205653001400218100001800232700002200250856003600272 2013 en d00aMultiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian0 aMultiplicity result for a nonhomogeneous Yamabe type equation in bElsevier10aCR-Yamabe1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://hdl.handle.net/1963/737400408nas a2200109 4500008004100000245005900041210005700100490000700157100002300164700002000187856009100207 2013 eng d00aA New Quadratic Potential for Scalar Conservation Laws0 aNew Quadratic Potential for Scalar Conservation Laws0 v291 aBianchini, Stefano1 aModena, Stefano uhttps://www.math.sissa.it/publication/new-quadratic-potential-scalar-conservation-laws01020nas a2200145 4500008004100000020001500041245007100056210006500127520044300192653007200635100001900707700002500726700002200751856010100773 2013 en d a887642472400aThe nonlinear multidomain model: a new formal asymptotic analysis.0 anonlinear multidomain model a new formal asymptotic analysis3 aWe study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

10abidomain model, anisotropic mean curvature, star-shaped combination1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttps://www.math.sissa.it/publication/nonlinear-multidomain-model-new-formal-asymptotic-analysis01376nas a2200145 4500008004100000245007300041210006900114260003400183520083400217653001701051100001301068700002401081700002301105856010201128 2013 en d00aA note on KAM theory for quasi-linear and fully nonlinear forced KdV0 anote on KAM theory for quasilinear and fully nonlinear forced Kd bEuropean Mathematical Society3 aWe present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.10aKAM for PDEs1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttps://www.math.sissa.it/publication/note-kam-theory-quasi-linear-and-fully-nonlinear-forced-kdv00784nas a2200109 4500008004100000245008400041210006900125520032000194100002500514700002300539856011200562 2013 eng d00aA note on non-homogeneous hyperbolic operators with low-regularity coefficients0 anote on nonhomogeneous hyperbolic operators with lowregularity c3 aIn this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

1 aColombini, Ferruccio1 aFanelli, Francesco uhttps://www.math.sissa.it/publication/note-non-homogeneous-hyperbolic-operators-low-regularity-coefficients01596nas a2200133 4500008004100000245010900041210006900150260001000219520113200229100002101361700002201382700002201404856003601426 2013 en d00aOne-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls0 aOnedimensional swimmers in viscous fluids dynamics controllabili bSISSA3 aIn this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/646700555nas a2200133 4500008004100000245009600041210006900137260003700206300001200243490000700255100002300262700001900285856011700304 2013 eng d00aPairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions0 aPairs of nodal solutions for a class of nonlinear problems with bAdvanced Nonlinear Studies, Inc. a13–530 v131 aBoscaggin, Alberto1 aZanolin, Fabio uhttps://www.math.sissa.it/publication/pairs-nodal-solutions-class-nonlinear-problems-one-sided-growth-conditions00503nas a2200133 4500008004100000245006500041210006500106260003700171300001400208490000700222100002200229700001900251856009900270 2013 eng d00aPeriodic bouncing solutions for nonlinear impact oscillators0 aPeriodic bouncing solutions for nonlinear impact oscillators bAdvanced Nonlinear Studies, Inc. a179–1890 v131 aFonda, Alessandro1 aSfecci, Andrea uhttps://www.math.sissa.it/publication/periodic-bouncing-solutions-nonlinear-impact-oscillators01133nas a2200157 4500008004100000022001400041245008000055210007300135260000800208300001400216490000700230520064600237100002300883700002300906856004600929 2013 eng d a1420-900400aPlanar Hamiltonian systems at resonance: the Ahmad–Lazer–Paul condition0 aPlanar Hamiltonian systems at resonance the Ahmad–Lazer–Paul con cJun a825–8430 v203 aWe consider the planar Hamiltonian system\$\$Ju^{\backslashprime} = \backslashnabla F(u) + \backslashnabla_u R(t,u), \backslashquad t \backslashin [0,T], \backslash,u \backslashin \backslashmathbb{R}^2,\$\$with F(u) positive and positively 2-homogeneous and \$\${\backslashnabla_{u}R(t, u)}\$\$sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman–Lazer condition is analyzed, as well.

1 aBoscaggin, Alberto1 aGarrione, Maurizio uhttps://doi.org/10.1007/s00030-012-0181-200550nas a2200109 4500008004100000245002500041210002500066260001000091520025100101100002500352856006300377 2013 en d00aQuadratic cohomology0 aQuadratic cohomology bSISSA3 aWe study homological invariants of smooth families of real quadratic forms as\r\na step towards a \"Lagrange multipliers rule in the large\" that intends to\r\ndescribe topology of smooth vector functions in terms of scalar Lagrange\r\nfunctions.1 aAgrachev, Andrei, A. uhttps://www.math.sissa.it/publication/quadratic-cohomology01461nas a2200217 4500008004100000022001400041245008900055210006900144300001400213490000700227520075100234653001700985653002301002653003101025653002601056653003101082653001601113100001801129700002501147856007101172 2013 eng d a0294-144900aA quasistatic evolution model for perfectly plastic plates derived by Γ-convergence0 aquasistatic evolution model for perfectly plastic plates derived a615 - 6600 v303 aThe subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

10a-convergence10aPerfect plasticity10aPrandtl–Reuss plasticity10aQuasistatic evolution10aRate-independent processes10aThin plates1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://www.sciencedirect.com/science/article/pii/S029414491200103502183nas a2200145 4500008004100000245015300041210006900194260001300263520163200276653003401908100002101942700001801963700002001981856003602001 2013 en d00aReduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants0 aReduced basis approximation and a posteriori error estimation fo bSpringer3 aIn this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.10aparametrized Stokes equations1 aRozza, Gianluigi1 aHuynh, Phuong1 aManzoni, Andrea uhttp://hdl.handle.net/1963/633900531nas a2200121 4500008004100000245011700041210006900158300001100227490000700238100001800245700002100263856012500284 2013 eng d00aReduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)0 aReduced Basis Approximation for the StructuralAcoustic Design ba a98-1150 v481 aDevaud, Denis1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-structural-acoustic-design-based-energy-finite-element00548nas a2200133 4500008004100000245009200041210006900133260001000202100001800212700002000230700002200250700002100272856012100293 2013 en d00aA Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics0 aReduced Computational and Geometrical Framework for Inverse Prob bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-computational-and-geometrical-framework-inverse-problems-haemodynamics00568nas a2200133 4500008004100000245010500041210006900146260001000215100001800225700002000243700002200263700002100285856012800306 2013 en d00aA reduced-order strategy for solving inverse Bayesian identification problems in physiological flows0 areducedorder strategy for solving inverse Bayesian identificatio bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-order-strategy-solving-inverse-bayesian-identification-problems-physiological00490nas a2200121 4500008004100000245007900041210006900120260001000189100001800199700002000217700002100237856011000258 2013 en d00aReduction Strategies for Shape Dependent Inverse Problems in Haemodynamics0 aReduction Strategies for Shape Dependent Inverse Problems in Hae bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduction-strategies-shape-dependent-inverse-problems-haemodynamics00793nas a2200145 4500008004100000245004800041210004800089260003500137300001200172490000600184520038200190100002200572700002000594856003300614 2013 en d00aRemarks on the Moser–Trudinger inequality0 aRemarks on the Moser–Trudinger inequality bAdvances in Nonlinear Analysis a389-4250 v23 aWe extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

1 aMancini, Gabriele1 aBattaglia, Luca uhttp://edoc.unibas.ch/43974/00494nas a2200097 4500008004100000245012100041210006900162100001700231700001800248856013000266 2013 eng d00aSelf-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces0 aSelfadjoint extensions and stochastic completeness of the Laplac1 aBoscain, Ugo1 aPrandi, Dario uhttps://www.math.sissa.it/publication/self-adjoint-extensions-and-stochastic-completeness-laplace-beltrami-operator-conic-and01064nas a2200109 4500008004100000245002900041210002900070260001000099520079300109100001600902856003600918 2013 en d00aSoftly Constrained Films0 aSoftly Constrained Films bSISSA3 aThe shape of materials is often subject to a number of geometric constraints\r\nthat limit the size of the system or fix the structure of its boundary. In soft\r\nand biological materials, however, these constraints are not always hard, but\r\nare due to other physical mechanisms that affect the overall force balance. A\r\ncapillary film spanning a flexible piece of wire or a cell anchored to a\r\ncompliant substrate by mean of adhesive contacts are examples of these softly\r\nconstrained systems in the macroscopic and microscopic world. In this article I\r\nreview some of the important mathematical and physical developments that\r\ncontributed to our understanding of shape formation in softly constrained films\r\nand their recent application to the mechanics of adherent cells.1 aGiomi, Luca uhttp://hdl.handle.net/1963/656300403nas a2200109 4500008004100000245005300041210005300094260001000147653003300157100001800190856008500208 2013 en d00aSome models of crack growth in brittle materials0 aSome models of crack growth in brittle materials bSISSA10aQuasi-static crack evolution1 aRacca, Simone uhttps://www.math.sissa.it/publication/some-models-crack-growth-brittle-materials00401nas a2200121 4500008004100000245002300041210002300064260001000087520010800097653001300205100002500218856003600243 2013 en d00aSome open problems0 aSome open problems bSISSA3 aWe discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.10aGeometry1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/707000835nas a2200145 4500008004100000245006200041210006200103260001000165490000600175520040600181653002300587100002400610700001900634856003600653 2013 en d00aSome remarks on the viscous approximation of crack growth0 aSome remarks on the viscous approximation of crack growth bSISSA0 v63 aWe describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

10aVariational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/420600744nas a2200097 4500008004100000245004800041210004300089520044800132100001800580856004800598 2013 en d00aThe splitting theorem in non-smooth context0 asplitting theorem in nonsmooth context3 aWe prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.1 aGigli, Nicola uhttp://preprints.sissa.it/handle/1963/3530601218nas a2200121 4500008004100000245008200041210006900123520080800192100002201000700002301022700001501045856003601060 2013 en d00aStabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control0 aStabilization of Stochastic Quantum Dynamics via Open and Closed3 aIn this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control1 aAltafini, Claudio1 aTicozzi, Francesco1 aNishio, K. uhttp://hdl.handle.net/1963/650301660nas a2200145 4500008004100000245010800041210006900149260001000218520115900228653003501387100001701422700001701439700002201456856003601478 2013 en d00aA stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions0 astable and adaptive semiLagrangian potential model for unsteady bSISSA3 aWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

10aUnsteady ship-wave interaction1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/566900757nas a2200133 4500008004100000245008600041210006900127260002100196300001200217490000700229520031600236100002200552856004900574 2013 eng d00aStable determination of a body immersed in a fluid: the nonlinear stationary case0 aStable determination of a body immersed in a fluid the nonlinear bTaylor & Francis a460-4810 v923 aWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier–Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log–log type.

1 aBallerini, Andrea uhttps://doi.org/10.1080/00036811.2011.62817300932nas a2200109 4500008004100000245011500041210006900156260001000225520044500235100001200680856013000692 2013 en d00aThe structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension0 astructure and regularity of admissible BV solutions to hyperboli bSISSA3 aThis thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws.1 aYu, Lei uhttps://www.math.sissa.it/publication/structure-and-regularity-admissible-bv-solutions-hyperbolic-conservation-laws-one-space01092nas a2200205 4500008004100000022001400041245010400055210006900159300000700228490000700235520037600242653003000618653003400648653002300682653003700705653002600742100002300768700001900791856007600810 2013 eng d a1078-094700aSubharmonic solutions for nonlinear second order equations in presence of lower and upper solutions0 aSubharmonic solutions for nonlinear second order equations in pr a890 v333 aWe study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

10alower and upper solutions10aparameter dependent equations10aPeriodic solutions10aPoincaré-Birkhoff twist theorem10asubharmonic solutions1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f00380nas a2200109 4500008004100000245007400041210006900115260001000184100002300194700001700217856003600234 2013 en d00aOn Sudakov's type decomposition of transference plans with norm costs0 aSudakovs type decomposition of transference plans with norm cost bSISSA1 aBianchini, Stefano1 aDaneri, Sara uhttp://hdl.handle.net/1963/720600725nas a2200121 4500008004100000245006600041210006400107260001000171520034800181100002200529700001600551856003600567 2013 en d00aA variational Analysis of the Toda System on Compact Surfaces0 avariational Analysis of the Toda System on Compact Surfaces bWiley3 aIn this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/655800934nas a2200133 4500008004100000245005700041210005100098260005100149520050200200100002100702700001700723700002400740856003600764 2012 en d00aOn 2-step, corank 2 nilpotent sub-Riemannian metrics0 a2step corank 2 nilpotent subRiemannian metrics bSociety for Industrial and Applied Mathematics3 aIn this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics\\r\\nthat are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.1 aBarilari, Davide1 aBoscain, Ugo1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/606500868nas a2200145 4500008004100000245004700041210004400088260004800132520037400180100002100554700002100575700002500596700002200621856007900643 2012 en d00aAsymptotics of the s-perimeter as s →0 0 aAsymptotics of the sperimeter as s →0 bAmerican Institute of Mathematical Sciences3 aWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

1 aDipierro, Serena1 aFigalli, Alessio1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/asymptotics-s-perimeter-s-%E2%86%92001737nas a2200145 4500008004100000245007100041210006400112260001900176520126500195653002501460100002001485700002301505700002701528856003601555 2012 en d00aOn the behaviour of flexible retaining walls under seismic actions0 abehaviour of flexible retaining walls under seismic actions bICE Publishing3 aThis paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value.10aCentrifuge modelling1 aConti, Riccardo1 aMadabhushi, G.S.P.1 aViggiani, Giulia, M.B. uhttp://hdl.handle.net/1963/693301501nas a2200157 4500008004100000245010600041210006900147260003100216520095600247653002301203100001801226700002001244700002201264700002101286856003601307 2012 en d00aBoundary control and shape optimization for the robust design of bypass anastomoses under uncertainty0 aBoundary control and shape optimization for the robust design of bCambridge University Press3 aWe review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.10ashape optimization1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/633701113nas a2200145 4500008004100000245009600041210006900137260001300206300001200219490000700231520057100238100002000809700002400829856011400853 2012 en d00aOn a class of vector fields with discontinuity of divide-by-zero type and its applications0 aclass of vector fields with discontinuity of dividebyzero type a bSpringer a135-1580 v183 aWe study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

1 aGhezzi, Roberta1 aRemizov, Alexey, O. uhttps://www.math.sissa.it/publication/class-vector-fields-discontinuity-divide-zero-type-and-its-applications01152nas a2200145 4500008004100000245009700041210006900138260001000207520067600217100002200893700001500915700002000930700002000950856003600970 2012 en d00aA Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group.0 aCodazzilike equation and the singular set for C1 smooth surfaces bSISSA3 aIn this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 11 aMalchiodi, Andrea1 aYang, Paul1 aCheng, Jih-Hsin1 aHwang, JennFang uhttp://hdl.handle.net/1963/655600824nas a2200169 4500008004100000020001800041245006300059210006300122260001300185520030800198653002400506100002200530700001700552700002300569700002600592856003600618 2012 en d a978146143996700aComputing optimal strokes for low reynolds number swimmers0 aComputing optimal strokes for low reynolds number swimmers bSpringer3 aWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

10aNumerical analysis.1 aDeSimone, Antonio1 aHeltai, Luca1 aAlouges, François1 aAline, Lefebvre-Lepot uhttp://hdl.handle.net/1963/644500854nas a2200157 4500008004100000245012200041210007200163260002100235300001200256490000700268520031300275100002000588700002300608700001900631856004600650 2012 eng d00aConcentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity0 aConcentration on circles for nonlinear Schrödinger–Poisson syste bWorld Scientific a12500090 v143 aThe present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

1 aBonheure, Denis1 aDi Cosmo, Jonathan1 aMercuri, Carlo uhttps://doi.org/10.1142/S021919971250009501031nas a2200133 4500008004100000245009200041210006900133260002100202300001400223490000700237520058100244100002300825856004900848 2012 eng d00aConservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids0 aConservation of Geometric Structures for NonHomogeneous Inviscid bTaylor & Francis a1553-15950 v373 aIn this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

1 aFanelli, Francesco uhttps://doi.org/10.1080/03605302.2012.69834300925nas a2200121 4500008004100000245010900041210006900150260001300219520049100232100002500723700001900748856003600767 2012 en d00aConvergence of equilibria of thin elastic plates under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic plates under physical bElsevier3 aThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

1 aMora, Maria Giovanna1 aScardia, Lucia uhttp://hdl.handle.net/1963/346601015nas a2200109 4500008004100000245004300041210004300084260001300127520070800140100002100848856003600869 2012 en d00aConvex pencils of real quadratic forms0 aConvex pencils of real quadratic forms bSpringer3 aWe study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2).1 aLerario, Antonio uhttp://hdl.handle.net/1963/709901915nas a2200121 4500008004100000245008100041210006900122260001300191520151100204100002201715700002001737856003601757 2012 en d00aCrawling motility through the analysis of model locomotors: two case studies0 aCrawling motility through the analysis of model locomotors two c bSpringer3 aWe study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.1 aDeSimone, Antonio1 aTatone, Amabile uhttp://hdl.handle.net/1963/701702153nas a2200181 4500008004100000245015200041210006900193260001000262520154500272100001101817700002101828700001601849700001501865700001401880700001901894700002201913856003601935 2012 en d00aDetection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis0 aDetection of transcriptional triggers in the dynamics of microbi bSISSA3 aThe capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems1 aBeg, Q1 aZampieri, Mattia1 aKlitgord, N1 aCollins, S1 aSerres, M1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650601693nas a2200157 4500008004100000245008400041210006900125260003400194520117300228100002201401700002001423700001701443700001701460700002201477856003601499 2012 en d00aA dynamical feedback model for adaptation in the olfactory transduction pathway0 adynamical feedback model for adaptation in the olfactory transdu bBiophysical Society, Elsevier3 aOlfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.1 aDe Palo, Giovanna1 aBoccaccio, Anna1 aMiri, Andrew1 aMenini, Anna1 aAltafini, Claudio uhttp://hdl.handle.net/1963/701901741nas a2200133 4500008004100000245007700041210006900118260001000187520130700197100002401504700002101528700002201549856003601571 2012 en d00aExploring the low-energy landscape of large-scale signed social networks0 aExploring the lowenergy landscape of largescale signed social ne bSISSA3 aAnalogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650401179nas a2200133 4500008004100000245006000041210005500101260001000156520076500166653004100931100001600972700002100988856003601009 2012 en d00aA formula for Popp\'s volume in sub-Riemannian geometry0 aformula for Popps volume in subRiemannian geometry bSISSA3 aFor an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property.10asubriemannian, volume, Popp, control1 aRizzi, Luca1 aBarilari, Davide uhttp://hdl.handle.net/1963/650101763nas a2200169 4500008004100000245010700041210006900148260001000217520118200227653002601409653002901435653003501464100001701499700001701516700002401533856003601557 2012 en d00aA Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library0 aFully Coupled Immersed Finite Element Method for Fluid Structure bSISSA3 aWe present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.10aFinite Element Method10aImmersed Boundary Method10aImmersed Finite Element Method1 aHeltai, Luca1 aRoy, Saswati1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/625500456nas a2200133 4500008004100000245006900041210006700110260001300177653003000190100001800220700002100238700002700259856003600286 2012 en d00aGamma-convergence and H-convergence of linear elliptic operators0 aGammaconvergence and Hconvergence of linear elliptic operators bElsevier10aLinear elliptic operators1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/587801004nas a2200169 4500008004100000022001400041245009800055210006900153300001600222490000800238520043000246653002300676653002300699100002200722700001900744856007100763 2012 eng d a0022-039600aA general method for the existence of periodic solutions of differential systems in the plane0 ageneral method for the existence of periodic solutions of differ a1369 - 13910 v2523 aWe propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

10aNonlinear dynamics10aPeriodic solutions1 aFonda, Alessandro1 aSfecci, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002203961100319601643nas a2200157 4500008004100000245012600041210006900167260001300236520109700249653002201346100001801368700002001386700002201406700002101428856003601449 2012 en d00aGeneralized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs0 aGeneralized reduced basis methods and nwidth estimates for the a bSpringer3 aThe set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.10asolution manifold1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/634001194nas a2200133 4500008004100000245005500041210004700096260001000143520080800153100002500961700002100986700001701007856003601024 2012 en d00aOn the Hausdorff volume in sub-Riemannian geometry0 aHausdorff volume in subRiemannian geometry bSISSA3 aFor a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral.1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/645401971nas a2200169 4500008004100000245009100041210006900132260003100201520131900232100002201551700001701573700002001590700002201610700002201632700002501654856012201679 2012 en d00aHybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment0 aHybridization in nanostructured DNA monolayers probed by AFM the bRoyal Society of Chemistry3 aNanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters.1 aBosco, Alessandro1 aBano, Fouzia1 aParisse, Pietro1 aCasalis, Loredana1 aDeSimone, Antonio1 aMicheletti, Cristian uhttps://www.math.sissa.it/publication/hybridization-nanostructured-dna-monolayers-probed-afm-theory-versus-experiment00389nas a2200121 4500008004100000245005900041210005800100260001000158100002500168700002100193700001700214856003600231 2012 en d00aIntroduction to Riemannian and sub-Riemannian geometry0 aIntroduction to Riemannian and subRiemannian geometry bSISSA1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/587700709nas a2200169 4500008004100000245011000041210006900151260003000220300001200250490000700262520014000269653002500409100002600434700002100460700002200481856003600503 2012 en d00aLinear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions0 aLinear elasticity obtained from finite elasticity by Gammaconver bGauthier-Villars;Elsevier a715-7350 v293 aThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/426701914nas a2200145 4500008004100000020001800041245010100059210006900160260003100229520140500260653002201665100002301687700002201710856003601732 2012 en d a978160511380700aMathematical and numerical modeling of liquid crystal elastomer phase transition and deformation0 aMathematical and numerical modeling of liquid crystal elastomer bCambridge University Press3 aLiquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking.10aArtificial muscle1 aDe Luca, Mariarita1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/702001486nas a2200121 4500008004100000245006100041210006000102260005400162520106700216100002201283700002301305856003601328 2012 en d00aModeling and control of quantum systems: An introduction0 aModeling and control of quantum systems An introduction bInstitute of Electrical and Electronics Engineers3 aThe scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/650500591nas a2200145 4500008004100000022001400041245003800055210003400093260000800127300001400135490000700149520022100156100002200377856004600399 2012 eng d a1432-083500aThe Monge problem in Wiener space0 aMonge problem in Wiener space cSep a101–1240 v453 aWe address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure γ.

1 aCavalletti, Fabio uhttps://doi.org/10.1007/s00526-011-0452-500826nas a2200133 4500008004300000245007200043210006900115260002100184520038600205100002000591700002500611700002000636856003600656 2012 en_Ud 00aNonlinear thin-walled beams with a rectangular cross-section-Part I0 aNonlinear thinwalled beams with a rectangular crosssectionPart I bWorld Scientific3 aOur aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results.1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/410401058nas a2200181 4500008004100000022001400041245009000055210006900145300001600214490000700230520047800237653002000715653001700735653002100752653001300773100001900786856007100805 2012 eng d a0362-546X00aA nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem0 anonresonance condition for radial solutions of a nonlinear Neuma a6191 - 62020 v753 aWe prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

10aNeumann problem10aNonresonance10aRadial solutions10aTime-map1 aSfecci, Andrea uhttp://www.sciencedirect.com/science/article/pii/S0362546X1200265901662nas a2200121 4500008004100000245009600041210006900137260001300206520124300219100002001462700002201482856003601504 2012 en d00aNon-uniqueness results for critical metrics of regularized determinants in four dimensions0 aNonuniqueness results for critical metrics of regularized determ bSpringer3 aThe regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger's half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions.1 aGursky, Matthew1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/655901861nas a2200145 4500008004100000245007600041210006900117260001300186520138500199653002701584100002001611700002101631700002701652856003601679 2012 en d00aNumerical modelling of installation effects for diaphragm walls in sand0 aNumerical modelling of installation effects for diaphragm walls bSpringer3 aThe scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic.10aConstitutive relations1 aConti, Riccardo1 ade Sanctis, Luca1 aViggiani, Giulia, M.B. uhttp://hdl.handle.net/1963/693401684nas a2200157 4500008004100000245004700041210004600088260001300134300001200147490000700159520120600166653002501372100002601397700002201423856008101445 2012 en d00aOgden-type energies for nematic elastomers0 aOgdentype energies for nematic elastomers bElsevier a402-4120 v473 aOgden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/ogden-type-energies-nematic-elastomers00559nas a2200121 4500008004100000245012000041210006900161260003700230300001400267490000700281100002300288856012600311 2012 eng d00aOne-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations0 aOnesigned harmonic solutions and signchanging subharmonic soluti bAdvanced Nonlinear Studies, Inc. a445–4630 v121 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/one-signed-harmonic-solutions-and-sign-changing-subharmonic-solutions-scalar-second00376nas a2200109 4500008004100000245007700041210006900118300001200187490000700199100002200206856003800228 2012 eng d00aOptimal Transport with Branching Distance Costs and the Obstacle Problem0 aOptimal Transport with Branching Distance Costs and the Obstacle a454-4820 v441 aCavalletti, Fabio uhttps://doi.org/10.1137/10080143301215nas a2200193 4500008004100000022001400041245010000055210006900155300001600224490000800240520056000248653002000808653002500828653003200853653002300885100002300908700001900931856007100950 2012 eng d a0022-039600aPairs of positive periodic solutions of second order nonlinear equations with indefinite weight0 aPairs of positive periodic solutions of second order nonlinear e a2900 - 29210 v2523 aWe study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu″+λa(t)g(u)=0,λ>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

10aCritical points10aNecessary conditions10aPairs of positive solutions10aPeriodic solutions1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961100389500499nas a2200133 4500008004100000245010300041210006900144260003300213300001500246490000700261100002200268700001900290856005600309 2012 eng d00aPeriodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces0 aPeriodic solutions of a system of coupled oscillators with onesi bKhayyam Publishing, Inc.c11 a993–10100 v251 aFonda, Alessandro1 aSfecci, Andrea uhttps://projecteuclid.org:443/euclid.die/135601224800752nas a2200133 4500008004100000245006500041210006500106260005100171300001400222490000700236520025200243100002300495856010000518 2012 eng d00aPeriodic solutions to superlinear planar Hamiltonian systems0 aPeriodic solutions to superlinear planar Hamiltonian systems bEuropean Mathematical Society Publishing House a127–1410 v693 aWe prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincare-Birkhoff fixed point theorem.

1 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/periodic-solutions-superlinear-planar-hamiltonian-systems01126nas a2200193 4500008004100000022001400041245013400055210006900189300001600258490000800274520044900282653002100731653001800752653003200770653001700802100002300819700001900842856007100861 2012 eng d a0022-039600aPositive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics0 aPositive periodic solutions of second order nonlinear equations a2922 - 29500 v2523 aWe prove the existence of a pair of positive T-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODEu″+aλ,μ(t)g(u)=0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T-periodic and sign indefinite weight of the form λa+(t)−μa−(t), with λ,μ>0 and large.

10aComplex dynamics10aPoincaré map10aPositive periodic solutions10aSubharmonics1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961100388302201nas a2200133 4500008004100000245010400041210006900145260001900214520173100233100002401964700002201988700002102010856003602031 2012 en d00aPredicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.0 aPredicting and characterizing selective multiple drug treatments bBioMed Central3 aBackground: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.1 aFacchetti, Giuseppe1 aAltafini, Claudio1 aZampieri, Mattia uhttp://hdl.handle.net/1963/651501387nas a2200133 4500008004300000245008800043210006900131260001300200520093500213100002101148700002201169700002601191856003601217 2012 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution0 aQuasistatic evolution for CamClay plasticity properties of the v bSpringer3 aCam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/390000946nas a2200145 4500008004100000245007300041210006900114260000900183520047100192653002200663100002900685700002500714700002500739856003600764 2012 en d00aQuasistatic evolution in non-associative plasticity - the cap models0 aQuasistatic evolution in nonassociative plasticity the cap model bSIAM3 aNon-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled.10aElasto-plasticity1 aBabadjian, Jean-Francois1 aFrancfort, Gilles A.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/413901651nas a2200133 4500008004100000245008400041210006900125520120500194653002101399100002101420700002001441700002001461856003601481 2012 en d00aReduction strategies for PDE-constrained oprimization problems in Haemodynamics0 aReduction strategies for PDEconstrained oprimization problems in3 aSolving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation.10ainverse problems1 aRozza, Gianluigi1 aManzoni, Andrea1 aNegri, Federico uhttp://hdl.handle.net/1963/633800498nas a2200121 4500008004100000245013300041210006900174260003300243300001400276490000700290100002300297856005600320 2012 eng d00aResonance at the first eigenvalue for first-order systems in the plane: vanishing Hamiltonians and the Landesman-Lazer condition0 aResonance at the first eigenvalue for firstorder systems in the bKhayyam Publishing, Inc.c05 a505–5260 v251 aGarrione, Maurizio uhttps://projecteuclid.org:443/euclid.die/135601267602076nas a2200145 4500008004100000245004700041210004700088520166300135653001801798100001901816700001701835700002001852700002201872856003601894 2012 en d00aReverse engineering the euglenoid movement0 aReverse engineering the euglenoid movement3 aEuglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.10amicroswimmers1 aArroyo, Marino1 aHeltai, Luca1 aMillán, Daniel1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/644400821nas a2200121 4500008004100000245007700041210006900118520040700187100002500594700002300619700002100642856003600663 2012 en d00aOn robust Lie-algebraic stability conditions for switched linear systems0 arobust Liealgebraic stability conditions for switched linear sys3 aThis paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters.1 aAgrachev, Andrei, A.1 aBaryshnikov, Yurij1 aLiberzon, Daniel uhttp://hdl.handle.net/1963/645500431nas a2200109 4500008004300000245011600043210006900159260001300228100002300241700002100264856003600285 2012 en_Ud 00aSBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension0 aSBV regularity for genuinely nonlinear strictly hyperbolic syste bSpringer1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/409100447nas a2200133 4500008004100000245008500041210006900126260001000195300001400205490000700219100002300226700001900249856004500268 2012 en d00aSBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)0 aSBV regularity for HamiltonJacobi equations with Hamiltonian dep bSISSA a2179-22030 v441 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1406600755nas a2200121 4500008004100000245010500041210006900146260001300215520032300228653002300551100002300574856003600597 2012 en d00aSBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension0 aSBV regularity of genuinely nonlinear hyperbolic systems of cons bElsevier3 aThe problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity10aHyperbolic systems1 aBianchini, Stefano uhttp://hdl.handle.net/1963/653500509nas a2200121 4500008004100000245009900041210006900140300001400209490000700223100002300230700001200253856012200265 2012 eng d00aSBV-like regularity for general hyperbolic systems of conservation laws in one space dimension0 aSBVlike regularity for general hyperbolic systems of conservatio a439–4720 v441 aBianchini, Stefano1 aYu, Lei uhttps://www.math.sissa.it/publication/sbv-regularity-general-hyperbolic-systems-conservation-laws-one-space-dimension00441nas a2200133 4500008004100000245008000041210006900121260001000190300001200200490000800212100002300220700001900243856004500262 2012 en d00aSBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian0 aSBVlike regularity for HamiltonJacobi equations with a convex Ha bSISSA a190-2080 v3911 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1390901260nas a2200193 4500008004100000022001400041245008600055210006900141300000900210490000700219520060600226653002800832653002500860653002800885653002700913653002400940100002600964856007600990 2012 eng d a1078-094700aSecond order approximations of quasistatic evolution problems in finite dimension0 aSecond order approximations of quasistatic evolution problems in a11250 v323 aIn this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

10adiscrete approximations10aperturbation methods10asaddle-node bifurcation10aSingular perturbations10avanishing viscosity1 aAgostiniani, Virginia uhttp://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f801314nas a2200133 4500008004100000245005400041210005200095260002100147300001100168490000600179520092400185100002201109856004901131 2012 eng d00aSelf-propelled micro-swimmers in a Brinkman fluid0 aSelfpropelled microswimmers in a Brinkman fluid bTaylor & Francis a88-1030 v63 aWe prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system.

1 aMorandotti, Marco uhttps://doi.org/10.1080/17513758.2011.61126001580nas a2200145 4500008004100000245008700041210006900128260001000197520093400207653011301141100001501254700002201269700002101291856012201312 2012 en d00aSimulation-based uncertainty quantification of human arterial network hemodynamics0 aSimulationbased uncertainty quantification of human arterial net bWiley3 aThis work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time.10auncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/simulation-based-uncertainty-quantification-human-arterial-network-hemodynamics00790nas a2200121 4500008004100000245014600041210006900187300001400256490000600270520032300276100001900599856005000618 2012 eng d00aSome applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles0 aSome applications of the SBV Regularity Theorem for entropy solu a163–1750 v33 aWe show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

1 aTonon, Daniela uhttps://hal.archives-ouvertes.fr/hal-0091840900518nas a2200109 4500008004100000245011900041210006900160100001700229700001700246700002200263856012300285 2012 eng d00aA stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves0 astable semilagrangian potential method for the simulation of shi1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/stable-semi-lagrangian-potential-method-simulation-ship-interaction-unsteady-and00752nas a2200121 4500008004100000245004700041210004600088260001000134520040400144100002500548700002100573856003600594 2012 en d00aSub-Riemannian structures on 3D Lie groups0 aSubRiemannian structures on 3D Lie groups bSISSA3 aWe give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

1 aAgrachev, Andrei, A.1 aBarilari, Davide uhttp://hdl.handle.net/1963/645300723nas a2200121 4500008004100000245003800041210003800079260001000117520039200127100002500519700002100544856003600565 2012 en d00aSystems of Quadratic Inequalities0 aSystems of Quadratic Inequalities bSISSA3 aWe present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2.1 aAgrachev, Andrei, A.1 aLerario, Antonio uhttp://hdl.handle.net/1963/707201511nas a2200145 4500008004100000245007100041210006900112260001000181520099600191653006801187100002001255700002901275700002501304856003601329 2012 en d00aTopological sensitivity analysis for high order elliptic operators0 aTopological sensitivity analysis for high order elliptic operato bSISSA3 aThe topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.10aTopological derivative, Elliptic operators, Polarization tensor1 aAmstutz, Samuel1 aNovotny, Antonio, André1 aVan Goethem, Nicolas uhttp://hdl.handle.net/1963/634302171nas a2200133 4500008004100000245006600041210006600107260001300173520175500186653001901941100001701960700002401977856003602001 2012 en d00aVariational implementation of immersed finite element methods0 aVariational implementation of immersed finite element methods bElsevier3 aDirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

10aTurbulent flow1 aHeltai, Luca1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/646201110nas a2200109 4500008004100000245003900041210003600080260001000116520082000126100001800946856003600964 2012 en d00aA Viscosity-driven crack evolution0 aViscositydriven crack evolution bSISSA3 aWe present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith’s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

1 aRacca, Simone uhttp://hdl.handle.net/1963/513001567nas a2200121 4500008004100000245008300041210006900124260001300193520115600206100002501362700002201387856003601409 2012 en d00aWeighted barycentric sets and singular Liouville equations on compact surfaces0 aWeighted barycentric sets and singular Liouville equations on co bElsevier3 aGiven a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]).1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/521800772nas a2200157 4500008004300000245008600043210007000129260003400199520023700233653003600470100001900506700002200525700001600547700001500563856003600578 2011 en_Ud 00aAxial symmetry of some steady state solutions to nonlinear Schrödinger equations0 aAxial symmetry of some steady state solutions to nonlinear Schrö bAmerican Mathematical Society3 aIn this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space.10aNonlinear Schrödinger equation1 aGui, Changfeng1 aMalchiodi, Andrea1 aXu, Haoyuan1 aYang, Paul uhttp://hdl.handle.net/1963/410000585nas a2200121 4500008004100000245011300041210006900154260001000223520015500233100002500388700001400413856003600427 2011 en d00aBishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry0 aBishop and Laplacian Comparison Theorems on Three Dimensional Co bSISSA3 aWe prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650800981nas a2200121 4500008004100000245006900041210006700110260001300177520058600190100002500776700002200801856003600823 2011 en d00aA class of existence results for the singular Liouville equation0 aclass of existence results for the singular Liouville equation bElsevier3 aWe consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional.1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/579300505nas a2200133 4500008004100000245010600041210007000147260004400217300001400261490000700275100001600282700001700298856005600315 2011 eng d00aCluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential0 aCluster solutions for the SchrödingerPoissonSlater problem aroun bReal Sociedad Matemática Españolac01 a253–2710 v271 aRuiz, David1 aVaira, Giusi uhttps://projecteuclid.org:443/euclid.rmi/129682883400613nas a2200097 4500008004100000245003000041210003000071520034600101100002000447856004800467 2011 en d00aCompactness by maximality0 aCompactness by maximality3 aWe derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$.1 aZagatti, Sandro uhttp://preprints.sissa.it/handle/1963/3531700435nas a2200121 4500008004100000245009600041210006900137260001300206300001200219490000700231100002100238856005400259 2011 eng d00aConcentration of solutions for a singularly perturbed Neumann problem in non-smooth domains0 aConcentration of solutions for a singularly perturbed Neumann pr bElsevier a107-1260 v281 aDipierro, Serena uhttp://www.numdam.org/item/AIHPC_2011__28_1_107_000974nas a2200121 4500008004300000245009300043210006900136260004800205520051800253100002100771700002400792856003600816 2011 en_Ud 00aCrack growth with non-interpenetration : a simplified proof for the pure Neumann problem0 aCrack growth with noninterpenetration a simplified proof for the bAmerican Institute of Mathematical Sciences3 aWe present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in.1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/380100428nas a2200133 4500008004100000245005400041210005300095260001000148653003100158100002600189700002200215700002100237856003600258 2011 en d00aCritical points of the Moser-Trudinger functional0 aCritical points of the MoserTrudinger functional bSISSA10aMoser-Trudinger inequality1 aDe Marchis, Francesca1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/459200524nas a2200133 4500008004100000245012600041210006900167260003300236100002000269700002100289700002200310700002200332856003600354 2011 en d00aCytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions0 aCytoskeletal actin networks in motile cells are critically selfo bNational Academy of Sciences1 aCardamone, Luca1 aLaio, Alessandro1 aShahapure, Rajesh1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/435800421nas a2200133 4500008004300000245004500043210004300088260004800131300001400179490000700193100002300200700001900223856004500242 2011 en_Ud 00aA Decomposition Theorem for BV functions0 aDecomposition Theorem for BV functions bAmerican Institute of Mathematical Sciences a1549-15660 v101 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1459900653nas a2200109 4500008004100000245009700041210006900138260001000207520027300217100001700490856003600507 2011 en d00aDimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms0 aDimensional Reduction and Approximation of Measures and Weakly D bSISSA3 aThis thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane.1 aDaneri, Sara uhttp://hdl.handle.net/1963/534801344nas a2200181 4500008004100000022001400041245010900055210007100164300001600235490000800251520070400259653002100963653003300984653002901017100002201046700002301068856007101091 2011 eng d a0022-039600aDouble resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations0 aDouble resonance with Landesman–Lazer conditions for planar syst a1052 - 10820 v2503 aWe prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman–Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer–Fučik spectrum.

10aDouble resonance10aLandesman–Lazer conditions10aNonlinear planar systems1 aFonda, Alessandro1 aGarrione, Maurizio uhttp://www.sciencedirect.com/science/article/pii/S002203961000290101116nas a2200145 4500008004100000245013000041210007000171260001300241300001600254490000800270520060700278100002000885700001900905856004600924 2011 eng d00aEmbedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials0 aEmbedding theorems and existence results for nonlinear Schröding bElsevier a1056–10850 v2513 aMotivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

1 aBonheure, Denis1 aMercuri, Carlo uhttps://doi.org/10.1016/j.jde.2011.04.01000728nas a2200121 4500008004300000245007600043210006900119260001300188520032600201100002400527700001900551856003600570 2011 en_Ud 00aEnergy release rate and stress intensity factor in antiplane elasticity0 aEnergy release rate and stress intensity factor in antiplane ela bElsevier3 aIn the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/378000628nas a2200109 4500008004100000245003900041210003800080260004800118520029500166100002100461856003600482 2011 en d00aEnnio De Giorgi and Γ-convergence0 aEnnio De Giorgi and Γconvergence bAmerican Institute of Mathematical Sciences3 aΓ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/530800369nas a2200109 4500008004300000245006000043210005700103260002100160100002300181700001900204856003600223 2011 en_Ud 00aAn Estimate on the Flow Generated by Monotone Operators0 aEstimate on the Flow Generated by Monotone Operators bTaylor & Francis1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/364601548nas a2200157 4500008004300000245008600043210006900129260005100198300001400249490000800263520101800271100002101289700002201310700002201332856003601354 2011 en_Ud 00aAn Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers0 aExistence and Uniqueness Result for the Motion of SelfPropelled bSociety for Industrial and Applied Mathematics a1345-13680 v 433 aWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/389401004nas a2200133 4500008004100000245007400041210006900115260003400184520055100218653001800769100002100787700002600808856003600834 2011 en d00aExistence for wave equations on domains with arbitrary growing cracks0 aExistence for wave equations on domains with arbitrary growing c bEuropean Mathematical Society3 aIn this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.10aWave equation1 aDal Maso, Gianni1 aLarsen, Cristopher J. uhttp://hdl.handle.net/1963/428400878nas a2200109 4500008004100000245008900041210006900130260002200199520048900221100002200710856003600732 2011 en d00aFracture and plastic models as Gamma-limits of damage models under different regimes0 aFracture and plastic models as Gammalimits of damage models unde bWalter de Gruyter3 aWe consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/506900898nas a2200145 4500008004100000245008300041210006900124260001300193490000800206520043400214653002000648100002600668700002200694856003600716 2011 en d00aGamma-convergence of energies for nematic elastomers in the small strain limit0 aGammaconvergence of energies for nematic elastomers in the small bSpringer0 v 233 aWe study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

10aLiquid crystals1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/414101081nas a2200121 4500008004100000245004900041210004900090260001000139520061100149653014200760100002100902856003600923 2011 en d00aGeneralised functions of bounded deformation0 aGeneralised functions of bounded deformation bSISSA3 aWe introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

10afree discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/637400398nas a2200109 4500008004100000245009300041210006900134260001000203100002500213700001400238856003600252 2011 en d00aGeneralized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds0 aGeneralized Ricci Curvature Bounds for Three Dimensional Contact bSISSA1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650700442nas a2200109 4500008004100000245003800041210003400079520013500113100002500248700002300273856003600296 2011 en d00aThe geometry of Maximum Principle0 ageometry of Maximum Principle3 aAn invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.1 aAgrachev, Andrei, A.1 aGamkrelidze, Revaz uhttp://hdl.handle.net/1963/645601189nas a2200109 4500008004100000245004200041210004200083260001000125520088700135100002101022856003601043 2011 en d00aHomology invariants of quadratic maps0 aHomology invariants of quadratic maps bSISSA3 aGiven a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete...1 aLerario, Antonio uhttp://hdl.handle.net/1963/624500860nas a2200181 4500008004100000022001400041245007500055210007200130300001600202490000700218520024700225653004900472653002400521100002300545700002200568700001700590856007100607 2011 eng d a0362-546X00aInfinitely many positive solutions for a Schrödinger–Poisson system0 aInfinitely many positive solutions for a Schrödinger–Poisson sys a5705 - 57210 v743 aWe are interested in the existence of infinitely many positive solutions of the Schrödinger–Poisson system −Δu+u+V(|x|)ϕu=|u|p−1u,x∈R3,−Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<p<5 and V(r

10aNon-autonomous Schrödinger–Poisson system10aPerturbation method1 ad’Avenia, Pietro1 aPomponio, Alessio1 aVaira, Giusi uhttp://www.sciencedirect.com/science/article/pii/S0362546X1100351801512nas a2200109 4500008004100000245009500041210006900136260002200205520111900227100002001346856003601366 2011 en d00aAn Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations0 aIntegroExtremization Approach for Non Coercive and Evolution Ham bHeldermann Verlag3 aWe devote the \\\\textit{integro-extremization} method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations \\\\begin{displaymath} \\\\begin{cases} F(Du)=0 & \\\\quad \\\\textrm{in} \\\\quad\\\\O\\\\cr u(x)=\\\\varphi(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in \\\\partial \\\\O, \\\\end{cases} \\\\end{displaymath} with a particular interest for non coercive hamiltonians $F$, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations \\\\begin{displaymath} \\\\begin{cases} \\\\frac{\\\\partial u}{\\\\partial t}+ F(\\\\nabla u)=0 & \\\\quad \\\\textrm{in} \\\\quad ]0,T[\\\\times \\\\O\\\\cr u(0,x)=\\\\eta(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in\\\\O \\\\cr u(t,x)=\\\\psi(x) & \\\\quad \\\\textrm{for} \\\\quad (t,x)\\\\in[0,T]\\\\times \\\\partial \\\\O. \\\\end{cases} \\\\end{displaymath} We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian $F$, on the domain $\\\\O$ and on the boundary datum, without any growth assumptions on $F$.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/553800383nas a2200109 4500008004300000245007000043210006900113260001300182100002300195700001900218856003600237 2011 en_Ud 00aInvariant manifolds for a singular ordinary differential equation0 aInvariant manifolds for a singular ordinary differential equatio bElsevier1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255401397nas a2200121 4500008004100000245006800041210006600109260001000175520100500185653002801190100002101218856003601239 2011 en d00aInvariants, volumes and heat kernels in sub-Riemannian geometry0 aInvariants volumes and heat kernels in subRiemannian geometry bSISSA3 aSub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]).10aSub-Riemannian geometry1 aBarilari, Davide uhttp://hdl.handle.net/1963/612401000nas a2200133 4500008004300000245005100043210005100094260002100145520060100166100001800767700002500785700002000810856003600830 2011 en_Ud 00aLarge Time Existence for Thin Vibrating Plates0 aLarge Time Existence for Thin Vibrating Plates bTaylor & Francis3 aWe construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/375501120nas a2200133 4500008004300000245010500043210006900148260001300217520065000230100001900880700002500899700002600924856003600950 2011 en_Ud 00aThe matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells0 amatching property of infinitesimal isometries on elliptic surfac bSpringer3 aUsing the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/339201329nas a2200169 4500008004100000022001400041245008700055210006900142260000800211300001400219490000700233520081100240100001801051700002201069700002201091856004601113 2011 eng d a1432-095900aMetastable equilibria of capillary drops on solid surfaces: a phase field approach0 aMetastable equilibria of capillary drops on solid surfaces a pha cSep a453–4710 v233 aWe discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

1 aFedeli, Livio1 aTurco, Alessandro1 aDeSimone, Antonio uhttps://doi.org/10.1007/s00161-011-0189-601532nas a2200277 4500008004100000022001600041245006500057210006300122260009400185300001600279490000900295520056700304653002100871653002200892653002200914653002400936653003200960653002500992653002101017653002901038653002401067653002401091100002401115700001901139856009601158 2011 eng d a{0218-2025}00aA MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION0 aMODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION a{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}b{WORLD SCIENTIFIC PUBL CO PTE LTD}c{OCT} a{2019-2047}0 v{21}3 a{In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.}

10aBrittle fracture10aCrack propagation10aenergy derivative10aenergy release rate10afree-discontinuity problems10aGriffith's criterion10alocal minimizers10astress intensity factor}10avanishing viscosity10a{Variational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttps://www.math.sissa.it/publication/model-crack-propagation-based-viscous-approximation-001064nas a2200193 4500008004100000020002200041245004100063210003700104260002800141300001400169520049000183100002300673700002200696700002100718700002400739700001900763700001600782856007200798 2011 eng d a978-1-4419-9554-400aThe Monge Problem in Geodesic Spaces0 aMonge Problem in Geodesic Spaces aBoston, MAbSpringer US a217–2333 aWe address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

1 aBianchini, Stefano1 aCavalletti, Fabio1 aBressan, Alberto1 aChen, Gui-Qiang, G.1 aLewicka, Marta1 aWang, Dehua uhttps://www.math.sissa.it/publication/monge-problem-geodesic-spaces00786nas a2200121 4500008004100000245007600041210006900117300001400186490000600200520033000206100002600536856010200562 2011 eng d00aMultiplicity of solutions for a mean field equation on compact surfaces0 aMultiplicity of solutions for a mean field equation on compact s a245–2570 v43 aWe consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

1 aDe Marchis, Francesca uhttps://www.math.sissa.it/publication/multiplicity-solutions-mean-field-equation-compact-surfaces00729nas a2200121 4500008004300000245009900043210006900142260001300211520030900224100002200533700001600555856003600571 2011 en_Ud 00aNew improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces0 aNew improved MoserTrudinger inequalities and singular Liouville bSpringer3 aWe consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/409900992nas a2200145 4500008004100000245009400041210006900135260003700204300001400241490000700255520041000262100002200672700002300694856012900717 2011 eng d00aNonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions0 aNonlinear resonance a comparison between LandesmanLazer and Ahma bAdvanced Nonlinear Studies, Inc. a391–4040 v113 aWe show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

1 aFonda, Alessandro1 aGarrione, Maurizio uhttps://www.math.sissa.it/publication/nonlinear-resonance-comparison-between-landesman-lazer-and-ahmad-lazer-paul-conditions00668nas a2200145 4500008004100000245007500041210006900116260001000185520019000195653003600385100002000421700002500441700002000466856003600486 2011 en d00aNonlinear thin-walled beams with a rectangular cross-section - Part II0 aNonlinear thinwalled beams with a rectangular crosssection Part bSISSA3 aIn this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..10aThin-walled cross-section beams1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/416901454nas a2200145 4500008004100000022001400041245009100055210007000146260000900216490000800225520090000233100002401133700002101157856013001178 2011 eng d a0012-709400aNonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces0 aNonlinear wave and Schrödinger equations on compact Lie groups a c20110 v1593 aWe develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr¨odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.1 aBerti, Massimiliano1 aProcesi, Michela uhttps://www.math.sissa.it/publication/nonlinear-wave-and-schr%C3%B6dinger-equations-compact-lie-groups-and-homogeneous-spaces00897nas a2200181 4500008004100000022001400041245008800055210006900143300001400212490000800226520028400234653002200518653003800540653002300578653002000601100002300621856007100644 2011 eng d a0022-247X00aA note on a superlinear indefinite Neumann problem with multiple positive solutions0 anote on a superlinear indefinite Neumann problem with multiple p a259 - 2680 v3773 aWe prove the existence of three positive solutions for the Neumann problem associated to u″+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta−(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

10aIndefinite weight10aNonlinear boundary value problems10apositive solutions10aShooting method1 aBoscaggin, Alberto uhttp://www.sciencedirect.com/science/article/pii/S0022247X1000879600977nas a2200145 4500008004300000245007900043210006900122260002100191520050000212653002100712100002300733700002200756700001700778856003600795 2011 en_Ud 00aNumerical Strategies for Stroke Optimization of Axisymmetric Microswimmers0 aNumerical Strategies for Stroke Optimization of Axisymmetric Mic bWorld Scientific3 aWe propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.10aOptimal swimming1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/365700449nas a2200109 4500008004300000245005100043210005100094260003400145520010000179100002400279856003600303 2011 en_Ud 00aOsservazioni sui teoremi di inversione globale0 aOsservazioni sui teoremi di inversione globale bEuropean Mathematical Society3 aSome global inversion theorems with applications to semilinear elliptic equation are discussed.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/406800295nas a2200097 4500008004100000245004400041210004100085100001700126700001900143856003500162 2011 eng d00aA planar bi-Lipschitz extension Theorem0 aplanar biLipschitz extension Theorem1 aDaneri, Sara1 aPratelli, Aldo uhttp://arxiv.org/abs/1110.612400420nas a2200109 4500008004300000245009100043210006900134260003400203653001700237100002000254856003600274 2011 en_Ud 00aPlanar loops with prescribed curvature: existence, multiplicity and uniqueness results0 aPlanar loops with prescribed curvature existence multiplicity an bAmerican Mathematical Society10aPlane curves1 aMusina, Roberta uhttp://hdl.handle.net/1963/384200842nas a2200109 4500008004300000245005800043210005600101260001300157520050500170100002100675856003600696 2011 en_Ud 00aA proof of Sudakov theorem with strictly convex norms0 aproof of Sudakov theorem with strictly convex norms bSpringer3 aWe establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem.1 aCaravenna, Laura uhttp://hdl.handle.net/1963/296700673nas a2200109 4500008004300000245010600043210006900149520026500218100002200483700002200505856003600527 2011 en_Ud 00aQuasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications0 aQuasiconvex envelopes of energies for nematic elastomers in the 3 aWe provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments.1 aCesana, Pierluigi1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/406500919nas a2200121 4500008004300000245013400043210006900177260004600246520042800292100002200720700001900742856003600761 2011 en_Ud 00aQuasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach0 aQuasistatic crack evolution for a cohesive zone model with diffe bCambridge University Press / EDP Sciences3 aA new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [6] is recovered. In this case, the convergence of the discrete time approximations is improved.1 aCagnetti, Filippo1 aToader, Rodica uhttp://hdl.handle.net/1963/235501263nas a2200277 4500008004100000022001600041245007000057210006900127260008600196300001400282490001000296520028400306653002100590653002200611653002400633653002200657653003200679653002500711653002600736653001800762653002600780653003100806653002400837100002400861856010000885 2011 eng d a{0373-3114}00aQuasistatic crack growth in finite elasticity with Lipschitz data0 aQuasistatic crack growth in finite elasticity with Lipschitz dat a{TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY}b{SPRINGER HEIDELBERG}c{JAN} a{165-194}0 v{190}3 a{We extend the recent existence result of Dal Maso and Lazzaroni (Ann Inst H Poincare Anal Non Lineaire 27:257-290, 2010) for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.}

10aBrittle fracture10aCrack propagation10aEnergy minimization10aFinite elasticity10afree-discontinuity problems10aGriffith's criterion10aNon-interpenetration}10aPolyconvexity10aQuasistatic evolution10aRate-independent processes10a{Variational models1 aLazzaroni, Giuliano uhttps://www.math.sissa.it/publication/quasistatic-crack-growth-finite-elasticity-lipschitz-data01427nas a2200145 4500008004300000245012100043210006900164260001300233520090600246653002401152100002101176700002201197700002601219856003601245 2011 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling0 aQuasistatic evolution for CamClay plasticity a weak formulation bSpringer3 aCam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

10aCam-Clay plasticity1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/367000823nas a2200121 4500008004100000245007200041210006900113260001300182520042600195100002200621700002200643856003600665 2011 en d00aQuasistatic evolution of sessile drops and contact angle hysteresis0 aQuasistatic evolution of sessile drops and contact angle hystere bSpringer3 aWe consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.1 aAlberti, Giovanni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/491201079nas a2200121 4500008004100000245007600041210006900117300001400186490000700200520062100207100002300828856010600851 2011 eng d00aResonance and Landesman-Lazer conditions for first order systems in R^20 aResonance and LandesmanLazer conditions for first order systems a153–1600 v663 aThe first part of the paper surveys the concept of resonance for $T$-periodic nonlinear problems. In the second part, some new results about existence conditions for nonlinear planar systems are presented. In particular, the Landesman-Lazer conditions are generalized to systems in $\mathbbR^2$ where the nonlinearity interacts with two resonant Hamiltonians. Such results apply to second order equations, generalizing previous theorems by Fabry [4] (for the undamped case), and Frederickson-Lazer [9] (for the case with friction). The results have been obtained with A. Fonda, and have been published in [8].

1 aGarrione, Maurizio uhttps://www.math.sissa.it/publication/resonance-and-landesman-lazer-conditions-first-order-systems-r201464nas a2200193 4500008004100000022001400041245012500055210006900180300001600249490000700265520078200272653003201054653003301086653001401119653002001133100002301153700002301176856007101199 2011 eng d a0362-546X00aResonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincaré–Birkhoff theorem0 aResonance and rotation numbers for planar Hamiltonian systems Mu a4166 - 41850 v743 aIn the general setting of a planar first order system (0.1)u′=G(t,u),u∈R2, with G:[0,T]×R2→R2, we study the relationships between some classical nonresonance conditions (including the Landesman–Lazer one) — at infinity and, in the unforced case, i.e. G(t,0)≡0, at zero — and the rotation numbers of “large” and “small” solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincaré–Birkhoff fixed point theorem, new multiplicity results for T-periodic solutions of unforced planar Hamiltonian systems Ju′=∇uH(t,u) and unforced undamped scalar second order equations x″+g(t,x)=0. In particular, by means of the Landesman–Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.

10aMultiple periodic solutions10aPoincaré–Birkhoff theorem10aResonance10aRotation number1 aBoscaggin, Alberto1 aGarrione, Maurizio uhttp://www.sciencedirect.com/science/article/pii/S0362546X1100181700804nas a2200133 4500008004100000245005600041210005400097260001300151520040700164100002300571700002300594700001700617856003600634 2011 en d00aSBV regularity for Hamilton-Jacobi equations in R^n0 aSBV regularity for HamiltonJacobi equations in Rn bSpringer3 aIn this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

1 aBianchini, Stefano1 aDe Lellis, Camillo1 aRobyr, Roger uhttp://hdl.handle.net/1963/491101135nas a2200145 4500008004300000245008100043210006900124260002300193520065600216100002100872700002100893700001900914700002000933856003600953 2011 en_Ud 00aSingular perturbation models in phase transitions for second order materials0 aSingular perturbation models in phase transitions for second ord bIndiana University3 aA variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.1 aChermisi, Milena1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/385800674nas a2200121 4500008004100000245006800041210006100109260001000170520028700180653002400467100002500491856003600516 2011 en d00aOn the Space of Symmetric Operators with Multiple Ground States0 aSpace of Symmetric Operators with Multiple Ground States bSISSA3 aWe study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed.10aMultiple eigenvalue1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/706900991nas a2200169 4500008004100000245009900041210006900140260001300209300001200222490000800234520046000242100002100702700002300723700002000746700001900766856003600785 2011 en d00aThe sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry0 asphere and the cut locus at a tangency point in twodimensional a bSpringer a141-1610 v17 3 aWe study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

1 aBonnard, Bernard1 aCharlot, Grégoire1 aGhezzi, Roberta1 aJanin, Gabriel uhttp://hdl.handle.net/1963/491400415nas a2200121 4500008004100000245007100041210006900112260001000181100002200191700002300213700002100236856003600257 2011 en d00aStructure of level sets and Sard-type properties of Lipschitz maps0 aStructure of level sets and Sardtype properties of Lipschitz map bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/465700512nas a2200121 4500008004100000245008400041210006900125260003700194300001300231490000700244100002300251856011600274 2011 eng d00aSubharmonic solutions of planar Hamiltonian systems: a rotation number approach0 aSubharmonic solutions of planar Hamiltonian systems a rotation n bAdvanced Nonlinear Studies, Inc. a77–1030 v111 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/subharmonic-solutions-planar-hamiltonian-systems-rotation-number-approach00785nas a2200121 4500008004100000245009300041210006900134300001400203490000700217520028800224100002300512856012800535 2011 eng d00aSubharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem0 aSubharmonic solutions of planar Hamiltonian systems via the Poin a115–1220 v663 aWe revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

1 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/subharmonic-solutions-planar-hamiltonian-systems-poincar%C3%A9%CC%81-birkhoff-theorem00731nas a2200133 4500008004300000245007500043210006900118260002800187520027600215100002200491700002600513700002200539856003600561 2011 en_Ud 00aSupercritical conformal metrics on surfaces with conical singularities0 aSupercritical conformal metrics on surfaces with conical singula bOxford University Press3 aWe study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

1 aBardelloni, Mauro1 aDe Marchis, Francesca1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/409501043nas a2200097 4500008004100000245013400041210006900175520055400244100001800798856012900816 2011 eng d00aThin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity0 aThinwalled beams with a crosssection of arbitrary geometry deriv3 aThe subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/thin-walled-beams-cross-section-arbitrary-geometry-derivation-linear-theories-starting00881nas a2200133 4500008004300000245008900043210007100132260001300203520043200216100001800648700002500666700002000691856003600711 2011 en_Ud 00aThe time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity0 atimedependent von Kármán plate equation as a limit of 3d nonline bSpringer3 aThe asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/383500843nas a2200169 4500008004100000022001400041245011600055210006900171300001600240490000700256520022700263653002300490653003700513653002500550100002700575856007100602 2011 eng d a0362-546X00aUniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter0 aUniqueness and nondegeneracy of the ground state for a quasiline a1731 - 17370 v743 aWe study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

10aBifurcation theory10aNonlinear Schrödinger equations10aStationary solutions1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S0362546X1000761300413nas a2200121 4500008004100000245007000041210006800111260001000179100002200189700002300211700002100234856003600255 2011 en d00aA uniqueness result for the continuity equation in two dimensions0 auniqueness result for the continuity equation in two dimensions bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/466302515nas a2200205 4500008004100000022001400041245009600055210006900151300001400220490000700234520182300241653002202064653002402086653003502110653001302145653003502158100002202193700002302215856007102238 2011 eng d a0021-782400aThe well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces0 awellposedness issue for the densitydependent Euler equations in a253 - 2780 v963 aThis work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.

10aBlow-up criterion10aCritical regularity10aIncompressible Euler equations10aLifespan10aNonhomogeneous inviscid fluids1 aDanchin, Raphaël1 aFanelli, Francesco uhttp://www.sciencedirect.com/science/article/pii/S002178241100051100340nas a2200097 4500008004100000245006800041210006700109260001000176100002000186856003600206 2010 en d00aAlmost-Riemannian Geometry from a Control Theoretical Viewpoint0 aAlmostRiemannian Geometry from a Control Theoretical Viewpoint bSISSA1 aGhezzi, Roberta uhttp://hdl.handle.net/1963/470500856nas a2200133 4500008004300000245010300043210006900146520038600215100002600601700002200627700001900649700001800668856003600686 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems. Part I: existence results0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340600912nas a2200133 4500008004300000245011700043210006900160520042800229100002600657700002200683700001900705700001800724856003600742 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340900703nas a2200121 4500008004100000245007900041210006900120260001000189520030700199100002500506700001400531856003600545 2010 en d00aContinuity of optimal control costs and its application to weak KAM theory0 aContinuity of optimal control costs and its application to weak bSISSA3 aWe prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/645900908nas a2200109 4500008004300000245010700043210006900150520050000219100001800719700002500737856003600762 2010 en_Ud 00aConvergence of equilibria of thin elastic rods under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic rods under physical gr3 aThe subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory.1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/408600984nas a2200109 4500008004300000245008100043210006900124520060700193100002100800700001700821856003600838 2010 en_Ud 00aThe disintegration of the Lebesgue measure on the faces of a convex function0 adisintegration of the Lebesgue measure on the faces of a convex 3 aWe consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

1 aCaravenna, Laura1 aDaneri, Sara uhttp://hdl.handle.net/1963/362200778nas a2200133 4500008004100000245004800041210004700089260001000136520038900146653002700535100002500562700002100587856003600608 2010 en d00aDynamics control by a time-varying feedback0 aDynamics control by a timevarying feedback bSISSA3 aWe consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable.10aDiscrete-time dynamics1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/646101221nas a2200109 4500008004300000245005800043210005800101520086900159100002301028700002401051856003601075 2010 en_Ud 00aEstimates on path functionals over Wasserstein Spaces0 aEstimates on path functionals over Wasserstein Spaces3 aIn this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.1 aBianchini, Stefano1 aBrancolini, Alessio uhttp://hdl.handle.net/1963/358300371nas a2200097 4500008004300000245008300043210006900126100002300195700001900218856003600237 2010 en_Ud 00aOn the Euler-Lagrange equation for a variational problem : the general case II0 aEulerLagrange equation for a variational problem the general cas1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/255100773nas a2200145 4500008004300000245007900043210006900122260001300191520030200204100001900506700002000525700002100545700002500566856003600591 2010 en_Ud 00aExact reconstruction of damaged color images using a total variation model0 aExact reconstruction of damaged color images using a total varia bElsevier3 aIn this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.1 aFonseca, Irene1 aLeoni, Giovanni1 aMaggi, Francesco1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/403901347nas a2200133 4500008004300000245006300043210006300106260001300169520093400182100001701116700002301133700002101156856003601177 2010 en_Ud 00aExistence of planar curves minimizing length and curvature0 aExistence of planar curves minimizing length and curvature bSpringer3 aIn this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.1 aBoscain, Ugo1 aCharlot, Grégoire1 aRossi, Francesco uhttp://hdl.handle.net/1963/410702590nas a2200265 4500008004100000245013200041210006900173260001000242520175000252100001702002700002402019700002002043700001902063700002102082700001802103700003002121700001802151700001702169700001702186700002002203700002202223700002402245700001902269856003602288 2010 en d00aGene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.0 aGene expression analysis of the emergence of epileptiform activi bWiley3 aWe report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

1 aMotti, Dario1 aLe Duigou, Caroline1 aChemaly, Nicole1 aWittner, Lucia1 aLazarevic, Dejan1 aKrmac, Helena1 aMarstrand, Troels, Torben1 aValen, Eivind1 aSanges, Remo1 aStupka, Elia1 aSandelin, Albin1 aCherubini, Enrico1 aGustincich, Stefano1 aMiles, Richard uhttp://hdl.handle.net/1963/448000947nas a2200181 4500008004100000022001400041245007300055210006900128300001600197490000800213520035200221653002500573653002000598653002300618653002700641100002600668856007100694 2010 eng d a0022-123600aGeneric multiplicity for a scalar field equation on compact surfaces0 aGeneric multiplicity for a scalar field equation on compact surf a2165 - 21920 v2593 aWe prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

10aGeneric multiplicity10aGeometric PDE's10aMorse inequalities10aScalar field equations1 aDe Marchis, Francesca uhttp://www.sciencedirect.com/science/article/pii/S002212361000269700848nas a2200133 4500008004100000245008600041210006900127300001400196490000700210520038600217100001900603700001900622856007300641 2010 eng d00aA global compactness result for the p-Laplacian involving critical nonlinearities0 aglobal compactness result for the pLaplacian involving critical a469–4930 v283 aWe prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

1 aMercuri, Carlo1 aWillem, Michel uhttp://www.aimsciences.org/journals/displayArticles.jsp?paperID=509701051nas a2200169 4500008004300000245007900043210006900122260003000191520049800221100001800719700002600737700002300763700001800786700002200804700001900826856003600845 2010 en_Ud 00aHomogeneous binary trees as ground states of quantum critical Hamiltonians0 aHomogeneous binary trees as ground states of quantum critical Ha bAmerican Physical Society3 a

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aMontangero, Simone1 aRizzi, Matteo1 aCirac, J. Ignacio1 aFazio, Rosario uhttp://hdl.handle.net/1963/390901188nas a2200157 4500008004300000245010800043210006900151260001900220520065100239100001800890700002300908700001800931700002600949700001900975856003600994 2010 en_Ud 00aHomogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems0 aHomogeneous multiscale entanglement renormalization ansatz tenso bIOP Publishing3 aIn this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

1 aRizzi, Matteo1 aMontangero, Simone1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/406700629nas a2200121 4500008004300000245007900043210006900122260002200191520021000213100002100423700002700444856003600471 2010 en_Ud 00aHomogenization of fiber reinforced brittle material: the intermediate case0 aHomogenization of fiber reinforced brittle material the intermed bWalter de Gruyter3 aWe derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/360700468nas a2200109 4500008004100000245005900041210005900100260001000159520012800169100002500297856003600322 2010 en d00aInvariant Lagrange submanifolds of dissipative systems0 aInvariant Lagrange submanifolds of dissipative systems bSISSA3 aWe study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M .1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645700369nas a2200085 4500008004100000245006200041210006200103100002200165856009600187 2010 eng d00aNew approximation results for free discontinuity problems0 aNew approximation results for free discontinuity problems1 aIurlano, Flaviana uhttps://www.math.sissa.it/publication/new-approximation-results-free-discontinuity-problems00409nas a2200109 4500008004300000245009100043210006900134100002100203700001900224700002000243856003600263 2010 en_Ud 00aNonlocal character of the reduced theory of thin films with higher order perturbations0 aNonlocal character of the reduced theory of thin films with high1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/375400493nas a2200109 4500008004100000245009300041210006900134100001700203700002300220700002000243856012000263 2010 eng d00aA normal form for generic 2-dimensional almost-Riemannian structures at a tangency point0 anormal form for generic 2dimensional almostRiemannian structures1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta uhttps://www.math.sissa.it/publication/normal-form-generic-2-dimensional-almost-riemannian-structures-tangency-point00335nas a2200085 4500008004300000245007700043210006900120100002400189856003600213 2010 en_Ud 00aOn the number of positive solutions of some semilinear elliptic problems0 anumber of positive solutions of some semilinear elliptic problem1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/408301159nas a2200121 4500008004300000245006200043210005800105260001300163520078100176100002300957700002100980856003601001 2010 en_Ud 00aOn optimality of c-cyclically monotone transference plans0 aoptimality of ccyclically monotone transference plans bElsevier3 aAbstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/402301187nas a2200145 4500008004300000245004000043210004000083520078100123100002300904700002200927700001700949700002000966700001900986856003601005 2010 en_Ud 00aOptimally swimming Stokesian Robots0 aOptimally swimming Stokesian Robots3 aWe study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca1 aLefebvre, Aline1 aMerlet, Benoit uhttp://hdl.handle.net/1963/392900902nas a2200169 4500008004100000020002200041245007700063210006900140260003600209300001200245520028600257100002200543700001800565700002200583700001700605856011000622 2010 eng d a978-90-481-9195-600aA Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena0 aPhase Field Approach to Wetting and Contact Angle Hysteresis Phe aDordrechtbSpringer Netherlands a51–633 aWe discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

1 aDeSimone, Antonio1 aFedeli, Livio1 aTurco, Alessandro1 aHackl, Klaus uhttps://www.math.sissa.it/publication/phase-field-approach-wetting-and-contact-angle-hysteresis-phenomena00784nas a2200097 4500008004300000245010500043210006900148520041300217100002000630856003600650 2010 en_Ud 00aPoles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis0 aPoles of Integrale Tritronquee and Anharmonic Oscillators Asympt3 aPoles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

1 aMasoero, Davide uhttp://hdl.handle.net/1963/384100526nas a2200133 4500008004100000245007800041210007200119260001900191300001400210490000800224100002100232700001700253856012200270 2010 eng d00aPositive solutions for some non-autonomous Schrödinger–Poisson systems0 aPositive solutions for some nonautonomous Schrödinger–Poisson sy bAcademic Press a521–5430 v2481 aCerami, Giovanna1 aVaira, Giusi uhttps://www.math.sissa.it/publication/positive-solutions-some-non-autonomous-schr%C3%B6dinger%E2%80%93poisson-systems01299nas a2200109 4500008004300000245006000043210005600103520095600159100001701115700002101132856003601153 2010 en_Ud 00aProjective Reeds-Shepp car on $S^2$ with quadratic cost0 aProjective ReedsShepp car on S2 with quadratic cost3 aFix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/266800550nas a2200109 4500008004300000245008300043210006900126520016900195100002100364700001900385856003600404 2010 en_Ud 00aQuasistatic crack growth in elasto-plastic materials: the two-dimensional case0 aQuasistatic crack growth in elastoplastic materials the twodimen3 aWe study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/296400595nas a2200109 4500008004300000245007600043210006900119520021600188100002100404700002400425856003600449 2010 en_Ud 00aQuasistatic crack growth in finite elasticity with non-interpenetration0 aQuasistatic crack growth in finite elasticity with noninterpenet3 aWe present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/339701311nas a2200121 4500008004300000245008200043210006900125520088800194653002401082100002101106700002601127856003601153 2010 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case0 aQuasistatic evolution for CamClay plasticity the spatially homog3 aWe study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.

10aCam-Clay plasticity1 aDal Maso, Gianni1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/367101168nas a2200157 4500008004100000022001400041245008800055210006900143300000900212490000700221520061900228653003000847653003100877100002600908856007600934 2010 eng d a1078-094700aQuasistatic evolution for plasticity with softening: The spatially homogeneous case0 aQuasistatic evolution for plasticity with softening The spatiall a11890 v273 aThe spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.

10aplasticity with softening10arate independent processes1 aSolombrino, Francesco uhttp://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f01810nas a2200121 4500008004300000245007000043210006600113520141500179100001901594700002201613700001701635856003601652 2010 en_Ud 00aThe role of membrane viscosity in the dynamics of fluid membranes0 arole of membrane viscosity in the dynamics of fluid membranes3 aFluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.1 aArroyo, Marino1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/393000486nas a2200121 4500008004100000245011700041210006900158260003300227300001400260490000700274100002700281856005600308 2010 eng d00aSemiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential0 aSemiclassical evolution of two rotating solitons for the Nonline bKhayyam Publishing, Inc.c03 a315–3480 v151 aSelvitella, Alessandro uhttps://projecteuclid.org:443/euclid.ade/135585475200622nas a2200109 4500008004300000245010100043210006900144520021400213100002900427700002000456856003600476 2010 en_Ud 00aSharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials0 aSharp nonexistence results for a linear elliptic inequality invo3 aIn this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.1 aFall, Mouhamed Moustapha1 aMusina, Roberta uhttp://hdl.handle.net/1963/386900794nas a2200121 4500008004300000245008000043210006900123520037400192100001900566700002500585700002600610856003600636 2010 en_Ud 00aShell theories arising as low energy Gamma-limit of 3d nonlinear elasticity0 aShell theories arising as low energy Gammalimit of 3d nonlinear 3 aWe discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/260100741nas a2200133 4500008004100000245007400041210006900115260002400184300001100208490000700219520030000226100002200526856005900548 2010 eng d00aStable determination of an immersed body in a stationary Stokes fluid0 aStable determination of an immersed body in a stationary Stokes bIOP Publishingcnov a1250150 v263 aWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

1 aBallerini, Andrea uhttps://doi.org/10.1088%2F0266-5611%2F26%2F12%2F12501501029nas a2200157 4500008004100000245008100041210006900122300001000191490000800201520055000209100001800759700001700777700001600794700001800810856004300828 2010 eng d00aA three-dimensional model for the dynamics and hydrodynamics of rowing boats0 athreedimensional model for the dynamics and hydrodynamics of row a51-610 v2243 aThis paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

1 aFormaggia, L.1 aMola, Andrea1 aParolini, N1 aPischiutta, M uhttps://doi.org/10.1243/17543371jset4601439nas a2200181 4500008004300000245007000043210006800113260001300181300001200194490000700206520090200213100002501115700001701140700002301157700002001180700002101200856003601221 2010 en_Ud 00aTwo-dimensional almost-Riemannian structures with tangency points0 aTwodimensional almostRiemannian structures with tangency points bElsevier a793-8070 v273 aTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttp://hdl.handle.net/1963/387000894nas a2200109 4500008004100000245007500041210006900116260001000185520052800195100002500723856003600748 2010 en d00aWell-posed infinite horizon variational problems on a compact manifold0 aWellposed infinite horizon variational problems on a compact man bSISSA3 aWe give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645800396nas a2200109 4500008004300000245007300043210006900116100002200185700002300207700002000230856003600250 2009 en_Ud 00aBiological Fluid Dynamics, Non-linear Partial Differential Equations0 aBiological Fluid Dynamics Nonlinear Partial Differential Equatio1 aDeSimone, Antonio1 aAlouges, François1 aLefebvre, Aline uhttp://hdl.handle.net/1963/263002193nas a2200109 4500008004300000245008700043210006900130520180600199100002302005700001902028856003602047 2009 en_Ud 00aThe boundary Riemann solver coming from the real vanishing viscosity approximation0 aboundary Riemann solver coming from the real vanishing viscosity3 aWe study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/183100355nas a2200097 4500008004300000245006900043210006800112100002100180700002000201856003600221 2009 en_Ud 00aBubbles with prescribed mean curvature: the variational approach0 aBubbles with prescribed mean curvature the variational approach1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/365900337nas a2200097 4500008004300000245006000043210005800103100002300161700001900184856003600203 2009 en_Ud 00aA connection between viscous profiles and singular ODEs0 aconnection between viscous profiles and singular ODEs1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255501061nas a2200133 4500008004300000245009500043210006900138520060700207100002200814700001700836700002100853700001700874856003600891 2009 en_Ud 00aControllability of the discrete-spectrum Schrodinger equation driven by an external field0 aControllability of the discretespectrum Schrodinger equation dri3 aWe prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.1 aChambrion, Thomas1 aMason, Paolo1 aSigalotti, Mario1 aBoscain, Ugo uhttp://hdl.handle.net/1963/254700583nas a2200109 4500008004300000245005200043210005200095520024400147100002500391700002100416856003600437 2009 en_Ud 00aControllability on the group of diffeomorphisms0 aControllability on the group of diffeomorphisms3 aGiven a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/339600806nas a2200121 4500008004300000245007400043210006700117260004800184520037100232100002100603700002400624856003600648 2009 en_Ud 00aOn the convergence of viscous approximations after shock interactions0 aconvergence of viscous approximations after shock interactions bAmerican Institute of Mathematical Sciences3 aWe consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.1 aBressan, Alberto1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/341201885nas a2200121 4500008004300000245008700043210006900130260001300199520148100212100001801693700001601711856003601727 2009 en_Ud 00aDifferential geometry of curves in Lagrange Grassmannians with given Young diagram0 aDifferential geometry of curves in Lagrange Grassmannians with g bElsevier3 aCurves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions.1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/381901141nas a2200133 4500008004300000245014200043210006900185260004800254520060000302100002000902700002200922700002700944856003600971 2009 en_Ud 00aDiscrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers0 aDiscretetocontinuum limits for strainalignmentcoupled systems Ma bAmerican Institute of Mathematical Sciences3 aIn the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.1 aCicalese, Marco1 aDeSimone, Antonio1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/378800354nas a2200097 4500008004100000245007900041210006900120260001000189100002100199856003600220 2009 en d00aThe Disintegration Theorem and Applications to Optimal Mass Transportation0 aDisintegration Theorem and Applications to Optimal Mass Transpor bSISSA1 aCaravenna, Laura uhttp://hdl.handle.net/1963/590000512nas a2200097 4500008004300000245009600043210006900139520015000208100002000358856003600378 2009 en_Ud 00aExistence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities0 aExistence of extremals for the Mazya and for the CaffarelliKohnN3 aThis paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984.1 aMusina, Roberta uhttp://hdl.handle.net/1963/273900318nas a2200085 4500008004300000245006800043210006400111100002100175856003600196 2009 en_Ud 00aAn existence result for the Monge problem in R^n with norm cost0 aexistence result for the Monge problem in Rn with norm cost1 aCaravenna, Laura uhttp://hdl.handle.net/1963/364700624nas a2200109 4500008004300000245007200043210006400115520025500179100002300434700002100457856003600478 2009 en_Ud 00aOn the extremality, uniqueness and optimality of transference plans0 aextremality uniqueness and optimality of transference plans3 aWe consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/369208321nas a2200145 4500008004100000245008100041210006900122260001300191300001600204490000700220520785400227100003008081700001908111856004508130 2009 eng d00aFoliations of small tubes in Riemannian manifolds by capillary minimal discs0 aFoliations of small tubes in Riemannian manifolds by capillary m bElsevier a4422–44400 v703 aLetting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://doi.org/10.1016/j.na.2008.10.02400381nas a2200097 4500008004300000245009500043210006900138100002000207700002000227856003600247 2009 en_Ud 00aHardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions0 aHardySobolevMazja inequalities symmetry and breaking symmetry of1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/256900927nas a2200133 4500008004300000245007300043210006900116520048700185100002100672700001900693700002000712700002500732856003600757 2009 en_Ud 00aA higher order model for image restoration: the one dimensional case0 ahigher order model for image restoration the one dimensional cas3 aThe higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/317401152nas a2200121 4500008004300000245007700043210006900120260000900189520075400198100002100952700002100973856003600994 2009 en_Ud 00aHomogenization of fiber reinforced brittle materials: the extremal cases0 aHomogenization of fiber reinforced brittle materials the extrema bSIAM3 aWe analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.1 aBarchiesi, Marco1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/270501520nas a2200133 4500008004300000245008600043210006900129520106500198100002501263700001701288700002401305700002101329856003601350 2009 en_Ud 00aThe intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups0 aintrinsic hypoelliptic Laplacian and its heat kernel on unimodul3 aWe present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aGauthier, Jean-Paul1 aRossi, Francesco uhttp://hdl.handle.net/1963/266902238nas a2200109 4500008004300000245010000043210006900143520184600212100001602058700001802074856003602092 2009 en_Ud 00aJacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries0 aJacobi Equations and Comparison Theorems for Corank 1 SubRiemann3 aThe Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields.1 aChengbo, Li1 aZelenko, Igor uhttp://hdl.handle.net/1963/373600903nas a2200145 4500008004100000245006400041210006300105260002900168300001600197490000700213520043600220100003000656700001900686856005200705 2009 eng d00aMinimal disc-type surfaces embedded in a perturbed cylinder0 aMinimal disctype surfaces embedded in a perturbed cylinder bKhayyam Publishing, Inc. a1115–11240 v223 aIn the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://projecteuclid.org/euclid.die/135601940700530nas a2200121 4500008004300000245006400043210006200107520013300169100001900302700002500321700002600346856003600372 2009 en_Ud 00aA nonlinear theory for shells with slowly varying thickness0 anonlinear theory for shells with slowly varying thickness3 aWe study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/263200356nas a2200085 4500008004300000245010200043210006900145100002000214856003600234 2009 en_Ud 00aA note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas0 anote on the paper Optimizing improved Hardy inequalities by S Fi1 aMusina, Roberta uhttp://hdl.handle.net/1963/269801018nas a2200109 4500008004300000245005800043210005800101520067400159100002500833700001400858856003600872 2009 en_Ud 00aOptimal transportation under nonholonomic constraints0 aOptimal transportation under nonholonomic constraints3 aWe study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/217600735nas a2200109 4500008004300000245009500043210006900138520033900207100002100546700002200567856003600589 2009 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions0 aQuasistatic evolution for CamClay plasticity examples of spatial3 aWe study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation.1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/339501324nas a2200121 4500008004100000245008000041210006900121300001300190490000700203520085200210100002601062856011401088 2009 eng d00aQuasistatic evolution problems for nonhomogeneous elastic plastic materials0 aQuasistatic evolution problems for nonhomogeneous elastic plasti a89–1190 v163 aThe paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

1 aSolombrino, Francesco uhttps://www.math.sissa.it/publication/quasistatic-evolution-problems-nonhomogeneous-elastic-plastic-materials01411nas a2200121 4500008004300000245004300043210004300086260003000129520105300159100001901212700002201231856003601253 2009 en_Ud 00aRelaxation dynamics of fluid membranes0 aRelaxation dynamics of fluid membranes bAmerican Physical Society3 aWe study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/361800362nas a2200097 4500008004300000245007600043210006900119100002000188700002000208856003600228 2009 en_Ud 00aOn a Sobolev type inequality related to the weighted p-Laplace operator0 aSobolev type inequality related to the weighted pLaplace operato1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/261300857nas a2200133 4500008004100000245010700041210007200148300001200220490000700232520040100239100002000640700001700660856004600677 2009 eng d00aSolutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions0 aSolutions of the Schrödinger–Poisson problem concentrating on sp a707-7200 v193 aIn this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

1 aIanni, Isabella1 aVaira, Giusi uhttps://doi.org/10.1142/S021820250900358900350nas a2200097 4500008004300000245006900043210006900112260001300181100002200194856003600216 2009 en_Ud 00aSome new entire solutions of semilinear elliptic equations on Rn0 aSome new entire solutions of semilinear elliptic equations on Rn bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/364500893nas a2200109 4500008004300000245007600043210006900119520051500188100002200703700002200725856003600747 2009 en_Ud 00aStrain-order coupling in nematic elastomers: equilibrium configurations0 aStrainorder coupling in nematic elastomers equilibrium configura3 aWe consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations.1 aCesana, Pierluigi1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/270000754nas a2200121 4500008004300000245007200043210006900115520035700184100002200541700001600563700001700579856003600596 2009 en_Ud 00aStratos: a code for 3D free surface flows with floating constraints0 aStratos a code for 3D free surface flows with floating constrain3 aThis report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......1 aDeSimone, Antonio1 aBianchi, B.1 aHeltai, Luca uhttp://hdl.handle.net/1963/370100841nas a2200121 4500008004300000245007600043210006900119520043200188100002200620700001700642700002400659856003600683 2009 en_Ud 00aTools for the Solution of PDEs Defined on Curved Manifolds with deal.II0 aTools for the Solution of PDEs Defined on Curved Manifolds with 3 aThe deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.1 aDeSimone, Antonio1 aHeltai, Luca1 aManigrasso, Cataldo uhttp://hdl.handle.net/1963/370000454nas a2200109 4500008004300000245012300043210006900166100002100235700002600256700002600282856003600308 2009 en_Ud 00aA variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions0 avariational model for quasistatic crack growth in nonlinear elas1 aDal Maso, Gianni1 aGiacomini, Alessandro1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/267500547nas a2200109 4500008004300000245005600043210005200099260003400151520019600185100002000381856003600401 2009 en_Ud 00aOn viscosity solutions of Hamilton-Jacobi equations0 aviscosity solutions of HamiltonJacobi equations bAmerican Mathematical Society3 aWe consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/342000988nas a2200133 4500008004100000022001400041245012300055210007000178300001600248490000800264520048400272100002700756856007100783 2008 eng d a0022-039600aAsymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields0 aAsymptotic evolution for the semiclassical nonlinear Schrödinger a2566 - 25840 v2453 aIn this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S002203960800243X00588nas a2200097 4500008004300000245007600043210006900119520024400188100002200432856003600454 2008 en_Ud 00aConcentrating solutions of some singularly perturbed elliptic equations0 aConcentrating solutions of some singularly perturbed elliptic eq3 aWe study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/265700915nas a2200145 4500008004100000245009900041210007000140260003700210300001400247490000600261520034300267100002000610700001700630856012200647 2008 eng d00aOn concentration of positive bound states for the Schrödinger-Poisson problem with potentials0 aconcentration of positive bound states for the SchrödingerPoisso bAdvanced Nonlinear Studies, Inc. a573–5950 v83 aWe study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

1 aIanni, Isabella1 aVaira, Giusi uhttps://www.math.sissa.it/publication/concentration-positive-bound-states-schr%C3%B6dinger-poisson-problem-potentials01160nas a2200109 4500008004300000245007000043210006900113520078700182100002500969700002000994856003601014 2008 en_Ud 00aConvergence of equilibria of three-dimensional thin elastic beams0 aConvergence of equilibria of threedimensional thin elastic beams3 aA convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/189600386nas a2200109 4500008004300000245006300043210006300106260003100169100002100200700001900221856003600240 2008 en_Ud 00aDecomposition results for functions with bounded variation0 aDecomposition results for functions with bounded variation bUnione Matematica Italiana1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/353500657nas a2200097 4500008004300000245007900043210006900122520031000191100002200501856003600523 2008 en_Ud 00aEntire solutions of autonomous equations on Rn with nontrivial asymptotics0 aEntire solutions of autonomous equations on Rn with nontrivial a3 aWe prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/264000301nas a2200097 4500008004300000245004300043210003900086260002100125100002100146856003600167 2008 en_Ud 00aAn entropy based Glimm-type functional0 aentropy based Glimmtype functional bWorld Scientific1 aCaravenna, Laura uhttp://hdl.handle.net/1963/405100962nas a2200121 4500008004300000245008100043210006900124260000900193520056300202100001700765700002200782856003600804 2008 en_Ud 00aEulerian calculus for the displacement convexity in the Wasserstein distance0 aEulerian calculus for the displacement convexity in the Wasserst bSIAM3 aIn this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://hdl.handle.net/1963/341300797nas a2200109 4500008004300000245006300043210006000106520044300166100002000609700002200629856003600651 2008 en_Ud 00aExistence of conformal metrics with constant $Q$-curvature0 aExistence of conformal metrics with constant Qcurvature3 aGiven a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.1 aDjadli, Zindine1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/230800637nas a2200109 4500008004300000245004900043210004900092520031300141100001300454700002400467856003600491 2008 en_Ud 00aForced Vibrations of a Nonhomogeneous String0 aForced Vibrations of a Nonhomogeneous String3 aWe prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme.1 aBaldi, P1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/264301559nas a2200157 4500008004300000245008100043210006900124520105300193100001801246700001801264700002501282700002001307700001901327700001901346856003601365 2008 en_Ud 00aFulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices0 aFuldeFerrellLarkinOvchinnikov pairing in onedimensional optical 3 aSpin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

1 aRizzi, Matteo1 aPolini, Marco1 aCazalilla, Miguel A.1 aBakhtiari, M.R.1 aTosi, Mario P.1 aFazio, Rosario uhttp://hdl.handle.net/1963/269401551nas a2200121 4500008004300000245007900043210006900122520113900191100002501330700001701355700002101372856003601393 2008 en_Ud 00aA Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds0 aGaussBonnetlike formula on twodimensional almostRiemannian manif3 aWe consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/186901036nas a2200133 4500008004300000245007100043210006900114520059000183100002100773700002200794700002500816700002500841856003600866 2008 en_Ud 00aGlobally stable quasistatic evolution in plasticity with softening0 aGlobally stable quasistatic evolution in plasticity with softeni3 aWe study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/196500681nas a2200109 4500008004300000245012000043210006900163520026100232100002100493700002100514856003600535 2008 en_Ud 00aGradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics0 aGradient bounds for minimizers of free discontinuity problems re3 aIn this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.1 aDal Maso, Gianni1 aGarroni, Adriana uhttp://hdl.handle.net/1963/172300870nas a2200109 4500008004300000245007800043210006900121520049600190100001700686700002100703856003600724 2008 en_Ud 00aInvariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces0 aInvariant CarnotCaratheodory metrics on S3 SO3 SL2 and Lens Spac3 aIn this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/214400382nas a2200097 4500008004300000245009400043210006900137100002300206700001900229856003600248 2008 en_Ud 00aInvariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems0 aInvariant Manifolds for Viscous Profiles of a Class of Mixed Hyp1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/340001845nas a2200133 4500008004300000245006800043210006700111520142200178100001701600700002101617700001701638700002001655856003601675 2008 en_Ud 00aLimit Time Optimal Syntheses for a control-affine system on S²0 aLimit Time Optimal Syntheses for a controlaffine system on S²3 aFor $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.1 aMason, Paolo1 aSalmoni, Rebecca1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/186200334nas a2200085 4500008004300000245008000043210006900123100002000192856003600212 2008 en_Ud 00aMinimization of non quasiconvex functionals by integro-extremization method0 aMinimization of non quasiconvex functionals by integroextremizat1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276100355nas a2200085 4500008004300000245010100043210006900144100002000213856003600233 2008 en_Ud 00aMinimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations0 aMinimizers of non convex scalar functionals and viscosity soluti1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276000352nas a2200097 4500008004300000245006500043210006500108260002300173100002200196856003600218 2008 en_Ud 00aMorse theory and a scalar field equation on compact surfaces0 aMorse theory and a scalar field equation on compact surfaces bKhayyam Publishing1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353100342nas a2200097 4500008004300000245006300043210006200106100002400168700001600192856003600208 2008 en_Ud 00aMultiple bound states for the Schroedinger-Poisson problem0 aMultiple bound states for the SchroedingerPoisson problem1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/267900355nas a2200085 4500008004300000245009600043210006900139100002500208856003600233 2008 en_Ud 00aA note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces0 anote on the differentiability of Lipschitz functions and the cha1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/265401131nas a2200133 4500008004300000245006500043210006400108260001300172520071100185100002300896700002200919700002000941856003600961 2008 en_Ud 00aOptimal Strokes for Low Reynolds Number Swimmers: An Example0 aOptimal Strokes for Low Reynolds Number Swimmers An Example bSpringer3 aSwimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).1 aAlouges, François1 aDeSimone, Antonio1 aLefebvre, Aline uhttp://hdl.handle.net/1963/400600618nas a2200133 4500008004100000245011000041210007000151260001300221300001400234490000700248520012200255100001900377856008800396 2008 eng d00aPositive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity0 aPositive solutions of nonlinear SchrödingerPoisson systems with bCiteseer a211–2270 v193 aWe deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

1 aMercuri, Carlo uhttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635&rep=rep1&type=pdf00444nas a2200121 4500008004300000245009700043210006900140100001700209700001800226700002200244700002000266856003600286 2008 en_Ud 00aRelaxation of some transversally isotropic energies and applications to smectic A elastomers0 aRelaxation of some transversally isotropic energies and applicat1 aAdams, James1 aConti, Sergio1 aDeSimone, Antonio1 aDolzmann, Georg uhttp://hdl.handle.net/1963/191201111nas a2200121 4500008004300000245007200043210006900115520069700184100002200881700002500903700002500928856003600953 2008 en_Ud 00aA second order minimality condition for the Mumford-Shah functional0 asecond order minimality condition for the MumfordShah functional3 aA new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.1 aCagnetti, Filippo1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/195500611nas a2200121 4500008004300000245008600043210006900129520019400198100002400392700002100416700001600437856003600453 2008 en_Ud 00aSolitons of linearly coupled systems of semilinear non-autonomous equations on Rn0 aSolitons of linearly coupled systems of semilinear nonautonomous3 aUsing concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations.1 aAmbrosetti, Antonio1 aCerami, Giovanna1 aRuiz, David uhttp://hdl.handle.net/1963/217500349nas a2200097 4500008004300000245006900043210006800112100001700180700001800197856003600215 2008 en_Ud 00aStability of planar switched systems: the nondiagonalizable case0 aStability of planar switched systems the nondiagonalizable case1 aBoscain, Ugo1 aBalde, Moussa uhttp://hdl.handle.net/1963/185700725nas a2200097 4500008004300000245008100043210006900124520037600193100002200569856003600591 2008 en_Ud 00aTopological methods for an elliptic equation with exponential nonlinearities0 aTopological methods for an elliptic equation with exponential no3 aWe consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/259401148nas a2200121 4500008004300000245006300043210006200106520076200168100002000930700002200950700001800972856003600990 2008 en_Ud 00aTransition layer for the heterogeneous Allen-Cahn equation0 aTransition layer for the heterogeneous AllenCahn equation3 aWe consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aWei, Juncheng uhttp://hdl.handle.net/1963/265600781nas a2200133 4500008004100000020002200041245006700063210006700130260001300197520035900210100002300569700001900592856003600611 2008 en d a978-3-642-21718-000aTransport Rays and Applications to Hamilton–Jacobi Equations0 aTransport Rays and Applications to Hamilton–Jacobi Equations bSpringer3 aThe aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully).1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/546301276nas a2200133 4500008004300000245008900043210006900132520081200201100002101013700002201034700002501056700002501081856003601106 2008 en_Ud 00aA vanishing viscosity approach to quasistatic evolution in plasticity with softening0 avanishing viscosity approach to quasistatic evolution in plastic3 aWe deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/184400645nas a2200121 4500008004300000245011200043210006900155520019600224100002300420700002200443700002200465856003600487 2007 en_Ud 00aAsymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy0 aAsymptotic behaviour of smooth solutions for partially dissipati3 aWe study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition.1 aBianchini, Stefano1 aHanouzet, Bernard1 aNatalini, Roberto uhttp://hdl.handle.net/1963/178001700nas a2200121 4500008004300000245004200043210004200085520136200127100002101489700001601510700001601526856003601542 2007 en_Ud 00aAsymptotic variational wave equations0 aAsymptotic variational wave equations3 aWe investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data.1 aBressan, Alberto1 aPing, Zhang1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218200318nas a2200097 4500008004300000245005100043210005000094100002200144700001800166856003600184 2007 en_Ud 00aBoundary interface for the Allen-Cahn equation0 aBoundary interface for the AllenCahn equation1 aMalchiodi, Andrea1 aWei, Juncheng uhttp://hdl.handle.net/1963/202700420nas a2200121 4500008004100000245006400041210006300105260003700168100002200205700001700227700001800244856003600262 2007 en d00aBoundary-clustered interfaces for the Allen–Cahn equation0 aBoundaryclustered interfaces for the Allen–Cahn equation bMathematical Sciences Publishers1 aMalchiodi, Andrea1 aNi, Wei-Ming1 aWei, Juncheng uhttp://hdl.handle.net/1963/508900820nas a2200121 4500008004300000245004900043210004800092520045600140100001700596700002100613700002800634856003600662 2007 en_Ud 00aBV instability for the Lax-Friedrichs scheme0 aBV instability for the LaxFriedrichs scheme3 aIt is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.1 aBaiti, Paolo1 aBressan, Alberto1 aJenssen, Helge Kristian uhttp://hdl.handle.net/1963/233500919nas a2200109 4500008004300000245008500043210006900128520053400197100002000731700002200751856003600773 2007 en_Ud 00aConcentration on minimal submanifolds for a singularly perturbed Neumann problem0 aConcentration on minimal submanifolds for a singularly perturbed3 aWe consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $13 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series.1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218600873nas a2200133 4500008004300000245009700043210006900140520040800209100002500617700001900642700002100661700002100682856003600703 2007 en_Ud 00aOn finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s0 afinitedimensional projections of distributions for solutions of 3 aThe paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension.1 aAgrachev, Andrei, A.1 aKuksin, Sergei1 aSarychev, Andrey1 aShirikyan, Armen uhttp://hdl.handle.net/1963/201200617nas a2200109 4500008004300000245007000043210006900113520025100182100001700433700002100450856003600471 2007 en_Ud 00aGaussian estimates for hypoelliptic operators via optimal control0 aGaussian estimates for hypoelliptic operators via optimal contro3 aWe obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.1 aBoscain, Ugo1 aPolidoro, Sergio uhttp://hdl.handle.net/1963/199401180nas a2200109 4500008004300000245005200043210005000095520085100145100001700996700002101013856003601034 2007 en_Ud 00aHigh-order angles in almost-Riemannian geometry0 aHighorder angles in almostRiemannian geometry3 aLet X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/199501450nas a2200169 4500008004300000245007300043210006900116520092200185100001801107700001801125700001801143700001901161700001901180700002601199700001901225856003601244 2007 en_Ud 00aLuther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas0 aLutherEmery Phase and AtomicDensity Waves in a Trapped Fermion G3 a

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600410nas a2200097 4500008004300000245012400043210006900167100002000236700002000256856003600276 2007 en_Ud 00aOn the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights0 aMazya inequalities existence and multiplicity results for an ell1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/252200408nas a2200109 4500008004300000245008800043210006900131100002400200700002200224700001600246856003600262 2007 en_Ud 00aMulti-bump solitons to linearly coupled systems of nonlinear Schrödinger equations0 aMultibump solitons to linearly coupled systems of nonlinear Schr1 aAmbrosetti, Antonio1 aColorado, Eduardo1 aRuiz, David uhttp://hdl.handle.net/1963/183500894nas a2200109 4500008004300000245005300043210005300096520056000149100001800709700002100727856003600748 2007 en_Ud 00aNearly time optimal stabilizing patchy feedbacks0 aNearly time optimal stabilizing patchy feedbacks3 aWe consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/218500581nas a2200109 4500008004300000245009300043210006900136520018500205100002000390700002500410856003600435 2007 en_Ud 00aNecessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd)0 aNecessary and sufficient conditions for the chainrule in W11locR3 aIn this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/203701154nas a2200121 4500008004300000245004500043210004300088520080300131100002200934700002400956700001600980856003600996 2007 en_Ud 00aA new model for contact angle hysteresis0 anew model for contact angle hysteresis3 aWe present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.1 aDeSimone, Antonio1 aGruenewald, Natalie1 aOtto, Felix uhttp://hdl.handle.net/1963/184800613nas a2200109 4500008004300000245006800043210006200111520025400173100002100427700001900448856003600467 2007 en_Ud 00aOn a notion of unilateral slope for the Mumford-Shah functional0 anotion of unilateral slope for the MumfordShah functional3 aIn this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/205900311nas a2200097 4500008004300000245005000043210005000093100001800143700001600161856003600177 2007 en_Ud 00aParametrized curves in Lagrange Grassmannians0 aParametrized curves in Lagrange Grassmannians1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/256000408nas a2200097 4500008004100000245011900041210006900160260001000229100002300239856004800262 2007 en d00aPerturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem0 aPerturbation techniques applied to the real vanishing viscosity bSISSA1 aBianchini, Stefano uhttp://preprints.sissa.it/handle/1963/3531500626nas a2200109 4500008004300000245008200043210006900125520024600194100002100440700001900461856003600480 2007 en_Ud 00aQuasistatic crack growth for a cohesive zone model with prescribed crack path0 aQuasistatic crack growth for a cohesive zone model with prescrib3 aIn this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes.1 aDal Maso, Gianni1 aZanini, Chiara uhttp://hdl.handle.net/1963/168600558nas a2200121 4500008004300000245007600043210006900119520014800188100002100336700002100357700002200378856003600400 2007 en_Ud 00aQuasistatic evolution problems for pressure-sensitive plastic materials0 aQuasistatic evolution problems for pressuresensitive plastic mat3 aWe study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.1 aDal Maso, Gianni1 aDemyanov, Alexey1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/196200600nas a2200097 4500008004300000245005300043210004500096520030500141100002000446856003600466 2007 en_Ud 00aOn the regularity of weak solutions to H-systems0 aregularity of weak solutions to Hsystems3 aAbstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem....1 aMusina, Roberta uhttp://hdl.handle.net/1963/175300945nas a2200121 4500008004300000245006300043210006300106520056100169100002200730700001700752700001800769856003600787 2007 en_Ud 00aSoft elasticity and microstructure in smectic C elastomers0 aSoft elasticity and microstructure in smectic C elastomers3 aSmectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable.1 aDeSimone, Antonio1 aAdams, James1 aConti, Sergio uhttp://hdl.handle.net/1963/181100726nas a2200097 4500008004300000245009800043210006900141520036200210100002000572856003600592 2007 en_Ud 00aSolutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals0 aSolutions of vectorial HamiltonJacobi equations and minimizers o3 aWe provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276301231nas a2200109 4500008004300000245012500043210006900168520080600237100002001043700002201063856003601085 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/211101499nas a2200121 4500008004300000245014300043210006900186520102000255100002001275700002201295700002401317856003601341 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aMontenegro, Marcelo uhttp://hdl.handle.net/1963/211200914nas a2200109 4500008004300000245006600043210006600109520054400175100002200719700002700741856003600768 2007 en_Ud 00aSome existence results for the Toda system on closed surfaces0 aSome existence results for the Toda system on closed surfaces3 aGiven a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$.1 aMalchiodi, Andrea1 aNdiaye, Cheikh Birahim uhttp://hdl.handle.net/1963/177500406nas a2200097 4500008004300000245011700043210006900160100001900229700002400248856003600272 2007 en_Ud 00aStability of front tracking solutions to the initial and boundary value problem for systems of conservation laws0 aStability of front tracking solutions to the initial and boundar1 aMarson, Andrea1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/176900537nas a2200109 4500008004300000245006800043210006800111520016600179100002400345700002200369856003600391 2007 en_Ud 00aStanding waves of some coupled Nonlinear Schrödinger Equations0 aStanding waves of some coupled Nonlinear Schrödinger Equations3 aWe deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/182100907nas a2200121 4500008004300000245005500043210005300098520053100151100001900682700002500701700002300726856003600749 2007 en_Ud 00aSurfactants in Foam Stability: A Phase-Field Model0 aSurfactants in Foam Stability A PhaseField Model3 aThe role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.1 aFonseca, Irene1 aMorini, Massimiliano1 aSlastikov, Valeriy uhttp://hdl.handle.net/1963/203500512nas a2200121 4500008004300000245004900043210004800092520014900140100002500289700001700314700002300331856003600354 2007 en_Ud 00aTime optimal swing-up of the planar pendulum0 aTime optimal swingup of the planar pendulum3 aThis paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.1 aBroucke, Mireille E.1 aMason, Paolo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/186700987nas a2200133 4500008004300000245005700043210005600100520056800156100002100724700002200745700002500767700002500792856003600817 2007 en_Ud 00aTime-dependent systems of generalized Young measures0 aTimedependent systems of generalized Young measures3 aIn this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/179500718nas a2200097 4500008004300000245012400043210006900167520032800236100002000564856003600584 2007 en_Ud 00aUniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient0 aUniqueness and continuous dependence on boundary data for integr3 aWe study some qualitative properties of the integro-extremal minimizers of the functional of the gradient defined on Sobolev spaces with Dirichlet boundary conditions. We discuss their use in the non-convex case via viscosity methods and give conditions under which they are unique and depend continuously on boundary data.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276201073nas a2200121 4500008004300000245008500043210006900128260002100197520064400218100002800862700002500890856003600915 2007 en_Ud 00aViscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients0 aViscosity solutions of HamiltonJacobi equations with discontinuo bWorld Scientific3 aWe consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/290700572nas a2200121 4500008004300000245003600043210003500079520024300114100002200357700001900379700001600398856003600414 2006 en_Ud 00a2-d stability of the Néel wall0 a2d stability of the Néel wall3 aWe are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls.1 aDeSimone, Antonio1 aKnuepfer, Hans1 aOtto, Felix uhttp://hdl.handle.net/1963/219401031nas a2200121 4500008004300000245007500043210006900118520062400187100001800811700002500829700001900854856003600873 2006 en_Ud 00a4e-condensation in a fully frustrated Josephson junction diamond chain0 a4econdensation in a fully frustrated Josephson junction diamond 3 aFully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

1 aRizzi, Matteo1 aCataudella, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/240000611nas a2200109 4500008004300000245006500043210006200108520025700170100001900427700001900446856003600465 2006 en_Ud 00aAn artificial viscosity approach to quasistatic crack growth0 aartificial viscosity approach to quasistatic crack growth3 aWe introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero.1 aToader, Rodica1 aZanini, Chiara uhttp://hdl.handle.net/1963/185000957nas a2200109 4500008004300000245006000043210005600103520060900159100001900768700002400787856003600811 2006 en_Ud 00aA Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs0 aBirkhoffLewisType Theorem for Some Hamiltonian PDEs3 aIn this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.1 aBambusi, Dario1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/215900487nas a2200109 4500008004300000245007200043210007000115520011000185100002400295700002200319856003600341 2006 en_Ud 00aBound and ground states of coupled nonlinear Schrödinger equations0 aBound and ground states of coupled nonlinear Schrödinger equatio3 aWe prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/214900412nas a2200109 4500008004300000245009200043210006900135100002400204700002200228700001600250856003600266 2006 en_Ud 00aBound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity0 aBound states of Nonlinear Schroedinger Equations with Potentials1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/175600319nas a2200085 4500008004300000245006900043210006200112100002300174856003600197 2006 en_Ud 00aOn Bressan\\\'s conjecture on mixing properties of vector fields0 aBressans conjecture on mixing properties of vector fields1 aBianchini, Stefano uhttp://hdl.handle.net/1963/180600728nas a2200109 4500008004300000245007900043210006900122520035400191100001900545700001800564856003600582 2006 en_Ud 00aA Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class0 aCanonical Frame for Nonholonomic Rank Two Distributions of Maxim3 aIn 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n > 5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence.1 aDoubrov, Boris1 aZelenko, Igor uhttp://hdl.handle.net/1963/171201190nas a2200109 4500008004300000245009100043210006900134520079700203100002401000700002001024856003601044 2006 en_Ud 00aCantor families of periodic solutions for completely resonant nonlinear wave equations0 aCantor families of periodic solutions for completely resonant no3 aWe prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/216100378nas a2200109 4500008004300000245006600043210006400109100001700173700001900190700002300209856003600232 2006 en_Ud 00aClassification of stable time-optimal controls on 2-manifolds0 aClassification of stable timeoptimal controls on 2manifolds1 aBoscain, Ugo1 aNikolaev, Igor1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/219601052nas a2200121 4500008004300000245006900043210006900112520065900181100001700840700001700857700002000874856003600894 2006 en_Ud 00aCommon Polynomial Lyapunov Functions for Linear Switched Systems0 aCommon Polynomial Lyapunov Functions for Linear Switched Systems3 aIn this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/218100823nas a2200097 4500008004300000245007000043210006900113520048500182100002200667856003600689 2006 en_Ud 00aCompactness of solutions to some geometric fourth-order equations0 aCompactness of solutions to some geometric fourthorder equations3 aWe prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/212600921nas a2200109 4500008004300000245009700043210006900140520052400209100002000733700002200753856003600775 2006 en_Ud 00aConcentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem0 aConcentration at manifolds of arbitrary dimension for a singular3 aWe consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/217000638nas a2200109 4500008004300000245006800043210006800111520027600179100002100455700001600476856003600492 2006 en_Ud 00aConservative Solutions to a Nonlinear Variational Wave Equation0 aConservative Solutions to a Nonlinear Variational Wave Equation3 aWe establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values.1 aBressan, Alberto1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218400395nas a2200097 4500008004300000245010800043210006900151100002100220700002000241856003600261 2006 en_Ud 00aThe Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results0 aDirichlet problem for Hsystems with small boundary data blowup p1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/225200974nas a2200109 4500008004300000245009300043210006900136520057600205100002500781700002200806856003600828 2006 en_Ud 00aAn estimation of the controllability time for single-input systems on compact Lie Groups0 aestimation of the controllability time for singleinput systems o3 aGeometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.1 aAgrachev, Andrei, A.1 aChambrion, Thomas uhttp://hdl.handle.net/1963/213502436nas a2200169 4500008004100000245007600041210006900117260007200186520184400258100002002102700002202122700001802144700002502162700001902187700002402206856003602230 2006 en d00aExperimental and modeling studies of desensitization of P2X3 receptors.0 aExperimental and modeling studies of desensitization of P2X3 rec bthe American Society for Pharmacology and Experimental Therapeutics3 aThe function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain.1 aSokolova, Elena1 aSkorinkin, Andrei1 aMoiseev, Igor1 aAgrachev, Andrei, A.1 aNistri, Andrea1 aGiniatullin, Rashid uhttp://hdl.handle.net/1963/497400868nas a2200109 4500008004300000245007300043210006900116520049600185100002400681700001700705856003600722 2006 en_Ud 00aForced vibrations of wave equations with non-monotone nonlinearities0 aForced vibrations of wave equations with nonmonotone nonlinearit3 aWe prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz.1 aBerti, Massimiliano1 aBiasco, Luca uhttp://hdl.handle.net/1963/216001285nas a2200097 4500008004300000245007100043210006700114520095200181100001801133856003601151 2006 en_Ud 00aFundamental form and Cartan tensor of (2,5)-distributions coincide0 aFundamental form and Cartan tensor of 25distributions coincide3 aIn our previous paper for generic rank 2 vector distributions on n-dimensional manifold (n greater or equal to 5) we constructed a special differential invariant, the fundamental form. In the case n=5 this differential invariant has the same algebraic nature, as the covariant binary biquadratic form, constructed by E.Cartan in 1910, using his ``reduction- prolongation\\\'\\\' procedure (we call this form Cartan\\\'s tensor). In the present paper we prove that our fundamental form coincides (up to constant factor -35) with Cartan\\\'s tensor. This result explains geometric reason for existence of Cartan\\\'s tensor (originally this tensor was obtained by very sophisticated algebraic manipulations) and gives the true analogs of this tensor in Riemannian geometry. In addition, as a part of the proof, we obtain a new useful formula for Cartan\\\'s tensor in terms of structural functions of any frame naturally adapted to the distribution.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218701442nas a2200097 4500008004300000245010600043210006900149520107200218100001801290856003601308 2006 en_Ud 00aOn geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 10 ageodesic equivalence of Riemannian metrics and subRiemannian met3 aThe present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem.1 aZelenko, Igor uhttp://hdl.handle.net/1963/220500286nas a2200085 4500008004300000245004900043210004900092100002300141856003600164 2006 en_Ud 00aGlimm interaction functional for BGK schemes0 aGlimm interaction functional for BGK schemes1 aBianchini, Stefano uhttp://hdl.handle.net/1963/177000794nas a2200109 4500008004300000245005500043210005500098520044900153100002100602700002500623856003600648 2006 en_Ud 00aInfinite Horizon Noncooperative Differential Games0 aInfinite Horizon Noncooperative Differential Games3 aFor a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.1 aBressan, Alberto1 aPriuli, Fabio Simone uhttp://hdl.handle.net/1963/172000891nas a2200121 4500008004300000245004100043210003800084520054500122100002100667700002800688700001700716856003600733 2006 en_Ud 00aAn instability of the Godunov scheme0 ainstability of the Godunov scheme3 aWe construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes.1 aBressan, Alberto1 aJenssen, Helge Kristian1 aBaiti, Paolo uhttp://hdl.handle.net/1963/218300673nas a2200109 4500008004300000245005900043210005300102520033100155100002100486700002000507856003600527 2006 en_Ud 00aOn Palais-Smale sequences for H-systems: some examples0 aPalaisSmale sequences for Hsystems some examples3 aWe exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/215700273nas a2200097 4500008004300000245002800043210002600071100002200097700002000119856003600139 2006 en_Ud 00aQ-curvature flow on S^40 aQcurvature flow on S41 aMalchiodi, Andrea1 aStruwe, Michael uhttp://hdl.handle.net/1963/219300676nas a2200109 4500008004300000245007400043210006900117520029900186100002400485700002100509856003600530 2006 en_Ud 00aQuasi-periodic solutions of completely resonant forced wave equations0 aQuasiperiodic solutions of completely resonant forced wave equat3 aWe prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.1 aBerti, Massimiliano1 aProcesi, Michela uhttp://hdl.handle.net/1963/223401091nas a2200121 4500008004300000245008400043210006900127520066900196100002100865700002200886700002500908856003600933 2006 en_Ud 00aQuasistatic evolution problems for linearly elastic-perfectly plastic materials0 aQuasistatic evolution problems for linearly elasticperfectly pla3 aThe problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/212900669nas a2200109 4500008004300000245010800043210007000151520026200221100002400483700001600507856003600523 2006 en_Ud 00aRadial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials0 aRadial solutions concentrating on spheres of nonlinear Schröding3 aWe prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction.1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/175500420nas a2200133 4500008004300000020002200043245005300065210005300118100002200171700002100193700002000214700001600234856003600250 2006 en_Ud a978-0-12-480874-400aRecent analytical developments in micromagnetics0 aRecent analytical developments in micromagnetics1 aDeSimone, Antonio1 aKohn, Robert, V.1 aMüller, Stefan1 aOtto, Felix uhttp://hdl.handle.net/1963/223000968nas a2200121 4500008004300000245005100043210005100094520060400145100001700749700002300766700002100789856003600810 2006 en_Ud 00aStability of planar nonlinear switched systems0 aStability of planar nonlinear switched systems3 aWe consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.1 aBoscain, Ugo1 aCharlot, Grégoire1 aSigalotti, Mario uhttp://hdl.handle.net/1963/171002083nas a2200109 4500008004300000245007400043210006900117520171700186100001701903700001701920856003601937 2006 en_Ud 00aTime Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field0 aTime Minimal Trajectories for a Spin 12 Particle in a Magnetic f3 aIn this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| ≤ M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M → ∞ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E → 0, giving a partial proof of a conjecture formulated in a previous paper.1 aBoscain, Ugo1 aMason, Paolo uhttp://hdl.handle.net/1963/173401764nas a2200097 4500008004300000245008100043210006900124520141900193100001801612856003601630 2006 en_Ud 00aOn variational approach to differential invariants of rank two distributions0 avariational approach to differential invariants of rank two dist3 an the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his \\\"reduction-prolongation\\\" procedure. After Cartan\\\'s work the following questions remained open: first the geometric reason for existence of Cartan\\\'s tensor was not clear; secondly it was not clear how to generalize this tensor to other classes of distributions; finally there were no explicit formulas for computation of Cartan\\\'s tensor. Our paper is the first in the series of papers, where we develop an alternative approach, which gives the answers to the questions mentioned above. It is based on the investigation of dynamics of the field of so-called abnormal extremals (singular curves) of rank 2 distribution and on the general theory of unparametrized curves in the Lagrange Grassmannian, developed in our previous works with A. Agrachev . In this way we construct the fundamental form and the projective Ricci curvature of rank 2 vector distributions for arbitrary n greater than 4.\\nFor n=5 we give an explicit method for computation of these invariants and demonstrate it on several examples. In our next paper we show that in the case n=5 our fundamental form coincides with Cartan\\\'s tensor.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218800654nas a2200097 4500008004300000245004700043210004700090520036200137100002100499856003600520 2006 en_Ud 00aVariational problems in fracture mechanics0 aVariational problems in fracture mechanics3 aWe present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/181600897nas a2200121 4500008004300000245008900043210006900132260002400201520047200225100002000697700002200717856003600739 2005 en_Ud 00aAsymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$0 aAsymptotic Morse theory for the equation Delta v2vsb xwedge vsb bInternational Press3 aGiven a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron.1 aChanillo, Sagun1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353301579nas a2200121 4500008004100000245007400041210006700115260001800182520117500200100001801375700002801393856003601421 2005 en d00aOn the attainable set for Temple class systems with boundary controls0 aattainable set for Temple class systems with boundary controls bSISSA Library3 aConsider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/158100648nas a2200109 4500008004300000245006600043210005800109520029500167100002100462700001900483856003600502 2005 en_Ud 00aOn the Blow-up for a Discrete Boltzmann Equation in the Plane0 aBlowup for a Discrete Boltzmann Equation in the Plane3 aWe study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/224401949nas a2200097 4500008004300000245007900043210006900122520160600191100001801797856003601815 2005 en_Ud 00aComplete systems of invariants for rank 1 curves in Lagrange Grassmannians0 aComplete systems of invariants for rank 1 curves in Lagrange Gra3 aCurves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation.1 aZelenko, Igor uhttp://hdl.handle.net/1963/231000658nas a2200109 4500008004100000245010000041210006900141260001300210520026700223100002200490856003600512 2005 en d00aConcentration at curves for a singularly perturbed Neumann problem in three-dimensional domains0 aConcentration at curves for a singularly perturbed Neumann probl bSpringer3 aWe prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486600982nas a2200121 4500008004100000245006900041210006900110260001800179520057400197100002800771700002500799856003600824 2005 en d00aConservation laws with time dependent discontinuous coefficients0 aConservation laws with time dependent discontinuous coefficients bSISSA Library3 aWe consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/166602094nas a2200121 4500008004300000245013000043210006900173520162100242100002501863700003001888700001801918856003601936 2005 en_Ud 00aOn curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals0 acurvatures and focal points of distributions of dynamical Lagran3 aPairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem.1 aAgrachev, Andrei, A.1 aChtcherbakova, Natalia N.1 aZelenko, Igor uhttp://hdl.handle.net/1963/225400716nas a2200121 4500008004100000245009400041210006900135260001300204520029900217100002000516700002200536856003600558 2005 en d00aA fourth order uniformization theorem on some four manifolds with large total Q-curvature0 afourth order uniformization theorem on some four manifolds with bElsevier3 aGiven a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open.1 aDjadli, Zindine1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486800651nas a2200109 4500008004300000245005100043210005000094520031700144100002100461700002300482856003600505 2005 en_Ud 00aGlobal solutions of the Hunter-Saxton equation0 aGlobal solutions of the HunterSaxton equation3 aWe construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.1 aBressan, Alberto1 aConstantin, Adrian uhttp://hdl.handle.net/1963/225600958nas a2200121 4500008004300000245009200043210006900135520053000204100002400734700002000758700002200778856003600800 2005 en_Ud 00aGround states of nonlinear Schroedinger equations with potentials vanishing at infinity0 aGround states of nonlinear Schroedinger equations with potential3 aWe deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$.1 aAmbrosetti, Antonio1 aFelli, Veronica1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/235200679nas a2200121 4500008004100000245003100041210003100072260000900103520036500112100002100477700002300498856003600521 2005 en d00aHybrid necessary principle0 aHybrid necessary principle bSIAM3 aWe consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature.1 aGaravello, Mauro1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/164101933nas a2200145 4500008004100000245004900041210004900090260002900139520150600168100002001674700002001694700002201714700001501736856003601751 2005 en d00aMinimal surfaces in pseudohermitian geometry0 aMinimal surfaces in pseudohermitian geometry bScuola Normale Superiore3 aWe consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold.1 aCheng, Jih-Hsin1 aHwang, JennFang1 aMalchiodi, Andrea1 aYang, Paul uhttp://hdl.handle.net/1963/457900521nas a2200097 4500008004300000245006000043210005300103520021100156100002000367856003600387 2005 en_Ud 00aOn the Minimum Problem for Nonconvex Scalar Functionals0 aMinimum Problem for Nonconvex Scalar Functionals3 aWe study the minimum problem for scalar nonconvex functionals defined on Sobolev maps satisfying a Dirichlet boundary condition and refine well-known existence results under standard regularity assumptions.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276400421nas a2200121 4500008004300000245008100043210006900124260001300193100002200206700001700228700001800245856003600263 2005 en_Ud 00aMultiple clustered layer solutions for semilinear Neumann problems on a ball0 aMultiple clustered layer solutions for semilinear Neumann proble bElsevier1 aMalchiodi, Andrea1 aNi, Wei-Ming1 aWei, Juncheng uhttp://hdl.handle.net/1963/353201293nas a2200121 4500008004300000245009700043210006900140520086400209100001701073700002201090700002301112856003601135 2005 en_Ud 00aNonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy0 aNonisotropic 3level quantum systems complete solutions for minim3 aWe apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.1 aBoscain, Ugo1 aChambrion, Thomas1 aCharlot, Grégoire uhttp://hdl.handle.net/1963/225900367nas a2200097 4500008004300000245007600043210007000119100002400189700002000213856003600233 2005 en_Ud 00aNonlinear Schrödinger Equations with vanishing and decaying potentials0 aNonlinear Schrödinger Equations with vanishing and decaying pote1 aAmbrosetti, Antonio1 aZhi-Qiang, Wang uhttp://hdl.handle.net/1963/176000982nas a2200109 4500008004300000245008000043210006900123520060400192100002100796700001900817856003600836 2005 en_Ud 00aAn Optimal Transportation Metric for Solutions of the Camassa-Holm Equation0 aOptimal Transportation Metric for Solutions of the CamassaHolm E3 aIn this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/171900415nas a2200109 4500008004100000245008300041210006900124260003500193100002400228700001700252856003600269 2005 en d00aPeriodic solutions of nonlinear wave equations with non-monotone forcing terms0 aPeriodic solutions of nonlinear wave equations with nonmonotone bAccademia Nazionale dei Lincei1 aBerti, Massimiliano1 aBiasco, Luca uhttp://hdl.handle.net/1963/458100410nas a2200109 4500008004100000245007400041210006900115260003500184100002400219700002100243856003600264 2005 en d00aQuasi-periodic oscillations for wave equations under periodic forcing0 aQuasiperiodic oscillations for wave equations under periodic for bAccademia Nazionale dei Lincei1 aBerti, Massimiliano1 aProcesi, Michela uhttp://hdl.handle.net/1963/458300706nas a2200121 4500008004300000245005300043210005300096520033400149100002100483700002500504700001900529856003600548 2005 en_Ud 00aQuasistatic Crack Growth in Nonlinear Elasticity0 aQuasistatic Crack Growth in Nonlinear Elasticity3 aIn this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/229301167nas a2200109 4500008004100000245010100041210006900142260001300211520077600224100002101000856003601021 2005 en d00aRegularity properties of optimal trajectories of single-input control systems in dimension three0 aRegularity properties of optimal trajectories of singleinput con bSpringer3 aLet q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories.1 aSigalotti, Mario uhttp://hdl.handle.net/1963/479401313nas a2200133 4500008004300000245008200043210006900125260001300194520087600207100001801083700002201101700002001123856003601143 2005 en_Ud 00aSelf-similar folding patterns and energy scaling in compressed elastic sheets0 aSelfsimilar folding patterns and energy scaling in compressed el bElsevier3 aThin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves.1 aConti, Sergio1 aDeSimone, Antonio1 aMüller, Stefan uhttp://hdl.handle.net/1963/300000333nas a2200109 4500008004300000020001800043245004400061210004200105100001700147700002300164856003600187 2005 en_Ud a2 7056 6511 000aA short introduction to optimal control0 ashort introduction to optimal control1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/225700351nas a2200085 4500008004300000245009600043210006900139100002100208856003600229 2005 en_Ud 00aSolutions of Neumann problems in domains with cracks and applications to fracture mechanics0 aSolutions of Neumann problems in domains with cracks and applica1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/168401445nas a2200121 4500008004300000245006200043210006200105260001300167520106100180100002801241700001801269856003601287 2005 en_Ud 00aStability of solutions of quasilinear parabolic equations0 aStability of solutions of quasilinear parabolic equations bElsevier3 aWe bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth.1 aCoclite, Giuseppe Maria1 aHolden, Helge uhttp://hdl.handle.net/1963/289201246nas a2200109 4500008004300000245010500043210006900148520083800217100002201055700002301077856003601100 2005 en_Ud 00aStress-dilatancy based modelling of granular materials and extensions to soils with crushable grains0 aStressdilatancy based modelling of granular materials and extens3 aStress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws.1 aDeSimone, Antonio1 aTamagnini, Claudio uhttp://hdl.handle.net/1963/216500714nas a2200109 4500008004300000245007100043210006900114520035100183100001700534700001700551856003600568 2005 en_Ud 00aTime minimal trajectories for two-level quantum systems with drift0 aTime minimal trajectories for twolevel quantum systems with drif3 aOn a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds.1 aBoscain, Ugo1 aMason, Paolo uhttp://hdl.handle.net/1963/168801372nas a2200109 4500008004300000245007100043210006800114520100700182100001701189700002001206856003601226 2005 en_Ud 00aTime Optimal Synthesis for Left-Invariant Control Systems on SO(3)0 aTime Optimal Synthesis for LeftInvariant Control Systems on SO33 aConsider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations.1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/225801069nas a2200133 4500008004100000245003500041210003500076260001800111520069800129100002800827700002300855700002100878856003600899 2005 en d00aTraffic flow on a road network0 aTraffic flow on a road network bSISSA Library3 aThis paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.1 aCoclite, Giuseppe Maria1 aPiccoli, Benedetto1 aGaravello, Mauro uhttp://hdl.handle.net/1963/158401264nas a2200121 4500008004300000245006600043210006600109260002600175520086100201100002301062700002101085856003601106 2005 en_Ud 00aVanishing viscosity solutions of nonlinear hyperbolic systems0 aVanishing viscosity solutions of nonlinear hyperbolic systems bAnnals of Mathematics3 aWe consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/307401324nas a2200109 4500008004300000245005700043210005600100520097800156100002201134700002201156856003601178 2005 en_Ud 00aWetting of rough surfaces: a homogenization approach0 aWetting of rough surfaces a homogenization approach3 aThe contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.1 aDeSimone, Antonio1 aAlberti, Giovanni uhttp://hdl.handle.net/1963/225301188nas a2200121 4500008004100000245012000041210006900161260001800230520074100248100002100989700002001010856003601030 2004 en d00aAsymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains0 aAsymptotic behaviour and correctors for linear Dirichlet problem bSISSA Library3 aWe consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains.1 aDal Maso, Gianni1 aMurat, Francois uhttp://hdl.handle.net/1963/161100778nas a2200109 4500008004300000245007400043210006900117520040200186100002400588700002000612856003600632 2004 en_Ud 00aBifurcation of free vibrations for completely resonant wave equations0 aBifurcation of free vibrations for completely resonant wave equa3 aWe prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/224500524nas a2200145 4500008004100000245006800041210006800109300001400177490000700191100001800198700001700216700002300233700001900256856010300275 2004 eng d00aCalculation of impulsively started incompressible viscous flows0 aCalculation of impulsively started incompressible viscous flows a877–9020 v461 aMarra, Andrea1 aMola, Andrea1 aQuartapelle, Luigi1 aRiviello, Luca uhttps://www.math.sissa.it/publication/calculation-impulsively-started-incompressible-viscous-flows00910nas a2200109 4500008004100000245008500041210006900126260001300195520053400208100002200742856003600764 2004 en d00aCoarse-grained models of materials with non-convex free-energy: two case studies0 aCoarsegrained models of materials with nonconvex freeenergy two bElsevier3 aBridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response.1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/488401240nas a2200121 4500008004300000245006600043210005900109260001000168520086800178100002101046700001501067856003601082 2004 en_Ud 00aOn the convergence rate of vanishing viscosity approximations0 aconvergence rate of vanishing viscosity approximations bWiley3 aGiven a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.1 aBressan, Alberto1 aYang, Tong uhttp://hdl.handle.net/1963/291501258nas a2200145 4500008004300000245008600043210006900129260001700198520078200215100002300997700001801020700002201038700001601060856003601076 2004 en_Ud 00aEnergetics and switching of quasi-uniform states in small ferromagnetic particles0 aEnergetics and switching of quasiuniform states in small ferroma bEDP Sciences3 aWe present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.1 aAlouges, François1 aConti, Sergio1 aDeSimone, Antonio1 aPokern, Ivo uhttp://hdl.handle.net/1963/299900881nas a2200121 4500008004100000245005300041210005200094260001800146520051800164100002100682700002000703856003600723 2004 en d00aExistence of H-bubbles in a perturbative setting0 aExistence of Hbubbles in a perturbative setting bSISSA Library3 aGiven a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160601254nas a2200121 4500008004100000245008600041210006900127260001800196520084100214100002101055700002001076856003601096 2004 en d00aH-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method0 aHbubbles in a perturbative setting the finitedimensional reducti bSISSA Library3 aGiven a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160701010nas a2200145 4500008004300000245005800043210005800101260001300159520057100172100002100743700001900764700002000783700002500803856003600828 2004 en_Ud 00aHigher order quasiconvexity reduces to quasiconvexity0 aHigher order quasiconvexity reduces to quasiconvexity bSpringer3 aIn this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/291100956nas a2200133 4500008004100000245008400041210006900125260000900194520052900203100001700732700001700749700002000766856003600786 2004 en d00aOn the minimal degree of a common Lyapunov function for planar switched systems0 aminimal degree of a common Lyapunov function for planar switched bIEEE3 aIn this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/483400410nas a2200109 4500008004300000245008000043210006900123260002600192100002200218700002400240856003600264 2004 en_Ud 00aMultidimensional boundary layers for a singularly perturbed Neumann problem0 aMultidimensional boundary layers for a singularly perturbed Neum bDuke University Press1 aMalchiodi, Andrea1 aMontenegro, Marcelo uhttp://hdl.handle.net/1963/296000380nas a2200109 4500008004300000245006700043210006700110260001300177100002400190700002000214856003600234 2004 en_Ud 00aMultiplicity of periodic solutions of nonlinear wave equations0 aMultiplicity of periodic solutions of nonlinear wave equations bElsevier1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/297401171nas a2200133 4500008004300000245008600043210006900129260003700198520070300235100002400938700001700962700002200979856003601001 2004 en_Ud 00aPeriodic orbits close to elliptic tori and applications to the three-body problem0 aPeriodic orbits close to elliptic tori and applications to the t bScuola Normale Superiore di Pisa3 aWe prove, under suitable non-resonance and non-degeneracy ``twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.)1 aBerti, Massimiliano1 aBiasco, Luca1 aValdinoci, Enrico uhttp://hdl.handle.net/1963/298500759nas a2200121 4500008004300000245007800043210006900121520034600190100002100536700002500557700001900582856003600601 2004 en_Ud 00aQuasi-static evolution in brittle fracture: the case of bounded solutions0 aQuasistatic evolution in brittle fracture the case of bounded so3 aThe main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/222901180nas a2200121 4500008004300000245007900043210006900122260001700191520077400208100001700982700002300999856003601022 2004 en_Ud 00aResonance of minimizers for n-level quantum systems with an arbitrary cost0 aResonance of minimizers for nlevel quantum systems with an arbit bEDP Sciences3 aWe consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer.1 aBoscain, Ugo1 aCharlot, Grégoire uhttp://hdl.handle.net/1963/291000388nas a2200097 4500008004300000245008700043210006900130260003500199100002000234856003600254 2004 en_Ud 00aThe role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem0 arole of the spectrum of the Laplace operator on S2 in the Hbubbl bHebrew University Magnes Press1 aMusina, Roberta uhttp://hdl.handle.net/1963/289401056nas a2200121 4500008004300000245005500043210005400098260001300152520069800165100002100863700001400884856003600898 2004 en_Ud 00aSemi-cooperative strategies for differential games0 aSemicooperative strategies for differential games bSpringer3 aThe paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/289300741nas a2200121 4500008004300000245005600043210005400099260000900153520038500162100002100547700001500568856003600583 2004 en_Ud 00aA sharp decay estimate for positive nonlinear waves0 asharp decay estimate for positive nonlinear waves bSIAM3 aWe consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources.1 aBressan, Alberto1 aYang, Tong uhttp://hdl.handle.net/1963/291600490nas a2200121 4500008004100000245011600041210006900157260004300226100002400269700002200293700001700315856003600332 2004 en d00aSingularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II0 aSingularity perturbed elliptic equations with symmetry existence bIndiana University Mathematics Journal1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/166300818nas a2200121 4500008004300000245007100043210006900114260000900183520043300192100002100625700001400646856003600660 2004 en_Ud 00aSmall BV solutions of hyperbolic noncooperative differential games0 aSmall BV solutions of hyperbolic noncooperative differential gam bSIAM3 aThe paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/291700759nas a2200121 4500008004100000245005300041210005300094260001800147520038500165100002800550700002300578856003600601 2004 en d00aSolitary waves for Maxwell Schrodinger equations0 aSolitary waves for Maxwell Schrodinger equations bSISSA Library3 aIn this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated.1 aCoclite, Giuseppe Maria1 aGeorgiev, Vladimir uhttp://hdl.handle.net/1963/158200365nas a2200097 4500008004100000245008600041210006900127260001300196100002200209856003600231 2004 en d00aSolutions concentrating at curves for some singularly perturbed elliptic problems0 aSolutions concentrating at curves for some singularly perturbed bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486900322nas a2200097 4500008004100000245004600041210004600087260003100133100002400164856003600188 2004 en d00aSoluzioni periodiche di PDEs Hamiltoniane0 aSoluzioni periodiche di PDEs Hamiltoniane bUnione Matematica Italiana1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/458200736nas a2200109 4500008004300000245006600043210006600109260003500175520035900210100002100569856003600590 2004 en_Ud 00aSome remarks on multidimensional systems of conservation laws0 aSome remarks on multidimensional systems of conservation laws bAccademia Nazionale dei Lincei3 aThis note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation.1 aBressan, Alberto uhttp://hdl.handle.net/1963/364200882nas a2200121 4500008004300000245004500043210004500088260001700133520053500150100001800685700002100703856003600724 2004 en_Ud 00aStability rates for patchy vector fields0 aStability rates for patchy vector fields bEDP Sciences3 aThis paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/295900369nas a2200109 4500008004100000245006400041210006300105260001800168100001800186700001900204856003600223 2004 en d00aWell-posedness for general 2x2 systems of conservation laws0 aWellposedness for general 2x2 systems of conservation laws bSISSA Library1 aAncona, Fabio1 aMarson, Andrea uhttp://hdl.handle.net/1963/124100496nas a2200109 4500008004100000245017800041210006900219260001800288100002100306700002300327856003600350 2003 en d00aAutonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations0 aAutonomous integral functionals with discontinous nonconvex inte bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/162500697nas a2200133 4500008004300000245009100043210006900134260001300203520024900216100002200465700001900487700002100506856003600527 2003 en_Ud 00aThe calibration method for the Mumford-Shah functional and free-discontinuity problems0 acalibration method for the MumfordShah functional and freediscon bSpringer3 aWe present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.1 aAlberti, Giovanni1 aBouchitte, Guy1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/305100362nas a2200109 4500008004100000245005400041210005400095260001000149653002900159100002800188856003600216 2003 en d00aControl Problems for Systems of Conservation Laws0 aControl Problems for Systems of Conservation Laws bSISSA10aAsymptotic Stabilization1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/532501027nas a2200133 4500008004300000245008200043210006900125260001300194520058900207100002400796700001700820700002000837856003600857 2003 en_Ud 00aDrift in phase space: a new variational mechanism with optimal diffusion time0 aDrift in phase space a new variational mechanism with optimal di bElsevier3 aWe consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of ``transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory.1 aBerti, Massimiliano1 aBiasco, Luca1 aBolle, Philippe uhttp://hdl.handle.net/1963/302000803nas a2200109 4500008004100000245008400041210006900125260001800194520042700212100001800639856003600657 2003 en d00aA finite element approximation of the Griffith\\\'s model in fracture mechanics0 afinite element approximation of the Griffiths model in fracture bSISSA Library3 aThe Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown.1 aNegri, Matteo uhttp://hdl.handle.net/1963/154800868nas a2200145 4500008004300000245005900043210005800102260002300160520042200183100001800605700002100623700001900644700002300663856003600686 2003 en_Ud 00aHybrid optimal control: case study of a car with gears0 aHybrid optimal control case study of a car with gears bTaylor and Francis3 aThe purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis.1 aD'Apice, Ciro1 aGaravello, Mauro1 aManzo, Rosanna1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/302200871nas a2200109 4500008004300000245008000043210006900123260002600192520048600218100002100704856003600725 2003 en_Ud 00aAn ill posed Cauchy problem for a hyperbolic system in two space dimensions0 aill posed Cauchy problem for a hyperbolic system in two space di bUniversità di Padova3 aThe theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed.1 aBressan, Alberto uhttp://hdl.handle.net/1963/291300338nas a2200097 4500008004100000245006000041210005700101260001800158100002800176856003600204 2003 en d00aAn interior estimate for a nonlinear parabolic equation0 ainterior estimate for a nonlinear parabolic equation bSISSA Library1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/162200867nas a2200109 4500008004300000245005900043210005700102260002600159520051500185100002100700856003600721 2003 en_Ud 00aA lemma and a conjecture on the cost of rearrangements0 alemma and a conjecture on the cost of rearrangements bUniversità di Padova3 aConsider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement.1 aBressan, Alberto uhttp://hdl.handle.net/1963/291400867nas a2200121 4500008004100000245005700041210005000098260001800148520049700166100002500663700002100688856003600709 2003 en d00aOn the local structure of optimal trajectories in R30 alocal structure of optimal trajectories in R3 bSISSA Library3 aWe analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.1 aAgrachev, Andrei, A.1 aSigalotti, Mario uhttp://hdl.handle.net/1963/161200845nas a2200109 4500008004100000245007300041210006900114260001800183520047500201100002300676856003600699 2003 en d00aA note on singular limits to hyperbolic systems of conservation laws0 anote on singular limits to hyperbolic systems of conservation la bSISSA Library3 aIn this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation.1 aBianchini, Stefano uhttp://hdl.handle.net/1963/154200630nas a2200121 4500008004300000245007700043210006900120260002900189520021200218100002300430700001900453856003600472 2003 en_Ud 00aA note on the integral representation of functionals in the space SBD(O)0 anote on the integral representation of functionals in the space bRendiconti di Matematica3 aIn this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions.1 aEbobisse, Francois1 aToader, Rodica uhttp://hdl.handle.net/1963/306400397nas a2200109 4500008004100000245007900041210006900120260001800189100002400207700002000231856003600251 2003 en d00aPeriodic solutions of nonlinear wave equations with general nonlinearities0 aPeriodic solutions of nonlinear wave equations with general nonl bSISSA Library1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/164800551nas a2200121 4500008004100000245007300041210006900114260004800183520011800231100002400349700002000373856003600393 2003 en d00aPositive solutions to a class of quasilinear elliptic equations on R0 aPositive solutions to a class of quasilinear elliptic equations bAmerican Institute of Mathematical Sciences3 aWe discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.1 aAmbrosetti, Antonio1 aZhi-Qiang, Wang uhttp://hdl.handle.net/1963/162800736nas a2200133 4500008004300000245008800043210006900131260001300200520028300213100002000496700002200516700002800538856003600566 2003 en_Ud 00aPrescribing scalar and boundary mean curvature on the three dimensional half sphere0 aPrescribing scalar and boundary mean curvature on the three dime bSpringer3 aWe consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results.1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/308600579nas a2200109 4500008004300000245008900043210006900132260000900201520019800210100002500408856003600433 2003 en_Ud 00aSequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems0 aSequences of Singularly Perturbed Functionals Generating FreeDis bSIAM3 aWe prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown.1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/307100397nas a2200097 4500008004100000245012200041210006900163260001000232100002100242856003600263 2003 en d00aSingle-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem0 aSingleInput Control Affine Systems Local Regularity of Optimal T bSISSA1 aSigalotti, Mario uhttp://hdl.handle.net/1963/534200459nas a2200121 4500008004100000245011500041210006900156260001300225100002400238700002200262700001700284856003600301 2003 en d00aSingularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I0 aSingularly perturbed elliptic equations with symmetry existence bSpringer1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/163300426nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700002800240856003600268 2003 en d00aSome results on the boundary control of systems of conservation laws0 aSome results on the boundary control of systems of conservation bSISSA Library1 aBressan, Alberto1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/161500672nas a2200133 4500008004100000245008000041210006900121260001800190520022400208100002100432700002300453700002600476856003600502 2003 en d00aA stability result for nonlinear Neumann problems under boundary variations0 astability result for nonlinear Neumann problems under boundary v bSISSA Library3 aIn this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.1 aDal Maso, Gianni1 aEbobisse, Francois1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/161800399nas a2200109 4500008004100000245007900041210006900120260001800189100002300207700002300230856003600253 2002 en d00aAdmissible Riemann solvers for genuinely nonlinear P-systems of mixed type0 aAdmissible Riemann solvers for genuinely nonlinear Psystems of m bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149100800nas a2200109 4500008004100000245005300041210005200094260003600146520039600182100002400578856008800602 2002 en d00aArnold diffusion: a functional analysis approach0 aArnold diffusion a functional analysis approach bNatsīonal. Akad. Nauk Ukraïni3 aWe present, in the context of nearly integrable Hamiltonian systems, a functional analysis approach to study the “splitting of the whiskers” and the “shadowing problem” developed in collaboration with P. Bolle in the recent papers [1] and [2] . This method is applied to the problem of Arnold diffusion for nearly integrable partially isochronous systems improving known results.1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/arnold-diffusion-functional-analysis-approach00716nas a2200121 4500008004300000245006000043210005300103260000900156520034400165100002100509700002800530856003600558 2002 en_Ud 00aOn the Boundary Control of Systems of Conservation Laws0 aBoundary Control of Systems of Conservation Laws bSIAM3 aThe paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.1 aBressan, Alberto1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/307000668nas a2200109 4500008004300000245008100043210006900124260002200193520028200215100002500497856003600522 2002 en_Ud 00aThe Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps0 aCalibration Method for FreeDiscontinuity Problems on VectorValue bHeldermann Verlag3 aThe calibration method is a classical minimality criterion, which has been recently adapted to functionals with free discontinuities by Alberti, Bouchitté, Dal Maso. In this paper we present a further generalization of this theory to functionals defined on vector-valued maps.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/304900816nas a2200121 4500008004300000245005800043210005600101260004800157520040900205100002300614700002100637856003600658 2002 en_Ud 00aA center manifold technique for tracing viscous waves0 acenter manifold technique for tracing viscous waves bAmerican Institute of Mathematical Sciences3 aIn this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/307500397nas a2200109 4500008004100000245008300041210006900124260001300193100002400206700002100230856003600251 2002 en d00aChaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems0 aChaotic dynamics for perturbations of infinitedimensional Hamilt bElsevier1 aBerti, Massimiliano1 aCarminati, Carlo uhttp://hdl.handle.net/1963/127900727nas a2200121 4500008004300000245006600043210006400109260003400173520032000207100002000527700002200547856003600569 2002 en_Ud 00aCurvature theory of boundary phases: the two-dimensional case0 aCurvature theory of boundary phases the twodimensional case bEuropean Mathematical Society3 aWe describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.1 aBraides, Andrea1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353700315nas a2200109 4500008004100000245003500041210003400076260001800110100002100128700002000149856003600169 2002 en d00aExistence of minimal H-bubbles0 aExistence of minimal Hbubbles bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/152500795nas a2200121 4500008004300000245006000043210006000103260004800163520038200211100002400593700002000617856003600637 2002 en_Ud 00aFast Arnold diffusion in systems with three time scales0 aFast Arnold diffusion in systems with three time scales bAmerican Institute of Mathematical Sciences3 aWe consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diffusion takes place with fast (polynomial) speed, even though the \\\"splitting determinant\\\" is exponentially small.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/305800809nas a2200121 4500008004300000245007700043210006900120260000900189520041400198100001800612700002100630856003600651 2002 en_Ud 00aFlow Stability of Patchy Vector Fields and Robust Feedback Stabilization0 aFlow Stability of Patchy Vector Fields and Robust Feedback Stabi bSIAM3 aThe paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/307300697nas a2200121 4500008004300000245005500043210005300098260001300151520033100164100002400495700002000519856003600539 2002 en_Ud 00aA functional analysis approach to Arnold diffusion0 afunctional analysis approach to Arnold diffusion bElsevier3 aWe discuss in the context of nearly integrable Hamiltonian systems a functional analysis approach to the \\\"splitting of separatrices\\\" and to the \\\"shadowing problem\\\". As an application we apply our method to the problem of Arnold Diffusion for nearly integrable partially isochronous systems improving known results.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/315101353nas a2200121 4500008004300000245003200043210003200075260001300107520103200120100002501152700001801177856003601195 2002 en_Ud 00aGeometry of Jacobi Curves I0 aGeometry of Jacobi Curves I bSpringer3 aJacobi curves are deep generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. In our paper we develop differential geometry of these curves which provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. Two principal invariants are the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmannian endowing the curve with a natural projective structure, and a fundamental form, which is a fourth-order differential on the curve. The so-called rank 1 curves are studied in more detail. Jacobi curves of this class are associated with systems with scalar controls and with rank 2 vector distributions.\\nIn the forthcoming second part of the paper we will present the comparison theorems (i.e., the estimates for the conjugate points in terms of our invariants( for rank 1 curves an introduce an important class of \\\"flat curves\\\".1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/311000314nas a2200109 4500008004100000245003300041210003300074260001800107100002500125700001800150856003600168 2002 en d00aGeometry of Jacobi curves II0 aGeometry of Jacobi curves II bSISSA Library1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/158901286nas a2200109 4500008004300000245007200043210006900115260003700184520089400221100002501115856003601140 2002 en_Ud 00aGlobal calibrations for the non-homogeneous Mumford-Shah functional0 aGlobal calibrations for the nonhomogeneous MumfordShah functiona bScuola Normale Superiore di Pisa3 aUsing a calibration method we prove that, if $\\\\Gamma\\\\subset \\\\Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\\\\Gamma$ and regular outside, then the function $u_{\\\\beta}$ which solves $$ \\\\begin{cases} \\\\Delta u_{\\\\beta}=\\\\beta(u_{\\\\beta}-g)& \\\\text{in $\\\\Omega\\\\setminus\\\\Gamma$} \\\\partial_{\\\\nu} u_{\\\\beta}=0 & \\\\text{on $\\\\partial\\\\Omega\\\\cup\\\\Gamma$} \\\\end{cases} $$ is in turn discontinuous along $\\\\Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \\\\int_{\\\\Omega\\\\setminus S_u}|\\\\nabla u|^2 dx +{\\\\cal H}^{n-1}(S_u)+\\\\beta\\\\int_{\\\\Omega\\\\setminus S_u}(u-g)^2 dx, $$ over $SBV(\\\\Omega)$, for $\\\\beta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/308900435nas a2200121 4500008004100000245008600041210006900127260001800196100001700214700002200231700002400253856003600277 2002 en d00aOn the K+P problem for a three-level quantum system: optimality implies resonance0 aKP problem for a threelevel quantum system optimality implies re bSISSA Library1 aBoscain, Ugo1 aChambrion, Thomas1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/160100398nas a2200121 4500008004300000245006200043210006100105260001300166100002100179700001800200700002200218856003600240 2002 en_Ud 00aLinearized elasticity as gamma-limit of finite elasticity0 aLinearized elasticity as gammalimit of finite elasticity bSpringer1 aDal Maso, Gianni1 aNegri, Matteo1 aPercivale, Danilo uhttp://hdl.handle.net/1963/305200836nas a2200109 4500008004300000245009200043210006900135260002100204520044000225100002500665856003600690 2002 en_Ud 00aLocal calibrations for minimizers of the Mumford-Shah functional with a triple junction0 aLocal calibrations for minimizers of the MumfordShah functional bWorld Scientific3 aWe prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/305000788nas a2200121 4500008004100000245008600041210006900127260001300196520037700209100002300586700002100609856003600630 2002 en d00aOn a Lyapunov functional relating shortening curves and viscous conservation laws0 aLyapunov functional relating shortening curves and viscous conse bElsevier3 aWe study a nonlinear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the \\\"change of shape\\\" of a BV solution to a scalar conservation law.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/133701609nas a2200121 4500008004100000245009900041210006900140260001800209520118400227100002101411700001901432856003601451 2002 en d00aA model for the quasi-static growth of a brittle fracture: existence and approximation results0 amodel for the quasistatic growth of a brittle fracture existence bSISSA Library3 aWe study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/157101599nas a2200121 4500008004100000245008900041210006900130260001800199520118400217100002101401700001901422856003601441 2002 en d00aA model for the quasi-static growth of brittle fractures based on local minimization0 amodel for the quasistatic growth of brittle fractures based on l bSISSA Library3 aWe study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/162101237nas a2200121 4500008004300000245009800043210006900141260001300210520081600223100002101039700001901060856003601079 2002 en_Ud 00aA Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results0 aModel for the QuasiStatic Growth of Brittle Fractures Existence bSpringer3 aWe give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith\\\'s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/305600546nas a2200109 4500008004300000245008800043210006900131260001000200520016200210100002800372856003600400 2002 en_Ud 00aA multiplicity result for the Schrodinger-Maxwell equations with negative potential0 amultiplicity result for the SchrodingerMaxwell equations with ne bIMPAN3 aWe prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/305300451nas a2200109 4500008004100000245005400041210005400095260003300149520009900182100002400281856003600305 2002 en d00aMultiplicity results for the Yamabe problem on Sn0 aMultiplicity results for the Yamabe problem on Sn bNational Academy of Sciences3 aWe discuss some results related to the existence of multiple solutions for the Yamabe problem.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/588500423nas a2200121 4500008004100000245007600041210006900117260001800186100001700204700002400221700002000245856003600265 2002 en d00aAn optimal fast-diffusion variational method for non isochronous system0 aoptimal fastdiffusion variational method for non isochronous sys bSISSA Library1 aBiasco, Luca1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/157900446nas a2200121 4500008004100000245009900041210006900140260001800209100002400227700001700251700002000268856003600288 2002 en d00aOptimal stability and instability results for a class of nearly integrable Hamiltonian systems0 aOptimal stability and instability results for a class of nearly bSISSA Library1 aBerti, Massimiliano1 aBiasco, Luca1 aBolle, Philippe uhttp://hdl.handle.net/1963/159600481nas a2200121 4500008004300000245011600043210006900159260003000228100002000258700002400278700002100302856003600323 2002 en_Ud 00aThe passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case0 apassage from nonconvex discrete systems to variational problems bMAIK Nauka/Interperiodica1 aBraides, Andrea1 aGelli, Maria Stella1 aSigalotti, Mario uhttp://hdl.handle.net/1963/313000474nas a2200121 4500008004100000245011800041210006900159260001800228100002000246700002200266700002800288856003600316 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/154000461nas a2200121 4500008004100000245010500041210006900146260001800215100002000233700002800253700002200281856003600303 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aAhmedou, Mohameden Ould1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/153901129nas a2200133 4500008004100000245005300041210004600094260001800140520073800158100002000896700002000916700002300936856003600959 2002 en d00aOn the reachability of quantized control systems0 areachability of quantized control systems bSISSA Library3 aIn this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.1 aBicchi, Antonio1 aMarigo, Alessia1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150100355nas a2200097 4500008004100000245007800041210006700119260001300186100002200199856003600221 2002 en d00aThe scalar curvature problem on $S\\\\sp n$: an approach via Morse theory0 ascalar curvature problem on Ssp n an approach via Morse theory bSpringer1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/133100345nas a2200109 4500008004100000245005200041210005200093260001100145100002100156700002200177856003600199 2002 en d00aSingular elliptic problems with critical growth0 aSingular elliptic problems with critical growth bDekker1 aCaldiroli, Paolo1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/126800585nas a2200133 4500008004100000245008200041210006900123260001800192520014200210100002400352700002200376700001700398856003600415 2002 en d00aSolutions concentrating on spheres to symmetric singularly perturbed problems0 aSolutions concentrating on spheres to symmetric singularly pertu bSISSA Library3 aWe discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/159401393nas a2200109 4500008004100000245007100041210006900112260000900181520104000190100001701230856003601247 2002 en d00aStability of planar switched systems: the linear single input case0 aStability of planar switched systems the linear single input cas bSIAM3 aWe study the stability of the origin for the dynamical system $\\\\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where A and B are two 2 × 2 real matrices with eigenvalues having strictly negative real part, $x\\\\in {\\\\mbox{{\\\\bf R}}}^2$, and $u(.):[0,\\\\infty[\\\\to[0,1]$ is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). The result is obtained without looking for a common Lyapunov function but studying the locus in which the two vector fields Ax and Bx are collinear. There are only three relevant parameters: the first depends only on the eigenvalues of A, the second depends only on the eigenvalues of B, and the third contains the interrelation among the two systems, and it is the cross ratio of the four eigenvectors of A and B in the projective line CP1. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied.1 aBoscain, Ugo uhttp://hdl.handle.net/1963/152900355nas a2200109 4500008004100000245005500041210004800096260001800144100002300162700002400185856003600209 2002 en d00aOn the Stability of the Standard Riemann Semigroup0 aStability of the Standard Riemann Semigroup bSISSA Library1 aBianchini, Stefano1 aColombo, Rinaldo M. uhttp://hdl.handle.net/1963/152800433nas a2200121 4500008004100000245008600041210006900127260001800196100002400214700001500238700002200253856003600275 2002 en d00aOn the Yamabe problem and the scalar curvature problems under boundary conditions0 aYamabe problem and the scalar curvature problems under boundary bSISSA Library1 aAmbrosetti, Antonio1 aYanYan, Li1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/151000715nas a2200109 4500008004100000245007200041210006900113260001800182520034700200100002200547856003600569 2001 en d00aAdiabatic limits of closed orbits for some Newtonian systems in R-n0 aAdiabatic limits of closed orbits for some Newtonian systems in bSISSA Library3 aWe deal with a Newtonian system like x\\\'\\\' + V\\\'(x) = 0. We suppose that V: \\\\R^n \\\\to \\\\R possesses an (n-1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/151100359nas a2200109 4500008004300000245004000043210003800083260004800121100002300169700002100192856003600213 2001 en_Ud 00aA case study in vanishing viscosity0 acase study in vanishing viscosity bAmerican Institute of Mathematical Sciences1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/309100379nas a2200109 4500008004300000245006700043210006700110260001300177100002000190700002300210856003600233 2001 en_Ud 00aControllability for discrete systems with a finite control set0 aControllability for discrete systems with a finite control set bSpringer1 aChitour, Yacine1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311400362nas a2200121 4500008004100000245004000041210003900081260001800120100002100138700001900159700002600178856003600204 2001 en d00aDieletric breakdown: optimal bounds0 aDieletric breakdown optimal bounds bSISSA Library1 aGarroni, Adriana1 aNesi, Vincenzo1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/156900415nas a2200109 4500008004100000245010000041210006900141260001800210100002100228700002000249856003600269 2001 en d00aExistence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations0 aExistence and nonexistence results for a class of nonlinear sing bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/131900345nas a2200109 4500008004100000245005000041210005000091260001800141100001700159700002300176856003600199 2001 en d00aExtremal synthesis for generic planar systems0 aExtremal synthesis for generic planar systems bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150300385nas a2200109 4500008004100000245006700041210006700108260001800175100002100193700002500214856003600239 2001 en d00aFinite Difference Approximation of Free Discontinuity Problems0 aFinite Difference Approximation of Free Discontinuity Problems bSISSA Library1 aGobbino, Massimo1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/122800396nas a2200109 4500008004100000245007600041210006900117260001000186653002900196100002500225856003600250 2001 en d00aFree-discontinuity problems: calibration and approximation of solutions0 aFreediscontinuity problems calibration and approximation of solu bSISSA10aCalibration of solutions1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/539800435nas a2200121 4500008004100000245003800041210003700079260001800116520010100134100002100235700002100256856003600277 2001 en d00aGamma-limit of periodic obstacles0 aGammalimit of periodic obstacles bSISSA Library3 aWe compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles.1 aDal Maso, Gianni1 aTrebeschi, Paola uhttp://hdl.handle.net/1963/149500342nas a2200097 4500008004100000245006700041210006400108260001300172100002300185856003600208 2001 en d00aA Glimm type functional for a special Jin-Xin relaxation model0 aGlimm type functional for a special JinXin relaxation model bElsevier1 aBianchini, Stefano uhttp://hdl.handle.net/1963/135500375nas a2200109 4500008004100000245006200041210006200103260001800165100002300183700002300206856003600229 2001 en d00aGlobal continuous Riemann solver for nonlinear elasticity0 aGlobal continuous Riemann solver for nonlinear elasticity bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149300426nas a2200109 4500008004100000245010200041210006900143260001800212100002500230700002500255856003600280 2001 en d00aLocal calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set0 aLocal calibrations for minimizers of the MumfordShah functional bSISSA Library1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/147901054nas a2200121 4500008004100000245008200041210006900123260001800192520064300210100002100853700002200874856003600896 2001 en d00aA monotonicity approach to nonlinear Dirichlet problems in perforated domains0 amonotonicity approach to nonlinear Dirichlet problems in perfora bSISSA Library3 aWe study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that no uniformity is assumed in the monotonicity condition. Under a very general hypothesis on the holes of the domains, we construct a limit equation, which is satisfied by the weak limits of the solutions. The additional term in the limit problem depends only on the local behaviour of the holes, which can be expressed in terms of suitable nonlinear capacities associated with the monotone operator.1 aDal Maso, Gianni1 aSkrypnik, Igor V. uhttp://hdl.handle.net/1963/155500380nas a2200109 4500008004100000245006800041210006700109260001800176100001700194700002300211856003600234 2001 en d00aMorse properties for the minimum time function on 2-D manifolds0 aMorse properties for the minimum time function on 2D manifolds bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/154100362nas a2200097 4500008004300000245008100043210006900124260001300193100002200206856003600228 2001 en_Ud 00aMultiple positive solutions of some elliptic equations in \\\\bold R\\\\sp N0 aMultiple positive solutions of some elliptic equations in bold R bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/309400433nas a2200121 4500008004100000245008200041210006900123260001800192100002400210700002200234700001900256856003600275 2001 en d00aMultiplicity results for some nonlinear Schrodinger equations with potentials0 aMultiplicity results for some nonlinear Schrodinger equations wi bSISSA Library1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aSecchi, Simone uhttp://hdl.handle.net/1963/156400389nas a2200109 4500008004100000245007400041210006900115260001300184100002400197700002200221856003600243 2001 en d00aNon-compactness and multiplicity results for the Yamabe problem on Sn0 aNoncompactness and multiplicity results for the Yamabe problem o bElsevier1 aBerti, Massimiliano1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/134500408nas a2200109 4500008004100000245009600041210006900137260001000206653002800216100001800244856003600262 2001 en d00aNumerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence0 aNumerical Methods for FreeDiscontinuity Problems Based on Approx bSISSA10aMumford-Shah functional1 aNegri, Matteo uhttp://hdl.handle.net/1963/539900360nas a2200109 4500008004100000245005800041210005700099260001800156100001800174700002200192856003600214 2001 en d00aNumerical minimization of the Mumford-Shah functional0 aNumerical minimization of the MumfordShah functional bSISSA Library1 aNegri, Matteo1 aPaolini, Maurizio uhttp://hdl.handle.net/1963/146100395nas a2200109 4500008004100000245008300041210006900124260001500193100002100208700002000229856003600249 2001 en d00aS^2 type parametric surfaces with prescribed mean curvature and minimal energy0 aS2 type parametric surfaces with prescribed mean curvature and m bBirkhauser1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160500970nas a2200121 4500008004300000245007300043210006500116260003100181520055000212100002800762700002200790856003600812 2001 en_Ud 00aOn the spreading of characteristics for non-convex conservation laws0 aspreading of characteristics for nonconvex conservation laws bCambridge University Press3 aWe study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos\\\' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution.1 aJenssen, Helge Kristian1 aSinestrari, Carlo uhttp://hdl.handle.net/1963/326501077nas a2200109 4500008004100000245010100041210006900142260001800211520067900229100002300908856003600931 2001 en d00aStability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions0 aStability of Linfinity solutions for hyperbolic systems with coi bSISSA Library3 aWe consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\\\\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \\\\mathcal{S}_t u_0$, defined on initial data $u_0 \\\\in L^\\\\infty$. The semigroup $\\\\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\\\\text{loc}}$ topology. Moreover $\\\\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations.1 aBianchini, Stefano uhttp://hdl.handle.net/1963/152300389nas a2200109 4500008004100000245007400041210006900115260001800184100002100202700002000223856003600243 2001 en d00aStationary states for a two-dimensional singular Schrodinger equation0 aStationary states for a twodimensional singular Schrodinger equa bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/124900364nas a2200109 4500008004100000245005900041210005100100260001800151100002500169700002400194856003600218 2001 en d00aOn the subanalyticity of Carnot-Caratheodory distances0 asubanalyticity of CarnotCaratheodory distances bSISSA Library1 aAgrachev, Andrei, A.1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/148300499nas a2200121 4500008004300000245005900043210004800102260001300150520013200163100002400295700002200319856003600341 2001 en_Ud 00aOn the symmetric scalar curvature problem on S\\\\sp n0 asymmetric scalar curvature problem on Ssp n bElsevier3 aWe discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/309500436nas a2200121 4500008004300000245008800043210006900131260001300200100001700213700002500230700002300255856003600278 2001 en_Ud 00aUniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems0 aUniqueness of classical and nonclassical solutions for nonlinear bElsevier1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311301109nas a2200121 4500008004100000245009500041210006900136260001800205520068400223100002100907700002300928856003600951 2001 en d00aUniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations0 aUniqueness of solutions to HamiltonJacobi equations arising in t bSISSA Library3 aWe prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians.1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/151500351nas a2200109 4500008004100000245005300041210005300094260001800147100001700165700002300182856003600205 2000 en d00aAbnormal extremals for minimum time on the plane0 aAbnormal extremals for minimum time on the plane bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150800394nas a2200109 4500008004100000245007600041210006900117260001800186100002400204700002000228856003600248 2000 en d00aArnold's Diffusion in nearly integrable isochronous Hamiltonian systems0 aArnolds Diffusion in nearly integrable isochronous Hamiltonian s bSISSA Library1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/155401967nas a2200121 4500008004100000245006700041210006700108260001800175520158100193100002101774700001401795856003601809 2000 en d00aBV estimates for multicomponent chromatography with relaxation0 aBV estimates for multicomponent chromatography with relaxation bSISSA Library3 aWe consider the Cauchy problem for a system of $2n$ balance laws which arises from the modelling of multi-component chromatography: $$\\\\left\\\\{ \\\\eqalign{u_t+u_x&=-{1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr v_t&={1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr}\\\\right. \\\\eqno(1)$$ This model describes a liquid flowing with unit speed over a solid bed. Several chemical substances are partly dissolved in the liquid, partly deposited on the solid bed. Their concentrations are represented respectively by the vectors $u=(u_1,\\\\ldots,u_n)$ and $v=(v_1,\\\\ldots,v_n)$. We show that, if the initial data have small total variation, then the solution of (1) remains with small variation for all times $t\\\\geq 0$. Moreover, using the $\\\\L^1$ distance, this solution depends Lipschitz continuously on the initial data, with a Lipschitz constant uniform w.r.t.~$\\\\ve$. Finally we prove that as $\\\\ve\\\\to 0$, the solutions of (1) converge to a limit described by the system $$\\\\big(u+F(u)\\\\big)_t+u_x=0,\\\\qquad\\\\qquad v=F(u).\\\\eqno(2)$$ The proof of the uniform BV estimates relies on the application of probabilistic techniques. It is shown that the components of the gradients $v_x,u_x$ can be interpreted as densities of random particles travelling with speed 0 or 1. The amount of coupling between different components is estimated in terms of the expected number of crossing of these random particles. This provides a first example where BV estimates are proved for general solutions to a class of $2n\\\\times 2n$ systems with relaxation.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/133600394nas a2200109 4500008004300000245005900043210005900102260004300161100002300204700002100227856003600248 2000 en_Ud 00aBV solutions for a class of viscous hyperbolic systems0 aBV solutions for a class of viscous hyperbolic systems bIndiana University Mathematics Journal1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/319400508nas a2200109 4500008004100000245005900041210005500100260001800155520016800173100002100341856003600362 2000 en d00aThe Calibration Method for Free Discontinuity Problems0 aCalibration Method for Free Discontinuity Problems bSISSA Library3 aThe calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/149600395nas a2200109 4500008004100000245007400041210006700115260001800182100002100200700002800221856003600249 2000 en d00aOn the convergence of Godunov scheme for nonlinear hyperbolic systems0 aconvergence of Godunov scheme for nonlinear hyperbolic systems bSISSA Library1 aBressan, Alberto1 aJenssen, Helge Kristian uhttp://hdl.handle.net/1963/147300389nas a2200109 4500008004100000245007100041210006900112260001800181100002400199700002000223856003600243 2000 en d00aDiffusion time and splitting of separatrices for nearly integrable0 aDiffusion time and splitting of separatrices for nearly integrab bSISSA Library1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/154700420nas a2200121 4500008004100000245007100041210006400112260001800176100002400194700002600218700001800244856003600262 2000 en d00aElliptic variational problems in $ R\\\\sp N$ with critical growth0 aElliptic variational problems in Rsp N with critical growth bSISSA Library1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/125800442nas a2200121 4500008004100000245008800041210006900129260001800198100002400216700002600240700001800266856003600284 2000 en d00aExistence and multiplicity results for some nonlinear elliptic equations: a survey.0 aExistence and multiplicity results for some nonlinear elliptic e bSISSA Library1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/146200387nas a2200109 4500008004100000245008000041210006900121260001000190653001900200100002200219856003600241 2000 en d00aExistence and multiplicity results for some problems in Riemannian geometry0 aExistence and multiplicity results for some problems in Riemanni bSISSA10aYamabe problem1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/594800369nas a2200109 4500008004100000245005700041210005700098260001800155100002500173700002500198856003600223 2000 en d00aFunctionals depending on curvatures with constraints0 aFunctionals depending on curvatures with constraints bSISSA Library1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/129900338nas a2200097 4500008004100000245006300041210006100104260001800165100002100183856003600204 2000 en d00aHigh-order Averaging and Stability of Time-Varying Systems0 aHighorder Averaging and Stability of TimeVarying Systems bSISSA Library1 aSarychev, Andrey uhttp://hdl.handle.net/1963/146500462nas a2200121 4500008004100000245010500041210006900146260001800215100002100233700002500254700002500279856003600304 2000 en d00aLocal calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets0 aLocal calibrations for minimizers of the MumfordShah functional bSISSA Library1 aDal Maso, Gianni1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/126100916nas a2200109 4500008004300000245006700043210006600110260000900176520056500185100002000750856003600770 2000 en_Ud 00aMinimization of functionals of the gradient by Baire's theorem0 aMinimization of functionals of the gradient by Baires theorem bSIAM3 aWe give sufficient conditions for the existence of solutions of the minimum problem $$ {\mathcal{P}}_{u_0}: \qquad \hbox{Minimize}\quad \int_\Omega g(Du(x))dx, \quad u\in u_0 + W_0^{1,p}(\Omega,{\mathbb{R}}), $$ based on the structure of the epigraph of the lower convex envelope of g, which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space. No convexity conditions are required on g, and no assumptions are made on the boundary datum $u_0\in W_0^{1,p}(\Omega,\mathbb{R})$.

1 aZagatti, Sandro uhttp://hdl.handle.net/1963/351100420nas a2200121 4500008004100000245007300041210006900114260001800183100002400201700001500225700002200240856003600262 2000 en d00aA note on the scalar curvature problem in the presence of symmetries0 anote on the scalar curvature problem in the presence of symmetri bSISSA Library1 aAmbrosetti, Antonio1 aYanYan, Li1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/136500974nas a2200121 4500008004300000245004200043210004200085260001300127520063300140100002500773700001800798856003600816 2000 en_Ud 00aPrincipal invariants of Jacobi curves0 aPrincipal invariants of Jacobi curves bSpringer3 aJacobi curves are far going generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. Differential geometry of these curves provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. In the present paper we mainly discuss two principal invariants: the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmanian providing the curve with a natural projective structure, and a fundamental form, which is a 4-oder differential on the curve.1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/382500415nas a2200133 4500008004100000020001800041245005500059210005500114260001300169100002000182700002300202700002000225856003600245 2000 en d a0-08-043658-700aQuantized control systems and discrete nonholonomy0 aQuantized control systems and discrete nonholonomy bElsevier1 aMarigo, Alessia1 aPiccoli, Benedetto1 aBicchi, Antonio uhttp://hdl.handle.net/1963/150201019nas a2200133 4500008004300000245006700043210006700110260000900177520060000186100002000786700002300806700002000829856003600849 2000 en_Ud 00aReachability Analysis for a Class of Quantized Control Systems0 aReachability Analysis for a Class of Quantized Control Systems bIEEE3 aWe study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure.1 aMarigo, Alessia1 aPiccoli, Benedetto1 aBicchi, Antonio uhttp://hdl.handle.net/1963/351801450nas a2200121 4500008004300000245006400043210006400107260000900171520106500180100002301245700002401268856003601292 2000 en_Ud 00aRegular Synthesis and Sufficiency Conditions for Optimality0 aRegular Synthesis and Sufficiency Conditions for Optimality bSIAM3 aWe propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side.1 aPiccoli, Benedetto1 aSussmann, Hector J. uhttp://hdl.handle.net/1963/321300372nas a2200121 4500008004100000245004700041210004700088260001800135100002400153700001500177700002200192856003600214 2000 en d00aScalar curvature under boundary conditions0 aScalar curvature under boundary conditions bSISSA Library1 aAmbrosetti, Antonio1 aYanYan, Li1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/150600824nas a2200109 4500008004300000245008300043210006900126260002300195520043700218100002300655856003600678 2000 en_Ud 00aThe semigroup generated by a Temple class system with non-convex flux function0 asemigroup generated by a Temple class system with nonconvex flux bKhayyam Publishing3 aWe consider the Cauchy problem for a nonlinear n × n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation.1 aBianchini, Stefano uhttp://hdl.handle.net/1963/322100416nas a2200097 4500008004100000245010100041210006900142260004800211100002300259856003600282 2000 en d00aOn the shift differentiability of the flow generated by a hyperbolic system of conservation laws0 ashift differentiability of the flow generated by a hyperbolic sy bAmerican Institute of Mathematical Sciences1 aBianchini, Stefano uhttp://hdl.handle.net/1963/127400947nas a2200121 4500008004300000245005900043210005800102260002300160520056700183100002100750700001800771856003600789 2000 en_Ud 00aStability of L^infty Solutions of Temple Class Systems0 aStability of Linfty Solutions of Temple Class Systems bKhayyam Publishing3 aLet $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

1 aBressan, Alberto1 aGoatin, Paola uhttp://hdl.handle.net/1963/325600401nas a2200109 4500008004100000245008600041210006900127260001800196100002000214700002100234856003600255 2000 en d00aOn a Steffen\\\'s result about parametric surfaces with prescribed mean curvature0 aSteffens result about parametric surfaces with prescribed mean c bSISSA Library1 aMusina, Roberta1 aCaldiroli, Paolo uhttp://hdl.handle.net/1963/155800841nas a2200121 4500008004300000245007100043210006900114260004800183520041200231100002100643700001900664856003600683 2000 en_Ud 00aA Uniqueness Condition for Hyperbolic Systems of Conservation Laws0 aUniqueness Condition for Hyperbolic Systems of Conservation Laws bAmerican Institute of Mathematical Sciences3 aConsider the Cauchy problem for a hyperbolic $n\\\\times n$ system of conservation laws in one space dimension: $$u_t+f(u)_x=0, u(0,x)=\\\\bar u(x).\\\\eqno(CP)$$ Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves.1 aBressan, Alberto1 aLewicka, Marta uhttp://hdl.handle.net/1963/319500421nas a2200109 4500008004100000245010300041210006900144260001800213100002100231700002300252856003600275 2000 en d00aValue Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities0 aValue Functions for Bolza Problems with Discontinuous Lagrangian bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/151400449nam a2200121 4500008004300000245008000043210006900123260003400192100002100226700002100247700002300268856003600291 2000 en_Ud 00aWell-posedness of the Cauchy problem for n x n systems of conservation laws0 aWellposedness of the Cauchy problem for n x n systems of conserv bAmerican Mathematical Society1 aBressan, Alberto1 aCrasta, Graziano1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/349500595nas a2200109 4500008004100000245010900041210006900150260002300219520018900242100001800431856003600449 1999 en d00aThe anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional0 aanisotropy introduced by the mesh in the finite element approxim bTaylor and Francis3 aWe compute explicitly the anisotropy effect in the H1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations.1 aNegri, Matteo uhttp://hdl.handle.net/1963/127600329nas a2200097 4500008004100000245006300041210006200104260001000166100001900176856003600195 1999 en d00aApproximation, Stability and control for Conservation Laws0 aApproximation Stability and control for Conservation Laws bSISSA1 aMarson, Andrea uhttp://hdl.handle.net/1963/550000405nas a2200109 4500008004100000020001400041245009200055210006900147100002100216700002200237856003600259 1999 en d a1618-189100aAsymptotic behaviour of nonlinear elliptic higher order equations in perforated domains0 aAsymptotic behaviour of nonlinear elliptic higher order equation1 aDal Maso, Gianni1 aSkrypnik, Igor V. uhttp://hdl.handle.net/1963/643300394nas a2200109 4500008004300000245006600043210006600109260002300175100002800198700002200226856003600248 1999 en_Ud 00aBlowup asymptotics for scalar conservation laws with a source0 aBlowup asymptotics for scalar conservation laws with a source bTaylor and Francis1 aJenssen, Helge Kristian1 aSinestrari, Carlo uhttp://hdl.handle.net/1963/348200703nas a2200133 4500008004100000245005900041210005400100260001300154520030400167