The 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.

%G eng %0 Journal Article %D 2021 %T A Differential Perspective on Gradient Flows on CAT(K)-Spaces and Applications %A Nicola Gigli %A Francesco Nobili %XWe 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.

%V 31 %P 11780 - 11818 %8 2021/12/01 %@ 1559-002X %G eng %U https://doi.org/10.1007/s12220-021-00701-5 %N 12 %! The Journal of Geometric Analysis %0 Generic %D 2021 %T A first-order condition for the independence on p of weak gradients %A Nicola Gigli %A Francesco Nobili %G eng %0 Generic %D 2021 %T On master test plans for the space of BV functions %A Francesco Nobili %A Enrico Pasqualetto %A Timo Schultz %G eng %0 Journal Article %J Fluids %D 2021 %T A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems %A Monica Nonino %A F. Ballarin %A Gianluigi Rozza %XThe 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.

%B Fluids %V 6 %P 229 %G eng %U https://www.mdpi.com/2311-5521/6/6/229 %R 10.3390/fluids6060229 %0 Journal Article %J Acta Mechanica Sinica %D 2021 %T Non-intrusive data-driven ROM framework for hemodynamics problems %A Michele Girfoglio %A Leonardo Scandurra %A Francesco Ballarin %A Giuseppe Infantino %A Francesca Nicolò %A Andrea Montalto %A Gianluigi Rozza %A Roberto Scrofani %A Marina Comisso %A Francesco Musumeci %B Acta Mechanica Sinica %V 37 %P 1183–1191 %G eng %0 Journal Article %J Phil. Trans. R. Soc. A %D 2021 %T Nutations in growing plant shoots as a morphoelastic flutter instability %A Daniele Agostinelli %A Giovanni Noselli %A Antonio DeSimone %XGrowing 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.

%B Phil. Trans. R. Soc. A %V 379 %G eng %U https://doi.org/10.1098/rsta.2020.0116 %9 Journal article %R 10.1098/rsta.2020.0116 %0 Journal Article %J Frontiers in Plant Science %D 2021 %T Nutations in plant shoots: Endogenous and exogenous factors in the presence of mechanical deformations %A Daniele Agostinelli %A Antonio DeSimone %A Giovanni Noselli %XWe 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.

%B Frontiers in Plant Science %I Cold Spring Harbor Laboratory %V 12 %G eng %U https://www.frontiersin.org/article/10.3389/fpls.2021.608005 %9 Journal article %R 10.3389/fpls.2021.608005 %0 Journal Article %J Computer & Mathematics With Applications %D 2021 %T A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems %A Efthymios N Karatzas %A Monica Nonino %A F. Ballarin %A Gianluigi Rozza %K Cut Finite Element Method %K Navier–Stokes equations %K Parameter–dependent shape geometry %K Reduced Order Models %K Unfitted mesh %XWe 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.

%B Computer & Mathematics With Applications %8 2021/08/12/ %@ 0898-1221 %G eng %U https://www.sciencedirect.com/science/article/pii/S0898122121002790 %! Computers & Mathematics with Applications %0 Generic %D 2021 %T Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds %A Francesco Nobili %A Ivan Yuri Violo %X

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.%G eng %0 Journal Article %J Mathematics in Engineering %D 2020 %T MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales %A Daniele Agostinelli %A Roberto Cerbino %A Del Alamo, Juan C %A Antonio DeSimone %A Stephanie Höhn %A Cristian Micheletti %A Giovanni Noselli %A Eran Sharon %A Julia Yeomans %K active matter %K adhesive locomotion %K cell motility %K cell sheet folding %K knotted DNA %K topological defects %K unicellular swimmers %K unjamming transition %X

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.

Mathematical 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.

%B Mathematics in Engineering %V 2 %P 230 %G eng %U http://dx.doi.org/10.3934/mine.2020011 %9 Perspective %R 10.3934/mine.2020011 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2020 %T A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations %A Efthymios N Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %XWe 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.

%B Computer Methods in Applied Mechanics and Engineering %V 370 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087886522&doi=10.1016%2fj.cma.2020.113273&partnerID=40&md5=d864e4808190b682ecb1c8b27cda72d8 %R 10.1016/j.cma.2020.113273 %0 Journal Article %J Journal of Applied Mechanics %D 2020 %T A theoretical study on the transient morphing of linear poroelastic plates %A Dario Andrini %A Alessandro Lucantonio %A Giovanni Noselli %XBased 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.

%B Journal of Applied Mechanics %V 88 %8 12 %G eng %U https://doi.org/10.1115/1.4048806 %R 10.1115/1.4048806 %0 Journal Article %J Linear Algebra and its Applications %D 2019 %T Convergence analysis of LSQR for compact operator equations %A Noe Caruso %A Paolo Novati %K Compact operator %K Lanczos bidiagonalization %K Linear ill-posed problem %K LSQR %XIn this paper we analyze the behavior of the LSQR algorithm for the solution of compact operator equations in Hilbert spaces. We present results concerning existence of Krylov solutions and the rate of convergence in terms of an ℓp sequence where p depends on the summability of the singular values of the operator. Under stronger regularity requirements we also consider the decay of the error. Finally we study the approximation of the dominant singular values of the operator attainable with the bidiagonal matrices generated by the Lanczos bidiagonalization and the arising low rank approximations. Some numerical experiments on classical test problems are presented.

%B Linear Algebra and its Applications %V 583 %P 146-164 %G eng %U https://www.sciencedirect.com/science/article/pii/S0024379519303714 %R https://doi.org/10.1016/j.laa.2019.08.024 %0 Journal Article %J Reviews in Mathematical Physics %D 2019 %T Ground state energy of mixture of Bose gases %A Alessandro Michelangeli %A Phan Thanh Nam %A Alessandro Olgiati %XWe consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N−1), we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

%B Reviews in Mathematical Physics %V 31 %P 1950005 %G eng %U https://doi.org/10.1142/S0129055X19500053 %R 10.1142/S0129055X19500053 %0 Journal Article %J Calcolo %D 2019 %T On Krylov solutions to infinite-dimensional inverse linear problems %A Noe Caruso %A Alessandro Michelangeli %A Paolo Novati %XWe discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse problem, together with a series of model examples and numerical experiments.

%B Calcolo %V 56 %P 1–25 %G eng %0 Journal Article %J Journal of the Mechanics and Physics of Solids %D 2019 %T Nutations in growing plant shoots: The role of elastic deformations due to gravity loading %A Daniele Agostinelli %A Alessandro Lucantonio %A Giovanni Noselli %A Antonio DeSimone %K Circumnutations %K Flutter instability %K Gravitropism %K Hopf bifurcation %XThe 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.

%B Journal of the Mechanics and Physics of Solids %P 103702 %G eng %U https://doi.org/10.1016/j.jmps.2019.103702 %R 10.1016/j.jmps.2019.103702 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2019 %T A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow %A Efthymios N Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %XWe 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.

%B Computer Methods in Applied Mechanics and Engineering %V 347 %P 568-587 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060107322&doi=10.1016%2fj.cma.2018.12.040&partnerID=40&md5=1a3234f0cb000c91494d946428f8ebef %R 10.1016/j.cma.2018.12.040 %0 Book Section %B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %D 2019 %T A Spectral Element Reduced Basis Method in Parametric CFD %A Martin W. Hess %A Gianluigi Rozza %E Radu, Florin Adrian %E Kumar, Kundan %E Berre, Inga %E Nordbotten, Jan Martin %E Pop, Iuliu Sorin %XWe 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.

%B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %I Springer International Publishing %V 126 %G eng %U https://arxiv.org/abs/1712.06432 %& A Spectral Element Reduced Basis Method in Parametric CFD %R 10.1007/978-3-319-96415-7_64 pages = 693–701 %0 Journal Article %J Nature Physics %D 2019 %T Swimming Euglena respond to confinement with a behavioural change enabling effective crawling %A Giovanni Noselli %A Alfred Beran %A Marino Arroyo %A Antonio DeSimone %X Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modelling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells. %B Nature Physics %V 15 %P 496–502 %G eng %U https://doi.org/10.1038/s41567-019-0425-8 %R 10.1038/s41567-019-0425-8 %0 Journal Article %J SIAM Journal on Applied Mathematics %D 2018 %T Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness %A Giuliano Lazzaroni %A Lorenzo Nardini %XWe 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.

%B SIAM Journal on Applied Mathematics %V 78 %P 1206-1227 %G eng %U https://doi.org/10.1137/17M1147354 %R 10.1137/17M1147354 %0 Journal Article %J JOURNAL OF INDUSTRIAL TEXTILES %D 2018 %T An authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production %A Rafiei, S. %A Noroozi, B. %A Luca Heltai %A Haghi, A. K. %B JOURNAL OF INDUSTRIAL TEXTILES %V 47 %P 1791–1811 %G eng %R 10.1177/1528083717710711 %0 Report %D 2018 %T Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping %A Lorenzo Nardini %A Filippo Riva %XIn 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.

%G en %U http://preprints.sissa.it/xmlui/handle/1963/35319 %1 35629 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-07-16T13:11:24Z No. of bitstreams: 1 PREPRINT_28_2018_mate.pdf: 600708 bytes, checksum: 04321c1f671175dc8cf001c358699cba (MD5) %0 Journal Article %J Journal de Mathématiques Pures et Appliquées %D 2018 %T Minimizing movements for mean curvature flow of droplets with prescribed contact angle %A Giovanni Bellettini %A Matteo Novaga %A Shokhrukh Kholmatov %K Capillary functional %K Mean curvature flow with prescribed contact angle %K Minimizing movements %K Sets of finite perimeter %XWe 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.

%B Journal de Mathématiques Pures et Appliquées %V 117 %P 1 - 58 %G eng %U http://www.sciencedirect.com/science/article/pii/S0021782418300825 %R https://doi.org/10.1016/j.matpur.2018.06.003 %0 Journal Article %J Journal of Nonlinear Science %D 2018 %T On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One %A Giuliano Lazzaroni %A Lorenzo Nardini %XThe 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.

%B Journal of Nonlinear Science %V 28 %P 269–304 %8 Feb %G eng %U https://doi.org/10.1007/s00332-017-9407-0 %R 10.1007/s00332-017-9407-0 %0 Journal Article %J International Journal of Mechanical Sciences %D 2018 %T Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry %A Noe Caruso %A Aleksandar Cvetković %A Alessandro Lucantonio %A Giovanni Noselli %A Antonio DeSimone %K Bifurcation %K Elastic bilayer %K Pre-stretch %K Shape programming %XAn 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.

%B International Journal of Mechanical Sciences %V 149 %P 481-486 %G eng %U https://www.sciencedirect.com/science/article/pii/S0020740317311761 %R https://doi.org/10.1016/j.ijmecsci.2017.08.049 %0 Conference Paper %B Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research %D 2018 %T SRTP 2.0 - The evolution of the safe return to port concept %A D. Cangelosi %A A. Bonvicini %A M. Nardo %A Andrea Mola %A A. Marchese %A Marco Tezzele %A Gianluigi Rozza %XIn 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.

%B Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research %G eng %R 10.3233/978-1-61499-870-9-665 %0 Report %D 2018 %T Truncation and convergence issues for bounded linear inverse problems in Hilbert space %A Noe Caruso %A Alessandro Michelangeli %A Paolo Novati %X We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35326 %1 35637 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-11-20T13:02:23Z No. of bitstreams: 1 infinite_dim_truncation_sissapreprint.pdf: 1326956 bytes, checksum: 75a6af69b0bca0c5b9b5283e640d89be (MD5) %0 Report %D 2017 %T On the 1D wave equation in time-dependent domains and the problem of debond initiation %A Giuliano Lazzaroni %A Lorenzo Nardini %XMotivated 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.

%I SISSA %G en %U http://preprints.sissa.it/handle/1963/35302 %1 35608 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-12-04T07:54:16Z No. of bitstreams: 1 Laz-Nar-17b-initiation-preprint.pdf: 361257 bytes, checksum: faea0e34829456cb358a72d2020f0db4 (MD5) %0 Journal Article %J Calc. Var. Partial Differential Equations %D 2017 %T The Cheeger constant of a Jordan domain without necks %A Leonardi, G. P. %A Neumayer, R. %A Saracco, G. %B Calc. Var. Partial Differential Equations %V 56 %P 164 %G eng %R 10.1007/s00526-017-1263-0 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2017 %T Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes %A Massimiliano Rossi %A Giancarlo Cicconofri %A Alfred Beran %A Giovanni Noselli %A Antonio DeSimone %X Active flagella provide the propulsion mechanism for a large variety of swimming eukaryotic microorganisms, from protists to sperm cells. Planar and helical beating patterns of these structures are recurrent and widely studied. The fast spinning motion of the locomotory flagellum of the alga Euglena gracilis constitutes a remarkable exception to these patterns. We report a quantitative description of the 3D flagellar beating in swimming E. gracilis. Given their complexity, these shapes cannot be directly imaged with current microscopy techniques. We show how to overcome these limitations by developing a method to reconstruct in full the 3D kinematics of the cell from conventional 2D microscopy images, based on the exact characterization of the helical motion of the cell body.The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement. %B Proceedings of the National Academy of Sciences %V 114 %P 13085-13090 %G eng %U https://www.pnas.org/content/114/50/13085 %R 10.1073/pnas.1708064114 %0 Journal Article %J Communications on Pure & Applied Analysis %D 2017 %T Minimizers of anisotropic perimeters with cylindrical norms %A Giovanni Bellettini %A Matteo Novaga %A Shokhrukh Kholmatov %K anisotropic Bernstein problem; %K minimal cones %K Non parametric minimal surfaces %K Sets of finite perimeter %XWe 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.

%B Communications on Pure & Applied Analysis %V 16 %P 1427 %G eng %U http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d %R 10.3934/cpaa.2017068 %0 Journal Article %J Journal of Dynamics and Differential Equations %D 2017 %T A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations %A Lorenzo Nardini %B Journal of Dynamics and Differential Equations %V 29 %P 783–797 %8 Jun %G eng %U https://doi.org/10.1007/s10884-015-9461-y %R 10.1007/s10884-015-9461-y %0 Journal Article %J Journal of High Energy Physics %D 2017 %T Real topological string amplitudes %A Narain, K. S. %A Nicolò Piazzalunga %A Alessandro Tanzini %XWe discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'= −\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

%B Journal of High Energy Physics %V 2017 %P 80 %8 Mar %G eng %U https://doi.org/10.1007/JHEP03(2017)080 %R 10.1007/JHEP03(2017)080 %0 Journal Article %J Inventiones Mathematicae %D 2017 %T Symplectic geometry of the moduli space of projective structures in homological coordinates %A Marco Bertola %A Dmitry Korotkin %A Chaya Norton %B Inventiones Mathematicae %P 1–56 %8 06 %G eng %U https://arxiv.org/abs/1506.07918 %0 Journal Article %J Journal of Differential Equations %D 2016 %T Existence and uniqueness of dynamic evolutions for a peeling test in dimension one %A Gianni Dal Maso %A Giuliano Lazzaroni %A Lorenzo Nardini %K Dynamic debonding %K Dynamic energy release rate %K Dynamic fracture %K Griffith's criterion %K Maximum dissipation principle %K Wave equation in time-dependent domains %XIn 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.

%B Journal of Differential Equations %V 261 %P 4897 - 4923 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616301772 %R https://doi.org/10.1016/j.jde.2016.07.012 %0 Journal Article %J Journal of the Mechanics and Physics of Solids %D 2015 %T Liquid crystal elastomer strips as soft crawlers %A Antonio DeSimone %A Paolo Gidoni %A Giovanni Noselli %K Crawling motility %K Directional surfaces %K Frictional interactions %K Liquid crystal elastomers %K Soft biomimetic robots %XIn 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.

%B Journal of the Mechanics and Physics of Solids %V 84 %P 254 - 272 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022509615300430 %R https://doi.org/10.1016/j.jmps.2015.07.017 %0 Journal Article %J Computers and Mathematics with Applications %D 2015 %T Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations %A Federico Negri %A Andrea Manzoni %A Gianluigi Rozza %XThis 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.

%B Computers and Mathematics with Applications %V 69 %P 319–336 %G eng %R 10.1016/j.camwa.2014.12.010 %0 Journal Article %D 2014 %T Buckling dynamics of a solvent-stimulated stretched elastomeric sheet %A Alessandro Lucantonio %A Matthieu Roché %A Paola Nardinocchi %A Howard A. Stone %X When 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. %I Royal Society of Chemistry %G en %U http://urania.sissa.it/xmlui/handle/1963/34967 %1 35197 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-10T09:50:41Z No. of bitstreams: 1 preprint2014.pdf: 2111018 bytes, checksum: 568652d2ca6c44cdad3e520342c8042d (MD5) %R 10.1039/c3sm52941j %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2014 %T Crawling on directional surfaces %A Paolo Gidoni %A Giovanni Noselli %A Antonio DeSimone %K Bio-mimetic micro-robots %K Cell migration %K Crawling motility %K Directional surfaces %K Self-propulsion %XIn 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.

%B International Journal of Non-Linear Mechanics %V 61 %P 65 - 73 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746214000213 %R https://doi.org/10.1016/j.ijnonlinmec.2014.01.012 %0 Journal Article %D 2014 %T Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost %A Giovanni Noselli %A Amabile Tatone %A Antonio DeSimone %K Cell migration %X We 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. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/34449 %1 34591 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:44:40Z No. of bitstreams: 1 N-link_crawlers.pdf: 1005838 bytes, checksum: 685d5b41e7de190ec65c60090d397f93 (MD5) %R 10.1016/j.mechrescom.2013.10.023 %0 Journal Article %J Proceedings of the Royal Society A 470, 20140333 (2014) %D 2014 %T A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model %A Giovanni Noselli %A Antonio DeSimone %X We 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. %B Proceedings of the Royal Society A 470, 20140333 (2014) %I Royal Society Publishing %G en %1 34594 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T18:10:10Z No. of bitstreams: 1 bristle_crawlers.pdf: 9309327 bytes, checksum: 10f6df9814dd01c888aa9ec7836f1dff (MD5) %R 10.1098/rspa.2014.0333 %0 Journal Article %D 2014 %T Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch %A Alessandro Lucantonio %A Paola Nardinocchi %A Howard A. Stone %X It 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. %I American Institute of Physics %G en %U http://urania.sissa.it/xmlui/handle/1963/35113 %1 35370 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:28:53Z No. of bitstreams: 1 art2014.pdf: 777840 bytes, checksum: 2362b6250fd872264208d0d3b846a551 (MD5) %R 10.1063/1.4866576 %0 Journal Article %D 2014 %T Swelling-induced and controlled curving in layered gel beams %A Alessandro Lucantonio %A Paola Nardinocchi %A Matteo Pezzulla %X We 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. %I Royal Society of London %G en %U http://urania.sissa.it/xmlui/handle/1963/34987 %1 35229 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2015-11-12T09:25:24Z (GMT) No. of bitstreams: 0 %R 10.1098/rspa.2014.0467 %0 Journal Article %J International Journal of Non-Linear Mechanics 56, 142-147 (2013) %D 2013 %T Crawlers in viscous environments: linear vs nonlinear rheology %A Antonio DeSimone %A Federica Guarnieri %A Giovanni Noselli %A Amabile Tatone %X We 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. %B International Journal of Non-Linear Mechanics 56, 142-147 (2013) %I Elsevier %G en %1 34590 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:29:52Z No. of bitstreams: 1 viscous_crawlers.pdf: 887755 bytes, checksum: 6022e4160d2eced97b51326bf51e0827 (MD5) %R 10.1016/j.ijnonlinmec.2013.02.007 %0 Report %D 2013 %T Minimal partitions and image classification using a gradient-free perimeter approximation %A Samuel Amstutz %A Nicolas Van Goethem %A Antonio André Novotny %K Image classification, deblurring, optimal partitions, perimeter approximation %X In 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. %I SISSA %G en %U http://hdl.handle.net/1963/6976 %1 6964 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Nicolas Van Goethem (vangoeth@sissa.it) on 2013-06-27T11:35:17Z No. of bitstreams: 1 Image.pdf: 1182883 bytes, checksum: 9ca6dcd03d7fd901b0d843d0062dfc74 (MD5) %0 Journal Article %J SIAM Journal on Scientific Computing %D 2013 %T Reduced basis method for parametrized elliptic optimal control problems %A Federico Negri %A Gianluigi Rozza %A Andrea Manzoni %A Alfio Quarteroni %X We propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique. %B SIAM Journal on Scientific Computing %V 35 %P A2316–A2340 %G eng %R 10.1137/120894737 %0 Journal Article %J IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %D 2013 %T Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control %A Claudio Altafini %A Francesco Ticozzi %A K. Nishio %X In 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 control %B IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %G en %U http://hdl.handle.net/1963/6503 %1 6448 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:06:12Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2206713 %0 Conference Proceedings %B European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 %D 2012 %T Reduction strategies for PDE-constrained oprimization problems in Haemodynamics %A Gianluigi Rozza %A Andrea Manzoni %A Federico Negri %K inverse problems %X Solving 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. %B European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 %G en %U http://hdl.handle.net/1963/6338 %1 6268 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T16:30:48Z\\r\\nNo. of bitstreams: 1\\r\\npaper_ECCOMAS2012_AM_SISSAreport.pdf: 4599005 bytes, checksum: 014a5a01276f25177386ad374a5917c8 (MD5) %0 Report %D 2012 %T Topological sensitivity analysis for high order elliptic operators %A Samuel Amstutz %A Antonio André Novotny %A Nicolas Van Goethem %K Topological derivative, Elliptic operators, Polarization tensor %X The 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. %I SISSA %G en %U http://hdl.handle.net/1963/6343 %1 6272 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Nicolas Van Goethem (vangoeth@sissa.it) on 2012-12-14T17:45:48Z No. of bitstreams: 1 Degenerate_sub.pdf: 479352 bytes, checksum: eefab8b4e64b0ef0c7d7f0e16d529008 (MD5) %0 Journal Article %J J. Theoret. Biol. %D 2010 %T A spatial model of cellular molecular trafficking including active transport along microtubules %A Andrea Cangiani %A Natalini, R. %B J. Theoret. Biol. %V 267 %P 614–625 %G eng %U https://doi.org/10.1016/j.jtbi.2010.08.017 %R 10.1016/j.jtbi.2010.08.017 %0 Journal Article %J Comm. Pure Appl. Math. 60 (2007) 1559-1622 %D 2007 %T Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy %A Stefano Bianchini %A Bernard Hanouzet %A Roberto Natalini %X We 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. %B Comm. Pure Appl. Math. 60 (2007) 1559-1622 %G en_US %U http://hdl.handle.net/1963/1780 %1 2764 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T10:33:17Z\\nNo. of bitstreams: 1\\n83M.pdf: 393359 bytes, checksum: f3f7b61564332b98b8706af95942dd69 (MD5) %R 10.1002/cpa.20195 %0 Journal Article %J Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %D 2007 %T Boundary-clustered interfaces for the Allen–Cahn equation %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %I Mathematical Sciences Publishers %G en %U http://hdl.handle.net/1963/5089 %1 4905 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-17T13:19:29Z\\nNo. of bitstreams: 1\\nmnw-pjm-final.pdf: 287316 bytes, checksum: 2a18e3af66be7b9b793a528138cf493a (MD5) %0 Report %D 2007 %T Smooth toric DM stacks %A Barbara Fantechi %A Etienne Mann %A Fabio Nironi %X We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks. %G en_US %U http://hdl.handle.net/1963/2120 %1 2123 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T06:41:10Z\\nNo. of bitstreams: 1\\ntoricarxiv.pdf: 426672 bytes, checksum: e73e63b89023046b5d53b7f7f6c2e580 (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 %D 2007 %T Some existence results for the Toda system on closed surfaces %A Andrea Malchiodi %A Cheikh Birahim Ndiaye %X Given 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 $\\\\rho_2 < 4 \\\\pi$. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 %G en_US %U http://hdl.handle.net/1963/1775 %1 2769 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-29T08:29:06Z\\nNo. of bitstreams: 1\\n75M.pdf: 258110 bytes, checksum: 18821ff73b71e5079c15c32f59961ad9 (MD5) %R 10.4171/RLM/504 %0 Journal Article %J J. Math. Sci. 135 (2006) 3109-3124 %D 2006 %T Classification of stable time-optimal controls on 2-manifolds %A Ugo Boscain %A Igor Nikolaev %A Benedetto Piccoli %B J. Math. Sci. 135 (2006) 3109-3124 %G en_US %U http://hdl.handle.net/1963/2196 %1 2048 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-11T07:48:50Z\\nNo. of bitstreams: 1\\nboscain-paper.pdf: 322031 bytes, checksum: 560c6fdce3f93d196d1cc9d9c4115edb (MD5) %R 10.1007/s10958-006-0148-0 %0 Journal Article %J Molecular pharmacology. 2006 Jul; 70(1):373-82 %D 2006 %T Experimental and modeling studies of desensitization of P2X3 receptors. %A Elena Sokolova %A Andrei Skorinkin %A Igor Moiseev %A Andrei A. Agrachev %A Andrea Nistri %A Rashid Giniatullin %X The 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. %B Molecular pharmacology. 2006 Jul; 70(1):373-82 %I the American Society for Pharmacology and Experimental Therapeutics %G en %U http://hdl.handle.net/1963/4974 %1 4799 %2 Neuroscience %3 Neurobiology %4 -1 %$ Submitted by Alireza Alemi-neissi (alemi@sissa.it) on 2011-10-30T18:23:32Z\\nNo. of bitstreams: 0 %R 10.1124/mol.106.023564 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %D 2005 %T Multiple clustered layer solutions for semilinear Neumann problems on a ball %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3532 %1 732 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T10:15:49Z\\nNo. of bitstreams: 1\\nMalchiodiNiWei04.pdf: 340366 bytes, checksum: a0bb6df9ca59c557fdacb5e7142ecf3d (MD5) %R 10.1016/j.anihpc.2004.05.003 %0 Journal Article %J Indiana Univ. Math. J. 53 (2004) 297-392 %D 2004 %T Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Indiana Univ. Math. J. 53 (2004) 297-392 %I Indiana University Mathematics Journal %G en %U http://hdl.handle.net/1963/1663 %1 2455 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:06:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1512/iumj.2004.53.2400 %0 Journal Article %J Numer. Math., 2003, 95, 653 %D 2003 %T A finite element approximation of the Griffith\\\'s model in fracture mechanics %A Matteo Negri %X The 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. %B Numer. Math., 2003, 95, 653 %I SISSA Library %G en %U http://hdl.handle.net/1963/1548 %1 2570 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:58Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s00211-003-0456-y %0 Journal Article %J Comm. Math. Phys. 235 (2003) no.3, 427-466 %D 2003 %T Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Comm. Math. Phys. 235 (2003) no.3, 427-466 %I Springer %G en %U http://hdl.handle.net/1963/1633 %1 2485 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:37Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1007/s00220-003-0811-y %0 Journal Article %J Set-Valued Anal. 10 (2002), p.165-183 %D 2002 %T Linearized elasticity as gamma-limit of finite elasticity %A Gianni Dal Maso %A Matteo Negri %A Danilo Percivale %B Set-Valued Anal. 10 (2002), p.165-183 %I Springer %G en_US %U http://hdl.handle.net/1963/3052 %1 1281 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:20:52Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Neg-Per-01.pdf: 199909 bytes, checksum: ddd0bf6c6890234f6d9c820fd6ab7f47 (MD5) %R 10.1023/A:1016577431636 %0 Journal Article %J C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %D 2002 %T Solutions concentrating on spheres to symmetric singularly perturbed problems %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %X We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. %B C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %I SISSA Library %G en %U http://hdl.handle.net/1963/1594 %1 2524 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:03Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2002 %R 10.1016/S1631-073X(02)02414-7 %0 Journal Article %J Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %D 2001 %T Dieletric breakdown: optimal bounds %A Adriana Garroni %A Vincenzo Nesi %A Marcello Ponsiglione %B Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %I SISSA Library %G en %U http://hdl.handle.net/1963/1569 %1 2549 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:17Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2000 %0 Thesis %D 2001 %T Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence %A Matteo Negri %K Mumford-Shah functional %I SISSA %G en %U http://hdl.handle.net/1963/5399 %1 5226 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-02-08T08:42:37Z\\nNo. of bitstreams: 1\\nPhD_Negri_Matteo.pdf: 9815789 bytes, checksum: 517224e4dfc63645a4ba399a34d9cb8f (MD5) %0 Journal Article %J Calcolo, 2001, 38, 67 %D 2001 %T Numerical minimization of the Mumford-Shah functional %A Matteo Negri %A Maurizio Paolini %B Calcolo, 2001, 38, 67 %I SISSA Library %G en %U http://hdl.handle.net/1963/1461 %1 3079 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s100920170004 %0 Journal Article %J Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 %D 1999 %T The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional %A Matteo Negri %X We 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. %B Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 %I Taylor and Francis %G en %U http://hdl.handle.net/1963/1276 %1 3179 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1080/01630569908816934 %0 Journal Article %J Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %D 1998 %T Limits of variational problems for Dirichlet forms in varying domains %A Gianni Dal Maso %A Virginia De Cicco %A Lino Notarantonio %A Nicoletta A. Tchou %B Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %I SISSA %G en %U http://hdl.handle.net/1963/6440 %1 6377 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:44:35Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5) %R 10.1016/S0362-546X(98)00067-4 %0 Journal Article %J Phys. Lett. B 297 (1992) 82-88 %D 1992 %T Topological "observables" in semiclassical field theories %A Margherita Nolasco %A Cesare Reina %XWe give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}} \rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

%B Phys. Lett. B 297 (1992) 82-88 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3541 %1 1160 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-24T09:45:37Z\\nNo. of bitstreams: 1\\n9209096v1.pdf: 142343 bytes, checksum: 14465c321b35b3996ff40101c331960b (MD5) %R 10.1016/0370-2693(92)91073-I