The HWI inequality is an {\textquotedblleft}interpolation{\textquotedblright}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 Schr{\"o}dinger problem. Our approach consists in making rigorous the Otto{\textendash}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.

}, keywords = {Entropic interpolations, Fisher information, Relative entropy, Schr{\"o}dinger problem, Wasserstein distance}, issn = {0304-4149}, doi = {https://doi.org/10.1016/j.spa.2019.04.002}, url = {http://www.sciencedirect.com/science/article/pii/S0304414918303454}, author = {Ivan Gentil and Christian L{\'e}onard and Luigia Ripani and Luca Tamanini} } @article {Kozhasov2019, title = {On the Number of Flats Tangent to Convex Hypersurfaces in Random Position}, journal = {Discrete \& Computational Geometry}, year = {2019}, month = {Mar}, issn = {1432-0444}, doi = {10.1007/s00454-019-00067-0}, url = {https://doi.org/10.1007/s00454-019-00067-0}, author = {Khazhgali Kozhasov and Antonio Lerario} } @article {AGOSTINELLI2019103702, title = {Nutations in growing plant shoots: The role of elastic deformations due to gravity loading}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2019}, pages = {103702}, abstract = {The 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{\textquoteright}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.

}, keywords = {Circumnutations, Flutter instability, Gravitropism, Hopf bifurcation}, issn = {0022-5096}, doi = {10.1016/j.jmps.2019.103702}, url = {https://doi.org/10.1016/j.jmps.2019.103702}, author = {Daniele Agostinelli and Alessandro Lucantonio and Giovanni Noselli and Antonio DeSimone} } @article {Lu{\v c}i{\'c}2019, title = {The Serre{\textendash}Swan theorem for normed modules}, journal = {Rendiconti del Circolo Matematico di Palermo Series 2}, volume = {68}, number = {2}, year = {2019}, month = {Aug}, pages = {385{\textendash}404}, issn = {1973-4409}, doi = {10.1007/s12215-018-0366-6}, url = {https://doi.org/10.1007/s12215-018-0366-6}, author = {Danka Lu{\v c}i{\'c} and Enrico Pasqualetto} } @article {doi:10.1137/17M1147354, title = {Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness}, journal = {SIAM Journal on Applied Mathematics}, volume = {78}, number = {2}, year = {2018}, pages = {1206-1227}, abstract = {We 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{\textquoteright}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.

}, doi = {10.1137/17M1147354}, url = {https://doi.org/10.1137/17M1147354}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {doi:10.1142/S0218202518500379, title = {Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {28}, number = {07}, year = {2018}, pages = {1371-1412}, abstract = {In 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.

}, doi = {10.1142/S0218202518500379}, url = {https://doi.org/10.1142/S0218202518500379}, author = {Vito Crismale and Giuliano Lazzaroni and Gianluca Orlando} } @inbook {AuricchioContiLefieuxMorgantiRealiRozzaVeneziani2018, title = {Computational methods in cardiovascular mechanics}, booktitle = {Cardiovascular Mechanics}, year = {2018}, pages = {54}, publisher = {CRC Press}, organization = {CRC Press}, chapter = {Computational methods in cardiovascular mechanics}, abstract = {The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

}, url = {https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201\%2Fb21917-5}, author = {Auricchio, Ferdinando and Conti, Michele and Lefieux, Adrian and Morganti, Simone and Alessandro Reali and Gianluigi Rozza and Veneziani, Alessandro}, editor = {Michel F. Labrosse} } @article {1807.02060, title = {Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case}, year = {2018}, author = {Marta Lewicka and Danka Lu{\v c}i{\'c}} } @article {2018, title = {Energy-dissipation balance of a smooth moving crack}, number = {SISSA;31/2018/MATE}, year = {2018}, abstract = {In 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 [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.}, url = {http://preprints.sissa.it/handle/1963/35320}, author = {Maicol Caponi and Ilaria Lucardesi and Emanuele Tasso} } @article {2018, title = {Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition}, number = {SISSA;04/2018/MATE}, year = {2018}, abstract = {We 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.}, url = {http://preprints.sissa.it/handle/1963/35308}, author = {Gianni Dal Maso and Cristopher J. Larsen and Rodica Toader} } @article {agostiniani2018foldable, title = {Foldable structures made of hydrogel bilayers}, year = {2018}, author = {Virginia Agostiniani and Antonio DeSimone and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {agostiniani2018heterogeneous, title = {Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, year = {2018}, publisher = {EDP Sciences}, doi = {https://doi.org/10.1051/cocv/2018046}, author = {Virginia Agostiniani and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {Lazzaroni2018, title = {On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One}, journal = {Journal of Nonlinear Science}, volume = {28}, number = {1}, year = {2018}, month = {Feb}, pages = {269{\textendash}304}, abstract = {The 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{\textquoteright}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{\textquoteright}s (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

}, issn = {1432-1467}, doi = {10.1007/s00332-017-9407-0}, url = {https://doi.org/10.1007/s00332-017-9407-0}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @conference {demo2018shape, title = {Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition}, booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research}, year = {2018}, publisher = {IOS Press}, organization = {IOS Press}, chapter = {212}, address = {Trieste, Italy}, abstract = {Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship.}, doi = {10.3233/978-1-61499-870-9-212}, url = {http://ebooks.iospress.nl/publication/49229}, author = {Nicola Demo and Marco Tezzele and Gianluca Gustin and Gianpiero Lavini and Gianluigi Rozza} } @article {2017, title = {On the 1D wave equation in time-dependent domains and the problem of debond initiation}, number = {SISSA;56/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {Motivated 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.

}, url = {http://preprints.sissa.it/handle/1963/35302}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {2017, title = {Advances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method}, journal = {Communication in Applied Industrial Mathematics}, year = {2017}, type = {reviewed}, abstract = {Vortex 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.

}, keywords = {finite volume, CFD, Reduced order methods}, url = {https://arxiv.org/abs/1701.03424}, author = {Giovanni Stabile and Saddam Hijazi and Stefano Lorenzi and Andrea Mola and Gianluigi Rozza} } @article {2017, title = {Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours}, number = {SISSA;58/2016/MATE}, year = {2017}, abstract = {We 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35269}, author = {Roberto Alicandro and Giuliano Lazzaroni and Mariapia Palombaro} } @article {2017, title = {On the effect of interactions beyond nearest neighbours on non-convex lattice systems}, number = {SISSA;57/2016/MATE}, year = {2017}, abstract = {We 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35268}, author = {Roberto Alicandro and Giuliano Lazzaroni and Mariapia Palombaro} } @article {Agrachev2017, title = {Homotopically invisible singular curves}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {56}, number = {4}, year = {2017}, month = {Jul}, pages = {105}, issn = {1432-0835}, doi = {10.1007/s00526-017-1203-z}, url = {https://doi.org/10.1007/s00526-017-1203-z}, author = {Andrei A. Agrachev and Francesco Boarotto and Antonio Lerario} } @article {boarotto2017homotopy, title = {Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry}, journal = {Communications in Analysis and Geometry}, volume = {25}, number = {2}, year = {2017}, pages = {269{\textendash}301}, publisher = {International Press of Boston}, doi = {10.4310/CAG.2017.v25.n2.a1}, author = {Francesco Boarotto and Antonio Lerario} } @article {luzzatto_2017, title = {Integrability of dominated decompositions on three-dimensional manifolds}, journal = {Ergodic Theory and Dynamical Systems}, volume = {37}, number = {2}, year = {2017}, pages = {606{\textendash}620}, publisher = {Cambridge University Press}, abstract = {

We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.

Employing 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.

}, issn = {1420-9004}, doi = {10.1007/s00030-016-0426-6}, url = {https://doi.org/10.1007/s00030-016-0426-6}, author = {Vito Crismale and Giuliano Lazzaroni} } @article {1711.08253, title = {Random spectrahedra}, year = {2017}, author = {Paul Breiding and Khazhgali Kozhasov and Antonio Lerario} } @article {2017, title = {A reduced order model for investigating the dynamics of the Gen-IV LFR coolant pool}, journal = {Applied Mathematical Modelling}, volume = {46}, year = {2017}, pages = {263-284}, doi = {10.1016/j.apm.2017.01.066}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85020006623\&doi=10.1016\%2fj.apm.2017.01.066\&partnerID=40\&md5=f6e5715037eb0ef2ecb9ae03f373294f}, author = {Stefano Lorenzi and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2017, title = {Semistable Higgs Bundles on Calabi-Yau Manifolds}, number = {SISSA;40/2017/MATE;}, year = {2017}, abstract = {We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.}, url = {http://preprints.sissa.it/handle/1963/35295}, author = {Ugo Bruzzo and Valeriano Lanza and Alessio Lo Giudice} } @article {2016, title = {Confinement of dislocations inside a crystal with a prescribed external strain}, year = {2016}, note = {Preprint SISSA 20/2016/MATE}, abstract = {We 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35247}, author = {Ilaria Lucardesi and Marco Morandotti and Riccardo Scala and Davide Zucco} } @article {DALMASO20164897, title = {Existence and uniqueness of dynamic evolutions for a peeling test in dimension one}, journal = {Journal of Differential Equations}, volume = {261}, number = {9}, year = {2016}, pages = {4897 - 4923}, abstract = {In 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.

}, keywords = {Dynamic debonding, Dynamic energy release rate, Dynamic fracture, Griffith{\textquoteright}s criterion, Maximum dissipation principle, Wave equation in time-dependent domains}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2016.07.012}, url = {http://www.sciencedirect.com/science/article/pii/S0022039616301772}, author = {Gianni Dal Maso and Giuliano Lazzaroni and Lorenzo Nardini} } @article {doi:10.1142/S0129167X16500610, title = {A Frobenius theorem for corank-1 continuous distributions in dimensions two and three}, journal = {International Journal of Mathematics}, volume = {27}, number = {08}, year = {2016}, pages = {1650061}, abstract = {We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive C1 distribution is uniquely integrable.

}, doi = {10.1142/S0129167X16500610}, url = {https://doi.org/10.1142/S0129167X16500610}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @article {arici2016gysin, title = {The Gysin sequence for quantum lens spaces}, journal = {Journal of Noncommutative Geometry}, volume = {9}, number = {4}, year = {2016}, pages = {1077{\textendash}1111}, abstract = {We define quantum lens spaces as {\textquoteleft}direct sums of line bundles{\textquoteright} and exhibit them as {\textquoteleft}total spaces{\textquoteright} of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as {\textquoteleft}line bundles{\textquoteright} over quantum lens spaces and generically define {\textquoteleft}torsion classes{\textquoteright}. We work out explicit examples of these classes.

}, doi = {10.4171/JNCG/216}, author = {Francesca Arici and Simon Brain and Giovanni Landi} } @article {doi:10.1080/14689367.2015.1057480, title = {Integrability of C1 invariant splittings}, journal = {Dynamical Systems}, volume = {31}, number = {1}, year = {2016}, pages = {79-88}, publisher = {Taylor \& Francis}, abstract = {We derive some new conditions for integrability of dynamically defined C1 invariant splittings, formulated in terms of the singular values of the iterates of the derivative of the diffeomorphism which defines the splitting.

}, doi = {10.1080/14689367.2015.1057480}, url = {https://doi.org/10.1080/14689367.2015.1057480}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @article {11966, title = {A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel}, journal = {Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208}, volume = {87}, number = {Annals of Nuclear Energy;87}, year = {2016}, pages = {208}, publisher = {Elsevier}, chapter = {198}, abstract = {In 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.}, doi = {doi:10.1016/j.anucene.2015.09.002}, url = {http://urania.sissa.it/xmlui/handle/1963/35191}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @inbook {Arici2016, title = {Pimsner Algebras and Circle Bundles}, booktitle = {Noncommutative Analysis, Operator Theory and Applications}, year = {2016}, pages = {1{\textendash}25}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

}, isbn = {978-3-319-29116-1}, doi = {10.1007/978-3-319-29116-1_1}, url = {https://doi.org/10.1007/978-3-319-29116-1_1}, author = {Francesca Arici and Francesco D{\textquoteright}Andrea and Giovanni Landi}, editor = {Alpay, Daniel and Cipriani, Fabio and Colombo, Fabrizio and Guido, Daniele and Sabadini, Irene and Sauvageot, Jean-Luc} } @article {arici2016pimsner, title = {Pimsner algebras and Gysin sequences from principal circle actions}, journal = {Journal of Noncommutative Geometry}, volume = {10}, year = {2016}, pages = {29{\textendash}64}, issn = {1661-6952}, doi = {10.4171/jncg/228}, url = {http://hdl.handle.net/2066/162951}, author = {Francesca Arici and Jens Kaad and Giovanni Landi} } @article {2016, title = {POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations}, year = {2016}, publisher = {Computer Methods in Applied Mechanics and Engineering, Elsevier}, abstract = {Numerical 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 {\textendash} Reduced Order Model (POD {\textendash} 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.}, author = {Stefano Lorenzi and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {11967, title = {A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods}, journal = {NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019}, volume = {2}, number = {Journal of Nuclear Engineering and Radiation Science;2}, year = {2016}, note = {8 pages}, month = {02/2016}, pages = {8}, publisher = {ASME}, abstract = {This 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 {\textquotedblleft}classical{\textquotedblright} 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.}, doi = {10.1115/1.4031945}, url = {http://urania.sissa.it/xmlui/handle/1963/35192}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2015, title = {Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods}, journal = {Communications in Computational Physics}, year = {2016}, month = {2016}, publisher = {SISSA}, abstract = {In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a {\textquotedblleft}staircase{\textquotedblright} strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as {\textquotedblleft}truth{\textquotedblright} solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine {\textquotedblleft}truth{\textquotedblright} finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34963}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {Fiorenza2016, title = {t-Structures are Normal Torsion Theories}, journal = {Applied Categorical Structures}, volume = {24}, number = {2}, year = {2016}, month = {Apr}, pages = {181{\textendash}208}, abstract = {We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathcal{t}$ on a stable $\infty$-category $\mathbb{C}$ is equivalent to a normal torsion theory $\mathbf{F}$ on $\mathbb{C}$, i.e. to a factorization system $\mathbf{F} = (\mathcal{\epsilon}, \mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

}, issn = {1572-9095}, doi = {10.1007/s10485-015-9393-z}, url = {https://doi.org/10.1007/s10485-015-9393-z}, author = {Domenico Fiorenza and Fosco Loregian} } @mastersthesis {2016, title = {t-structures on stable (infinity,1)-categories}, year = {2016}, school = {SISSA}, abstract = {The present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosick{\'y}, Tholen, and Cassidy-H{\'e}bert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from.}, keywords = {category theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra}, url = {http://urania.sissa.it/xmlui/handle/1963/35202}, author = {Fosco Loregian} } @article {Crismale2016, title = {Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {55}, number = {1}, year = {2016}, month = {Jan}, pages = {17}, abstract = {Employing 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.

}, issn = {1432-0835}, doi = {10.1007/s00526-015-0947-6}, url = {https://doi.org/10.1007/s00526-015-0947-6}, author = {Vito Crismale and Giuliano Lazzaroni} } @article {1078-0947_2016_3_1465, title = {Young towers for product systems}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {36}, number = {1078-0947_2016_3_146}, year = {2016}, pages = {1465}, abstract = {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{\'e}non maps and partially hyperbolic systems.

}, issn = {1078-0947}, doi = {10.3934/dcds.2016.36.1465}, url = {http://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642}, author = {Stefano Luzzatto and Marks Ruziboev} } @article {2015, title = {A bridging mechanism in the homogenisation of brittle composites with soft inclusions}, number = {SISSA;02/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/7492}, author = {Marco Barchiesi and Giuliano Lazzaroni and Caterina Ida Zeppieri} } @article {2015, title = {Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition}, year = {2015}, abstract = {There 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35045}, author = {Gianni Dal Maso and Cristopher J. Larsen and Rodica Toader} } @article {agrachev2015geodesics, title = {Geodesics and horizontal-path spaces in Carnot groups}, journal = {Geometry \& Topology}, volume = {19}, number = {3}, year = {2015}, pages = {1569{\textendash}1630}, publisher = {Mathematical Sciences Publishers}, abstract = {We 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.

}, doi = {10.2140/gt.2015.19.1569}, author = {Andrei A. Agrachev and Alessandro Gentile and Antonio Lerario} } @article {2015, title = {The phototransduction machinery in the rod outer segment has a strong efficacy gradient}, number = {Proceedings of the National Academy of Sciences of the United States of America;Volume 112, issue 20; pp. E2715-E2724}, year = {2015}, note = {Open Access article}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1423162112}, url = {http://urania.sissa.it/xmlui/handle/1963/35157}, author = {Monica Mazzolini and Giuseppe Facchetti and L. Andolfi and R. Proietti Zaccaria and S. Tuccio and J. Treud and Claudio Altafini and Enzo M. Di Fabrizio and Marco Lazzarino and G. Rapp and Vincent Torre} } @article {2015, title = {Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires}, number = {SISSA;04/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {In 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 large}, url = {http://urania.sissa.it/xmlui/handle/1963/7494}, author = {Giuliano Lazzaroni and Mariapia Palombaro and Anja Schlomerkemper} } @article {MR3280250, title = {Strong asymptotics of the orthogonal polynomials with respect to a measure supported on the plane}, journal = {Comm. Pure Appl. Math.}, volume = {68}, number = {1}, year = {2015}, pages = {112{\textendash}172}, issn = {0010-3640}, doi = {10.1002/cpa.21541}, url = {http://dx.doi.org/10.1002/cpa.21541}, author = {Ferenc Balogh and Marco Bertola and Lee, Seung-Yeop and Kenneth McLaughlin} } @article {2015, title = {The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data}, number = {SISSA;47/2015/MATE}, year = {2015}, abstract = {Given 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/34629}, author = {Gianni Dal Maso and Ilaria Lucardesi} } @article {2014, title = {Achieving unanimous opinions in signed social networks}, number = {2014 European Control Conference;article number 6862161; pages 184-189;}, year = {2014}, publisher = {Institute of Electrical and Electronics Engineers Inc.}, abstract = {Being 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.}, doi = {10.1109/ECC.2014.6862161}, url = {http://urania.sissa.it/xmlui/handle/1963/34935}, author = {Claudio Altafini and Gabriele Lini} } @article {2014, title = {Buckling dynamics of a solvent-stimulated stretched elastomeric sheet}, number = {Soft Matter;volume 10; issue 16; pages 2800-2804;}, year = {2014}, publisher = {Royal Society of Chemistry}, abstract = {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.}, doi = {10.1039/c3sm52941j}, url = {http://urania.sissa.it/xmlui/handle/1963/34967}, author = {Alessandro Lucantonio and Matthieu Roch{\'e} and Paola Nardinocchi and Howard A. Stone} } @article {2014, title = {Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics}, journal = {Annals of Nuclear Energy}, volume = {71}, number = {Annals of Nuclear Energy;volume 71; pages 217-229;}, year = {2014}, month = {09/2014}, pages = {229}, publisher = {Elsevier}, chapter = {217}, abstract = {In this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

}, doi = {10.1016/j.anucene.2014.03.043}, url = {http://urania.sissa.it/xmlui/handle/1963/35039}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Davide Chiesa and Lelio Luzzi and Roberto R. Ponciroli and Ezio Previtali and Marco E. Ricotti and Gianluigi Rozza and Monica Sisti} } @article {2014, title = {Model Order Reduction in Fluid Dynamics: Challenges and Perspectives}, number = {Modeling simulation and applications;volume 9; pages 235-273;}, year = {2014}, publisher = {Springer}, abstract = {This 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.}, doi = {10.1007/978-3-319-02090-7_9}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {Rate-independent damage in thermo-viscoelastic materials with inertia}, number = {SISSA;52/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {We 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/7444}, author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader} } @proceedings {2014, title = {A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics}, number = {International Conference on Nuclear Engineering, Proceedings, ICONE;volume 5;}, year = {2014}, note = {2014 22nd International Conference on Nuclear Engineering, ICONE 2014; Prague; Czech Republic; 7 July 2014 through 11 July 2014; Code 109131;}, month = {07/2014}, pages = {V005T17A048-V005T17A048}, publisher = {American Society of Mechanical Engineers (ASME)}, edition = {American Society Mechanical Engineering}, address = {Prague, Czech Republic}, abstract = {In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

}, isbn = {978-079184595-0}, doi = {10.1115/ICONE22-30707}, url = {http://urania.sissa.it/xmlui/handle/1963/35123}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2014, title = {Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional}, year = {2014}, note = {This article is composed if 33 pages and recorded in PDF format}, publisher = {SISSA}, abstract = {The 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.}, keywords = {Gamma-convergence, Cahn-Hilliard functional, phase transitions}, url = {http://hdl.handle.net/1963/7390}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2014, title = {Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics}, number = {SISSA;53/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {This 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/7463}, author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader} } @article {2014, title = {Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch}, number = {Journal of Applied Physics;volume 115; issue 8; article number 083505;}, year = {2014}, publisher = {American Institute of Physics}, abstract = {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.}, doi = {10.1063/1.4866576}, url = {http://urania.sissa.it/xmlui/handle/1963/35113}, author = {Alessandro Lucantonio and Paola Nardinocchi and Howard A. Stone} } @article {2014, title = {Swelling-induced and controlled curving in layered gel beams}, number = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;volume 470; issue 2171;}, year = {2014}, publisher = {Royal Society of London}, abstract = {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.}, doi = {10.1098/rspa.2014.0467}, url = {http://urania.sissa.it/xmlui/handle/1963/34987}, author = {Alessandro Lucantonio and Paola Nardinocchi and Matteo Pezzulla} } @article {2013, title = {Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces}, number = {Archive for Rational Mechanics and Analysis}, year = {2013}, publisher = {Springer}, abstract = {In 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].}, keywords = {singular nonlinear parabolic equations, Hilbert transform, thin films}, doi = {10.1007/s00205-014-0730-4}, url = {http://hdl.handle.net/1963/7245}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @mastersthesis {2013, title = {On the desingularization of Kahler orbifolds with constant scalar curvature}, year = {2013}, school = {SISSA}, author = {Riccardo Lena} } @article {2013, title = {Genus stabilization for moduli of curves with symmetries}, number = {arXiv:1301.4409;}, year = {2013}, note = {21 pages, 2 figures}, publisher = {SISSA}, abstract = {In a previous paper, arXiv:1206.5498, we introduced a new homological\r\ninvariant $\\e$ for the faithful action of a finite group G on an algebraic\r\ncurve.\r\n We show here that the moduli space of curves admitting a faithful action of a\r\nfinite group G with a fixed homological invariant $\\e$, if the genus g\' of the\r\nquotient curve is sufficiently large, is irreducible (and non empty iff the\r\nclass satisfies the condition which we define as \'admissibility\'). In the\r\nunramified case, a similar result had been proven by Dunfield and Thurston\r\nusing the classical invariant in the second homology group of G, H_2(G, \\ZZ).\r\n We achieve our result showing that the stable classes are in bijection with\r\nthe set of admissible classes $\\e$.}, keywords = {group actions, mapping class group, Moduli space of curves, Teichm{\"u}ller space}, url = {http://hdl.handle.net/1963/6509}, author = {Fabrizio Catanese and Michael L{\"o}nne and Fabio Perroni} } @article {2013, title = {A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics}, number = {SISSA preprint;15/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows}, number = {SISSA preprint;14/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics}, number = {SISSA preprint;13/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Gianluigi Rozza} } @article {2001, title = {Some remarks on the viscous approximation of crack growth}, journal = {Discrete Contin. Dyn. Syst. Ser. S}, volume = {6}, number = {SISSA;24/2011/M}, year = {2013}, publisher = {SISSA}, chapter = {131-146}, abstract = {We 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.

}, keywords = {Variational models}, url = {http://hdl.handle.net/1963/4206}, author = {Giuliano Lazzaroni and Rodica Toader} } @mastersthesis {2013, title = {Some topics on Higgs bundles over projective varieties and their moduli spaces}, year = {2013}, school = {SISSA}, abstract = {In this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes.}, keywords = {Algebraic Geometry, Moduli spaces, Vector bundles}, author = {Alessio Lo Giudice} } @article {MR3117621, title = {Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes}, journal = {J. Stat. Phys.}, volume = {153}, number = {4}, year = {2013}, pages = {654{\textendash}697}, issn = {0022-4715}, doi = {10.1007/s10955-013-0845-2}, url = {http://dx.doi.org/10.1007/s10955-013-0845-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {2012, title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty}, journal = {Mathematical Modelling and Numerical Analysis, in press, 2012-13}, number = {SISSA;42/2012/M}, year = {2012}, publisher = {Cambridge University Press}, abstract = {We 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.}, keywords = {shape optimization}, url = {http://hdl.handle.net/1963/6337}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {Convex pencils of real quadratic forms}, journal = {Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047}, number = {arXiv:1106.4678v3;}, year = {2012}, note = {Updated version to be published in DCG ; was published in : Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047}, publisher = {Springer}, abstract = {We 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).}, doi = {10.1007/s00454-012-9460-2}, url = {http://hdl.handle.net/1963/7099}, author = {Antonio Lerario} } @inbook {2012, title = {Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs}, booktitle = {Springer, Indam Series, Vol. 4, 2012}, number = {SISSA Preprint;44/2012/M}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {The 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.}, keywords = {solution manifold}, url = {http://hdl.handle.net/1963/6340}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {On the genus two free energies for semisimple Frobenius manifolds}, journal = {Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298}, number = {arXiv:1205.5990;}, year = {2012}, note = {36 pages, 3 figures}, publisher = {SISSA}, abstract = {We represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.}, doi = {10.1134/S1061920812030028}, url = {http://hdl.handle.net/1963/6464}, author = {Boris Dubrovin and Si-Qi Liu and Youjin Zhang} } @article {2012, title = {Moduli spaces of noncommutative instantons: gauging away noncommutative parameters}, journal = {Quarterly Journal of Mathematics (2012) 63 (1): 41-86}, number = {SISSA;62/2009/FM}, year = {2012}, publisher = {Oxford University Press}, abstract = {Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\\\\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.}, doi = {10.1093/qmath/haq036}, url = {http://hdl.handle.net/1963/3777}, author = {Simon Brain and Giovanni Landi} } @article {2012, title = {On robust Lie-algebraic stability conditions for switched linear systems}, journal = {Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353}, year = {2012}, abstract = {This 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.}, doi = {10.1016/j.sysconle.2011.11.016}, url = {http://hdl.handle.net/1963/6455}, author = {Andrei A. Agrachev and Yurij Baryshnikov and Daniel Liberzon} } @article {MR2880030, title = {Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes}, journal = {J. Stat. Phys.}, volume = {146}, number = {3}, year = {2012}, pages = {475{\textendash}518}, issn = {0022-4715}, doi = {10.1007/s10955-011-0409-2}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {2012, title = {Systems of Quadratic Inequalities}, journal = {Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660}, number = {arXiv:1012.5731;}, year = {2012}, publisher = {SISSA}, abstract = {We 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.}, doi = {DOI: 10.1112/plms/pds010}, url = {http://hdl.handle.net/1963/7072}, author = {Andrei A. Agrachev and Antonio Lerario} } @article {2011, title = {Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry}, year = {2011}, note = {25 pages}, publisher = {SISSA}, abstract = {We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.}, url = {http://hdl.handle.net/1963/6508}, author = {Andrei A. Agrachev and Paul Lee} } @article {10654, title = {Cones of divisors of blow-ups of projective spaces}, journal = {Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187}, year = {2011}, publisher = {Universit{\`a} degli Studi di Catania. Dipartimento di matematica}, abstract = {We investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points.}, keywords = {Mori dream space}, doi = {10.4418/2011.66.2.13}, url = {http://hdl.handle.net/1963/6613}, author = {Alessio Lo Giudice and Salvatore Cacciola and M. Donten-Bury and O. Dumitrescu and J. Park} } @article {2011, title = {Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem}, journal = {Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231}, number = {SISSA;70/2009/M}, year = {2011}, publisher = {American Institute of Mathematical Sciences}, abstract = {We 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.}, doi = {10.3934/dcds.2011.31.1219}, url = {http://hdl.handle.net/1963/3801}, author = {Gianni Dal Maso and Giuliano Lazzaroni} } @article {2011, title = {Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions}, journal = {PNAS 108 (2011) 13978}, year = {2011}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1100549108}, url = {http://hdl.handle.net/1963/4358}, author = {Luca Cardamone and Alessandro Laio and Rajesh Shahapure and Antonio DeSimone} } @article {2011, title = {Energy release rate and stress intensity factor in antiplane elasticity}, journal = {Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584}, number = {SISSA;67/2009/M}, year = {2011}, publisher = {Elsevier}, abstract = {In 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.}, doi = {10.1016/j.matpur.2011.01.001}, url = {http://hdl.handle.net/1963/3780}, author = {Giuliano Lazzaroni and Rodica Toader} } @article {2011, title = {Existence for wave equations on domains with arbitrary growing cracks}, journal = {Rend. Lincei Mat. Appl. 22 (2011) 387-408}, number = {SISSA;32/2011/M}, year = {2011}, publisher = {European Mathematical Society}, abstract = {In 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.}, keywords = {Wave equation}, doi = {10.4171/RLM/606}, url = {http://hdl.handle.net/1963/4284}, author = {Gianni Dal Maso and Cristopher J. Larsen} } @article {2011, title = {Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds}, number = {arXiv:0903.2550;}, year = {2011}, note = {This is a revised extended version that contains new results.}, publisher = {SISSA}, url = {http://hdl.handle.net/1963/6507}, author = {Andrei A. Agrachev and Paul Lee} } @mastersthesis {2011, title = {Homology invariants of quadratic maps}, year = {2011}, school = {SISSA}, abstract = {Given 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...}, url = {http://hdl.handle.net/1963/6245}, author = {Antonio Lerario} } @article {2011, title = {The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells}, journal = {Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050}, number = {SISSA;75/2008/M}, year = {2011}, publisher = {Springer}, abstract = {Using 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.}, doi = {10.1007/s00205-010-0387-6}, url = {http://hdl.handle.net/1963/3392}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article { ISI:000296627000002, title = {A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION}, journal = {{MATHEMATICAL MODELS \& METHODS IN APPLIED SCIENCES}}, volume = {{21}}, number = {{10}}, year = {2011}, month = {{OCT}}, pages = {{2019-2047}}, publisher = {{WORLD SCIENTIFIC PUBL CO PTE LTD}}, type = {{Article}}, address = {{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}}, abstract = {{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.}

}, keywords = {Brittle fracture, Crack propagation, energy derivative, energy release rate, free-discontinuity problems, Griffith{\textquoteright}s criterion, local minimizers, stress intensity factor}, vanishing viscosity, {Variational models}, issn = {{0218-2025}}, doi = {{10.1142/S0218202511005647}}, author = {Giuliano Lazzaroni and Rodica Toader} } @conference {10.1007/978-1-4419-9554-4_10, title = {The Monge Problem in Geodesic Spaces}, booktitle = {Nonlinear Conservation Laws and Applications}, year = {2011}, pages = {217{\textendash}233}, publisher = {Springer US}, organization = {Springer US}, address = {Boston, MA}, abstract = {We 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.

}, isbn = {978-1-4419-9554-4}, author = {Stefano Bianchini and Fabio Cavalletti}, editor = {Alberto Bressan and Chen, Gui-Qiang G. and Marta Lewicka and Wang, Dehua} } @article { ISI:000286300100012, title = {Quasistatic crack growth in finite elasticity with Lipschitz data}, journal = {{ANNALI DI MATEMATICA PURA ED APPLICATA}}, volume = {{190}}, number = {{1}}, year = {2011}, month = {{JAN}}, pages = {{165-194}}, publisher = {{SPRINGER HEIDELBERG}}, type = {{Article}}, address = {{TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY}}, abstract = {{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.}

}, keywords = {Brittle fracture, Crack propagation, Energy minimization, Finite elasticity, free-discontinuity problems, Griffith{\textquoteright}s criterion, Non-interpenetration}, Polyconvexity, Quasistatic evolution, Rate-independent processes, {Variational models}, issn = {{0373-3114}}, doi = {{10.1007/s10231-010-0145-2}}, author = {Giuliano Lazzaroni} } @article {2011, title = {Singular perturbation models in phase transitions for second order materials}, journal = {Indiana Univ. Math. J. 60 (2011) 367-409}, number = {SISSA;20/2010/M}, year = {2011}, publisher = {Indiana University}, abstract = {A 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.}, doi = {10.1512/iumj.2011.60.4346}, url = {http://hdl.handle.net/1963/3858}, author = {Milena Chermisi and Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2011, title = {A system-level approach for deciphering the transcriptional response to prion infection}, journal = {Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14}, number = {PMID:22016408;}, year = {2011}, publisher = {Oxford University Press}, abstract = {MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.}, doi = {10.1093/bioinformatics/btr580}, url = {http://hdl.handle.net/1963/5745}, author = {Mattia Zampieri and Giuseppe Legname and Daniel Segr{\`e} and Claudio Altafini} } @article {2010, title = {Continuity of optimal control costs and its application to weak KAM theory}, journal = {Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232}, number = {arXiv:0909.3826;}, year = {2010}, note = {23 pages, 1 figures}, publisher = {SISSA}, abstract = {We 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.}, doi = {10.1007/s00526-010-0308-4}, url = {http://hdl.handle.net/1963/6459}, author = {Andrei A. Agrachev and Paul Lee} } @article {2010, title = {Exact reconstruction of damaged color images using a total variation model}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331}, year = {2010}, publisher = {Elsevier}, abstract = {In 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.}, doi = {10.1016/j.anihpc.2010.06.004}, url = {http://hdl.handle.net/1963/4039}, author = {Irene Fonseca and Giovanni Leoni and Francesco Maggi and Massimiliano Morini} } @article {Bertola:wj, title = {First colonization of a hard-edge in random matrix theory}, journal = {Constr. Approx.}, volume = {31}, number = {2}, year = {2010}, pages = {231{\textendash}257}, issn = {0176-4276}, doi = {10.1007/s00365-009-9052-4}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4}, author = {Marco Bertola and Lee, S. Y.} } @article {2010, title = {Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.}, journal = {The European journal of neuroscience. 2010 Oct; 32(8):1364-79}, number = {PMID:20950280;}, year = {2010}, publisher = {Wiley}, abstract = {We 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.

}, doi = {10.1111/j.1460-9568.2010.07403.x}, url = {http://hdl.handle.net/1963/4480}, author = {Dario Motti and Caroline Le Duigou and Nicole Chemaly and Lucia Wittner and Dejan Lazarevic and Helena Krmac and Troels Torben Marstrand and Eivind Valen and Remo Sanges and Elia Stupka and Albin Sandelin and Enrico Cherubini and Stefano Gustincich and Richard Miles} } @article {2010, title = {Nonlocal character of the reduced theory of thin films with higher order perturbations}, journal = {Adv. Calc. Var. 3 (2010) 287-319}, number = {SISSA;57/2009/M}, year = {2010}, doi = {10.1515/ACV.2010.012, /July/2010}, url = {http://hdl.handle.net/1963/3754}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2010, title = {Optimally swimming Stokesian Robots}, number = {SISSA;54/2010/M}, year = {2010}, abstract = {We 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.}, url = {http://hdl.handle.net/1963/3929}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet} } @article {2010, title = {Quasistatic crack growth in finite elasticity with non-interpenetration}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290}, number = {SISSA;80/2008/M}, year = {2010}, abstract = {We 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.

}, doi = {10.1016/j.anihpc.2009.09.006}, url = {http://hdl.handle.net/1963/3397}, author = {Gianni Dal Maso and Giuliano Lazzaroni} } @article {2010, title = {The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures}, journal = {J. Phys. A 43 (2010) 045201}, number = {arXiv.org;0910.1210v1}, year = {2010}, publisher = {IOP Publishing}, abstract = {We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.}, doi = {10.1088/1751-8113/43/4/045201}, url = {http://hdl.handle.net/1963/3846}, author = {Guido Carlet and Paolo Lorenzoni and Andrea Raimondo} } @article {2010, title = {Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295}, number = {SISSA;12/2008/M}, year = {2010}, abstract = {We 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.}, doi = {10.2422/2036-2145.2010.2.02}, url = {http://hdl.handle.net/1963/2601}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @inbook {2009, title = {Biological Fluid Dynamics, Non-linear Partial Differential Equations}, booktitle = {Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554}, number = {SISSA;21/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2630}, author = {Antonio DeSimone and Fran{\c c}ois Alouges and Aline Lefebvre} } @article {2009, title = {Families of Monads and Instantons from a Noncommutative ADHM Construction}, number = {SISSA;59/2008/FM}, year = {2009}, abstract = {We give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative {\textquoteleft}families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.}, url = {http://hdl.handle.net/1963/3478}, author = {Simon Brain and Giovanni Landi} } @article {Bertola:Lee, title = {First colonization of a spectral outpost in random matrix theory}, journal = {Constr. Approx.}, volume = {30}, number = {2}, year = {2009}, pages = {225{\textendash}263}, issn = {0176-4276}, doi = {10.1007/s00365-008-9026-y}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y}, author = {Marco Bertola and Lee, S. Y.} } @article {2009, title = {Gauged Laplacians on quantum Hopf bundles}, journal = {Comm. Math. Phys. 287 (2009) 179-209}, number = {arXiv.org;0801.3376v2}, year = {2009}, publisher = {Springer}, abstract = {We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe {\textquoteleft}excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.}, doi = {10.1007/s00220-008-0672-5}, url = {http://hdl.handle.net/1963/3540}, author = {Giovanni Landi and Cesare Reina and Alessandro Zampini} } @article {2009, title = {A higher order model for image restoration: the one dimensional case}, journal = {SIAM J. Math. Anal. 40 (2009) 2351-2391}, number = {SISSA;66/2008/M}, year = {2009}, abstract = {The 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.}, doi = {10.1137/070697823}, url = {http://hdl.handle.net/1963/3174}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini} } @article {2009, title = {Investigating the Conformational Stability of Prion Strains through a Kinetic Replication Model}, journal = {PLoS Comput Biol 2009;5(7): e1000420}, year = {2009}, publisher = {PLoS}, abstract = {Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior.}, doi = {10.1371/journal.pcbi.1000420}, url = {http://hdl.handle.net/1963/3989}, author = {Mattia Zampieri and Giuseppe Legname and Claudio Altafini} } @article {BertolaLeeMo, title = {Mesoscopic colonization in a spectral band}, journal = {J. Phys. A}, volume = {42}, number = {41}, year = {2009}, pages = {415204, 17}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/41/415204}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/415204}, author = {Marco Bertola and Lee, S. Y. and Mo, M. Y.} } @article {2009, title = {A nonlinear theory for shells with slowly varying thickness}, journal = {C. R. Math. 347 (2009) 211-216}, number = {SISSA;23/2008/M}, year = {2009}, abstract = {We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.}, doi = {10.1016/j.crma.2008.12.017}, url = {http://hdl.handle.net/1963/2632}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {2009, title = {Optimal transportation under nonholonomic constraints}, journal = {Trans. Amer. Math. Soc. 361 (2009) 6019-6047}, number = {SISSA;68/2007/M}, year = {2009}, abstract = {We 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.}, doi = {10.1090/S0002-9947-09-04813-2}, url = {http://hdl.handle.net/1963/2176}, author = {Andrei A. Agrachev and Paul Lee} } @article {2008, title = {The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere}, journal = {Comm. Math. Phys. 279 (2008) 77-116}, number = {SISSA;95/2007/MP}, year = {2008}, abstract = {Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an {\textquoteleft}instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of {\textquoteleft}infinitesimals\\\' is also introduced.}, doi = {10.1007/s00220-008-0420-x}, url = {http://hdl.handle.net/1963/2567}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi} } @article {2008, title = {Noncommutative families of instantons}, journal = {Int. Math. Res. Not. vol. 2008, Article ID rnn038}, number = {arXiv.org;0710.0721v2}, year = {2008}, publisher = {Oxford University Press}, abstract = {We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.}, doi = {10.1093/imrn/rnn038}, url = {http://hdl.handle.net/1963/3417}, author = {Giovanni Landi and Chiara Pagani and Cesare Reina and Walter van Suijlekom} } @article {2008, title = {The Noncommutative Geometry of the Quantum Projective Plane}, journal = {Rev. Math. Phys. 20 (2008) 979-1006}, number = {SISSA;100/2007/MP}, year = {2008}, abstract = {We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).}, doi = {10.1142/S0129055X08003493}, url = {http://hdl.handle.net/1963/2548}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi} } @article {2008, title = {Optimal Strokes for Low Reynolds Number Swimmers: An Example}, journal = {J. Nonlinear Sci. 18 (2008) 277-302}, year = {2008}, publisher = {Springer}, abstract = {Swimming, 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).}, doi = {10.1007/s00332-007-9013-7}, url = {http://hdl.handle.net/1963/4006}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Aline Lefebvre} } @article {2007, title = {Dirac operators on all Podles quantum spheres}, journal = {J. Noncomm. Geom. 1 (2007) 213-239}, number = {arXiv.org;math/0606480v2}, year = {2007}, abstract = {We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.}, doi = {10.4171/JNCG/5}, url = {http://hdl.handle.net/1963/2177}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi and Elmar Wagner} } @article {2007, title = {Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results}, journal = {Arch. Ration. Mech. Anal. 186 (2007) 477-537}, year = {2007}, abstract = {Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers.}, doi = {10.1007/s00205-007-0082-4}, url = {http://hdl.handle.net/1963/2350}, author = {Irene Fonseca and Nicola Fusco and Giovanni Leoni and Massimiliano Morini} } @article {2007, title = {Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd)}, journal = {J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252}, year = {2007}, abstract = {In 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.

}, doi = {10.4171/JEMS/78}, url = {http://hdl.handle.net/1963/2037}, author = {Giovanni Leoni and Massimiliano Morini} } @article {2007, title = {The number of eigenvalues of three-particle Schr{\"o}dinger operators on lattices}, journal = {J. Phys. A 40 (2007) 14819-14842}, number = {arXiv.org;math/0703191v1}, year = {2007}, abstract = {We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.}, doi = {10.1088/1751-8113/40/49/015}, url = {http://hdl.handle.net/1963/2576}, author = {Sergio Albeverio and Gianfausto Dell{\textquoteright}Antonio and Saidakhmat N. Lakaev} } @article {2006, title = {A Hopf bundle over a quantum four-sphere from the symplectic group}, journal = {Commun. Math. Phys. 263 (2006) 65-88}, number = {arXiv.org;math/0407342v2}, year = {2006}, abstract = {We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.}, doi = {10.1007/s00220-005-1494-3}, url = {http://hdl.handle.net/1963/2179}, author = {Giovanni Landi and Chiara Pagani and Cesare Reina} } @article {2005, title = {The Dirac operator on SU_q(2)}, journal = {Commun. Math. Phys. 259 (2005) 729-759}, number = {arXiv:math/0411609;}, year = {2005}, note = {v2: minor changes}, publisher = {Springer}, abstract = {We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.}, doi = {10.1007/s00220-005-1383-9}, url = {http://hdl.handle.net/1963/4425}, author = {Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Walter van Suijlekom and Joseph C. Varilly} } @article {2005, title = {The local index formula for SUq(2)}, journal = {K-Theory 35 (2005) 375-394}, number = {SISSA;01/2005/FM}, year = {2005}, abstract = {We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.}, doi = {10.1007/s10977-005-3116-4}, url = {http://hdl.handle.net/1963/1713}, author = {Walter van Suijlekom and Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Joseph C. Varilly} } @article {2005, title = {Principal fibrations from noncommutative spheres}, journal = {Comm. Math. Phys. 260 (2005) 203-225}, number = {SISSA;68/2004/FM}, year = {2005}, abstract = {We construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.}, doi = {10.1007/s00220-005-1377-7}, url = {http://hdl.handle.net/1963/2284}, author = {Giovanni Landi and Walter van Suijlekom} } @article {2005, title = {The spectral geometry of the equatorial Podles sphere}, journal = {C. R. Math. 340 (2005) 819-822}, number = {SISSA;71/2004/FM}, year = {2005}, abstract = {We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties.}, doi = {10.1016/j.crma.2005.04.003}, url = {http://hdl.handle.net/1963/2275}, author = {Ludwik Dabrowski and Giovanni Landi and Mario Paschke and Andrzej Sitarz} } @article {2004, title = {Fredholm modules for quantum euclidean spheres}, journal = {J. Geom. Phys. 49 (2004) 272-293}, number = {SISSA;66/2002/FM}, year = {2004}, publisher = {SISSA Library}, abstract = {The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\\\\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres $S_q^{N-1}$. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i. e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra $A(S^{N-1}_q)$.}, doi = {10.1016/S0393-0440(03)00092-5}, url = {http://hdl.handle.net/1963/1636}, author = {Eli Hawkins and Giovanni Landi} } @article {2004, title = {Higher order quasiconvexity reduces to quasiconvexity}, journal = {Arch. Ration. Mech. Anal. 171 (2004) 55-81}, number = {SISSA;41/2003/M}, year = {2004}, publisher = {Springer}, abstract = {In 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.}, doi = {10.1007/s00205-003-0278-1}, url = {http://hdl.handle.net/1963/2911}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini} } @article {2003, title = {Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces}, journal = {Mod. Phys. Lett. A 18 (2003) 2371-2379}, number = {arXiv.org;math/0309143v1}, year = {2003}, publisher = {World Scientific}, abstract = {We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.}, doi = {10.1142/S0217732303012593}, url = {http://hdl.handle.net/1963/3215}, author = {Ludwik Dabrowski and Thomas Krajewski and Giovanni Landi} } @article {2002, title = {Instanton algebras and quantum 4-spheres}, journal = {Differential Geom. Appl. 16 (2002) 277-284}, number = {arXiv.org;math/0101177v2}, year = {2002}, publisher = {Elsevier}, abstract = {We study some generalized instanton algebras which are required to describe {\textquoteleft}instantonic complex rank 2 bundles\\\'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural requirements on the instantons. They turn out to be quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IC$, and the instantons are described by self-adjoint idempotents e. We shall also clarify some issues related to the vanishing of the first Chern-Connes class $ch_1(e)$ and on the use of the second Chern-Connes class $ch_2(e)$ as a volume form.}, doi = {10.1016/S0926-2245(02)00066-9}, url = {http://hdl.handle.net/1963/3134}, author = {Ludwik Dabrowski and Giovanni Landi} } @article {2001, title = {Instantons on the Quantum 4-Spheres S^4_q}, journal = {Comm. Math. Phys. 221 (2001) 161-168}, number = {arXiv.org;math/0012103v2}, year = {2001}, publisher = {Springer}, abstract = {We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $ch_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $ch_2(e)$ does not vanish as well and the couple $(ch_1(e), ch_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology.}, doi = {10.1007/PL00005572}, url = {http://hdl.handle.net/1963/3135}, author = {Ludwik Dabrowski and Giovanni Landi and Tetsuya Masuda} } @article {2001, title = {Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems}, journal = {J. Differential Equations 172 (2001) 59-82}, year = {2001}, publisher = {Elsevier}, doi = {10.1006/jdeq.2000.3869}, url = {http://hdl.handle.net/1963/3113}, author = {Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli} } @article {2000, title = {Some Properties of Non-linear sigma-Models in Noncommutative Geometry}, journal = {Int. J. Mod. Phys. B 14 (2000) 2367-2382}, number = {SISSA;158/99/FM}, year = {2000}, publisher = {SISSA Library}, abstract = {We introduce non-linear $\\\\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some characteristic features of the corresponding $\\\\sigma$-models. In particular we construct a $\\\\sigma$-model instanton with topological charge equal to 1. We also define and investigate some properties of a noncommutative analogue of the Wess-Zumino-Witten model.}, doi = {10.1142/S0217979200001898}, url = {http://hdl.handle.net/1963/1373}, author = {Ludwik Dabrowski and Thomas Krajewski and Giovanni Landi} } @article {2000, title = {A Uniqueness Condition for Hyperbolic Systems of Conservation Laws}, journal = {Discrete Contin. Dynam. Systems 6 (2000) 673-682}, number = {SISSA;88/98/M}, year = {2000}, publisher = {American Institute of Mathematical Sciences}, abstract = {Consider 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.}, url = {http://hdl.handle.net/1963/3195}, author = {Alberto Bressan and Marta Lewicka} } @article {1999, title = {L-1 stability estimates for n x n conservation laws}, journal = {Arch. Ration. Mech. Anal. 149 (1999), no. 1, 1--22}, number = {SISSA;80/98/M}, year = {1999}, publisher = {Springer}, abstract = {Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws, each characteristic field being linearly degenerate or genuinely nonlinear. In this paper we explicitly define a functional $\\\\Phi=\\\\Phi(u,v)$, equivalent to the $L^1$ distance, which is {\textquoteleft}almost decreasing\\\', i.e., $\\\\Phi(u(t),v(t))-\\\\Phi(u(s),v(s))\\\\leq\\\\break O (\\\\epsilon){\textperiodcentered}(t-s)$ for all $t>s\\\\geq 0$, for every pair of $\\\\epsilon$-approximate solutions $u,v$ with small total variation, generated by a wave-front-tracking algorithm. The small parameter $\\\\epsilon$ here controls the errors in the wave speeds, the maximum size of rarefaction fronts and the total strength of all non-physical waves in $u$ and in $v$. From the above estimate, it follows that front-tracking approximations converge to a unique limit solution, depending Lipschitz continuously on the initial data, in the $L^1$ norm. This provides a new proof of the existence of the standard Riemann semigroup generated by an $n\\\\times n$ system of conservation laws.\\\'\\\'}, doi = {10.1007/s002050050165}, url = {http://hdl.handle.net/1963/3373}, author = {Alberto Bressan and Tai-Ping Liu and Tong Yang} } @article {1999, title = {Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws}, journal = {J. Differential Equations 151 (1999) 345-372}, number = {SISSA;139/97/M}, year = {1999}, publisher = {Elsevier}, abstract = {The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.}, doi = {10.1006/jdeq.1998.3513}, url = {http://hdl.handle.net/1963/3312}, author = {Debora Amadori and Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli} } @article {1999, title = {Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws}, journal = {Indiana Univ. Math. J. 48 (1999), no. 1, 43--84}, number = {SISSA;96/97/M}, year = {1999}, publisher = {Indiana University}, abstract = {The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm.}, doi = {10.1512/iumj.1999.48.1524}, url = {http://hdl.handle.net/1963/3374}, author = {Alberto Bressan and Philippe G. LeFloch} } @article {1990, title = {Algebraic differential calculus for gauge theories}, journal = {Nuclear Phys. B. Proc. Suppl. 18A (1990), 171}, number = {SISSA;135/89/FM}, year = {1990}, publisher = {SISSA Library}, doi = {10.1016/0920-5632(90)90649-F}, url = {http://hdl.handle.net/1963/891}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1990, title = {Chern-Simons forms on principal superfiber bundles}, journal = {J.Math.Phys.31:45,1990}, number = {SISSA;109/87/FM}, year = {1990}, publisher = {SISSA Library}, abstract = {A graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a {\textquoteleft}{\textquoteleft}superextension\\\'\\\' of the Dirac monopole is discussed.}, doi = {10.1063/1.528826}, url = {http://hdl.handle.net/1963/590}, author = {Giovanni Landi and Claudio Bartocci and Ugo Bruzzo} } @article {1989, title = {Limits of obstacle problems for the area functional.}, journal = {Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309}, number = {SISSA;96/87/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/577}, author = {Gianni Dal Maso and Michele Carriero and Antonio Leaci and Eduardo Pascali} } @article {1988, title = {Algebraic reduction of the \\\'t Hooft-Polyakov monopole to the Dirac monopole.}, journal = {Phys. Lett. B 201 (1988), no. 1, 101-104.}, number = {SISSA;97/87/FM}, year = {1988}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(88)90088-3}, url = {http://hdl.handle.net/1963/578}, author = {Giovanni Landi and Giuseppe Marmo} } @mastersthesis {1988, title = {An Algebraic Setting for Gauge Theories}, year = {1988}, school = {SISSA}, url = {http://hdl.handle.net/1963/5828}, author = {Giovanni Landi} } @article {1988, title = {Einstein algebras and the algebraic Kaluza-Klein monopole.}, journal = {Phys. Lett. B 210 (1988), no. 1-2, 68--72.}, number = {SISSA;7/88/FM}, year = {1988}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(88)90351-6}, url = {http://hdl.handle.net/1963/603}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1987, title = {Extensions of Lie superalgebras and supersymmetric Abelian gauge fields.}, journal = {Phys. Lett. B 193 (1987), no. 1, 61-66.}, number = {SISSA;26/87/FM}, year = {1987}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(87)90456-4}, url = {http://hdl.handle.net/1963/507}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1987, title = {Graded Chern-Simons terms}, journal = {Phys. Lett. B 192 (1987), no. 1-2, 81-88.}, number = {SISSA;27/87/FM}, year = {1987}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(87)91146-4}, url = {http://hdl.handle.net/1963/508}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1987, title = {Lie algebra extensions and abelian monopoles.}, journal = {Phys. Lett. B 195 (1987), no. 3, 429-434}, number = {SISSA;25/87/FM}, year = {1987}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(87)90043-8}, url = {http://hdl.handle.net/1963/506}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1986, title = {The natural spinor connection on $S\\\\sb 8$ is a gauge field}, journal = {Lett. Math. Phys. 11 (1986), no. 2, 171-175}, number = {SISSA;61/85/MP}, year = {1986}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/448}, author = {Giovanni Landi} } @article {1985, title = {Flat connections for Lax hierarchies on coadjoint orbits}, journal = {Phys. Lett. A 108 (1985), no. 7, 311-314}, number = {SISSA;73/85/MP}, year = {1985}, publisher = {SISSA Library}, doi = {10.1016/0375-9601(85)90102-1}, url = {http://hdl.handle.net/1963/460}, author = {Giovanni Landi and Sergio De Filippo} } @article {1985, title = {Maximal acceleration and Sakharov{\textquoteright}s limiting temperature}, journal = {Lett. Nuovo Cim. 42 (1985) 70-72}, number = {SISSA;69/84/EP}, year = {1985}, publisher = {Societ{\`a} Italiana di Fisica}, abstract = {It is shown that Sakharov{\textquoteright}s maximal temperature, derived by him from astrophysical considerations, is a straightforward consequence of the maximal acceleration introduced by us in previous works.

}, doi = {10.1007/BF02748306}, url = {http://hdl.handle.net/1963/372}, author = {Eduardo R. Caianiello and Giovanni Landi} }