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

JF - VIII International Conference on Computational Methods in Marine Engineering ER - TY - RPRT T1 - A continuous dependence result for a dynamic debonding model in dimension one Y1 - 2019 A1 - Filippo Riva AB -In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

PB - SISSA UR - http://preprints.sissa.it/xmlui/handle/1963/35329 U1 - 35640 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Canonical Surfaces and Hypersurfaces in Abelian Varieties Y1 - 2018 A1 - Luca Cesarano UR - https://arxiv.org/abs/1808.05302 ER - TY - RPRT T1 - On the Cauchy problem for the wave equation on time-dependent domains Y1 - 2018 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35314 U1 - 35622 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models JF - Journal of Scientific Computing Y1 - 2018 A1 - Immanuel Martini A1 - Bernard Haasdonk A1 - Gianluigi Rozza VL - 74 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a964 ER - TY - RPRT T1 - Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations Y1 - 2018 A1 - Stefano Bianchini A1 - Laura Spinolo AB - We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35325 U1 - 35635 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue JF - Mathematical Models and Methods in Applied Sciences Y1 - 2018 A1 - Vito Crismale A1 - Giuliano Lazzaroni A1 - Gianluca Orlando AB -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.

VL - 28 UR - https://doi.org/10.1142/S0218202518500379 ER - TY - CHAP T1 - Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods T2 - Mathematical and Numerical Modeling of the Cardiovascular System and Applications Y1 - 2018 A1 - Marco Tezzele A1 - Francesco Ballarin A1 - Gianluigi Rozza JF - Mathematical and Numerical Modeling of the Cardiovascular System and Applications PB - Springer ER - TY - JOUR T1 - A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials JF - J. Elast. Y1 - 2018 A1 - Giulia Giantesio A1 - Alessandro Musesti A1 - Davide Riccobelli PB - Springer Nature ER - TY - CHAP T1 - Computational methods in cardiovascular mechanics T2 - Cardiovascular Mechanics Y1 - 2018 A1 - Auricchio, Ferdinando A1 - Conti, Michele A1 - Lefieux, Adrian A1 - Morganti, Simone A1 - Alessandro Reali A1 - Gianluigi Rozza A1 - Veneziani, Alessandro ED - Michel F. Labrosse AB -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.

JF - Cardiovascular Mechanics PB - CRC Press UR - https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-5 ER - TY - RPRT T1 - On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) Y1 - 2018 A1 - Emanuele Tasso AB - In this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions. UR - http://preprints.sissa.it/handle/1963/35324 N1 - 27 pages U1 - 35634 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation T2 - Spectral and High Order Methods for Partial Differential Equations Y1 - 2017 A1 - Denis Devaud A1 - Gianluigi Rozza AB -In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

JF - Spectral and High Order Methods for Partial Differential Equations PB - Springer CY - Heildeberg VL - 119 SN - 978-3-319-65869-8 ER - TY - JOUR T1 - On a certified smagorinsky reduced basis turbulence model JF - SIAM Journal on Numerical Analysis Y1 - 2017 A1 - Rebollo, T.C. A1 - E.D. Ávila A1 - Marmol, M.G. A1 - Francesco Ballarin A1 - Gianluigi Rozza VL - 55 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c ER - TY - JOUR T1 - Clifford Tori and the singularly perturbed Cahn–Hilliard equation JF - Journal of Differential Equations Y1 - 2017 A1 - Matteo Rizzi KW - Cahn–Hilliard equation KW - Clifford Torus KW - Lyapunov–Schmidt reduction KW - Willmore surface AB -In this paper we construct entire solutions uε to the Cahn–Hilliard equation −ε2Δ(−ε2Δu+W′(u))+W″(u)(−ε2Δu+W′(u))=ε4λε(1−uε), under the volume constraint ∫R3(1−uε)2dx=82π2cε, with cε→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov–Schmidt reduction and on careful geometric expansions of the Laplacian.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039617300530 ER - TY - RPRT T1 - Complex Friedrichs systems and applications Y1 - 2017 A1 - Nenad Antonić A1 - Krešimir Burazin A1 - Ivana Crnjac A1 - Marko Erceg AB - We provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper. UR - http://urania.sissa.it/xmlui/handle/1963/35270 U1 - 35576 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology JF - Journal of Computational Physics Y1 - 2017 A1 - Giuseppe Pitton A1 - Annalisa Quaini A1 - Gianluigi Rozza KW - Parametrized Navier–Stokes equations KW - Reduced basis method KW - Stability of flows KW - Symmetry breaking bifurcation AB -We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

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

VL - 344 UR - http://www.sciencedirect.com/science/article/pii/S002199911730356X ER - TY - RPRT T1 - On contact interactions realised as Friedrichs systems Y1 - 2017 A1 - Marko Erceg A1 - Alessandro Michelangeli AB - We realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems. UR - http://preprints.sissa.it/handle/1963/35298 U1 - 35604 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators JF - Nonlinear Analysis Y1 - 2017 A1 - Davide Barilari A1 - Elisa Paoli KW - Curvature KW - Hypoelliptic heat equation KW - Small time asymptotics AB -We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

VL - 164 UR - http://www.sciencedirect.com/science/article/pii/S0362546X17302298 ER - TY - JOUR T1 - Curvature-adapted remeshing of CAD surfaces JF - Engineering with Computers Y1 - 2017 A1 - Franco Dassi A1 - Andrea Mola A1 - Hang Si PB - Springer Nature VL - 34 UR - https://doi.org/10.1007/s00366-017-0558-2 ER - TY - RPRT T1 - Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers Y1 - 2016 A1 - Giordano Cotti ER - TY - JOUR T1 - Comparing Poisson Sigma Model with A-model JF - Journal of High Energy Physics Y1 - 2016 A1 - Bonechi, F. A1 - Cattaneo, A.S. A1 - Riccardo Iraso AB -We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

VL - 2016 UR - https://doi.org/10.1007/JHEP10(2016)133 ER - TY - JOUR T1 - On the concentration of entropy for scalar conservation laws JF - Discrete & Continuous Dynamical Systems - S Y1 - 2016 A1 - Stefano Bianchini A1 - Elio Marconi KW - concentration KW - Conservation laws KW - entropy solutions KW - Lagrangian representation KW - shocks AB -We prove that the entropy for an $L^∞$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

VL - 9 UR - http://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae ER - TY - JOUR T1 - Confinement of dislocations inside a crystal with a prescribed external strain Y1 - 2016 A1 - Ilaria Lucardesi A1 - Marco Morandotti A1 - Riccardo Scala A1 - Davide Zucco AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35247 N1 - Preprint SISSA 20/2016/MATE U1 - 35558 U2 - Mathematics ER - TY - JOUR T1 - Conformal Equivalence of 3D Contact Structures on Lie Groups JF - Journal of Dynamical and Control Systems Y1 - 2016 A1 - Francesco Boarotto AB -In this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

VL - 22 UR - https://doi.org/10.1007/s10883-015-9273-8 ER - TY - JOUR T1 - Construction of Real-Valued Localized Composite Wannier Functions for Insulators JF - Annales Henri Poincaré Y1 - 2016 A1 - Domenico Fiorenza A1 - Domenico Monaco A1 - Gianluca Panati AB -We consider a real periodic Schrödinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

VL - 17 UR - https://doi.org/10.1007/s00023-015-0400-6 ER - TY - JOUR T1 - Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$ JF - Phys. D Y1 - 2016 A1 - Marco Bertola A1 - Boris Dubrovin A1 - Di Yang VL - 327 UR - http://dx.doi.org/10.1016/j.physd.2016.04.008 ER - TY - JOUR T1 - CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function Y1 - 2016 A1 - Marco Bertola UR - http://arxiv.org/abs/1601.04790 ER - TY - JOUR T1 - Critical points of a perturbed Otha-Kawasaki functional JF - arXiv preprint arXiv:1601.07093 Y1 - 2016 A1 - Matteo Rizzi ER - TY - JOUR T1 - Currents and dislocations at the continuum scale JF - Methods and Applications of Analysis Y1 - 2016 A1 - Riccardo Scala A1 - Nicolas Van Goethem AB -A striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

PB - International Press of Boston VL - 23 ER - TY - BOOK T1 - Certified Reduced Basis Methods for Parametrized Partial Differential Equations T2 - Springer Briefs in Mathematics Y1 - 2015 A1 - Jan S Hesthaven A1 - Gianluigi Rozza A1 - Benjamin Stamm KW - a posteriori error bounds KW - empirical interpolation KW - parametrized partial differential equations KW - reduced basis methods, greedy algorithms AB -This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

JF - Springer Briefs in Mathematics PB - Springer CY - Switzerland SN - 978-3-319-22469-5 ER - TY - RPRT T1 - A class of Hamiltonians for a three-particle fermionic system at unitarity Y1 - 2015 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide. UR - http://urania.sissa.it/xmlui/handle/1963/34469 N1 - This SISSA preprint is composed of 29 pages and is recorded in PDF format U1 - 34644 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity JF - Mathematical Methods in the Applied Sciences Y1 - 2015 A1 - Maggiani, Giovanni Battista A1 - Riccardo Scala A1 - Nicolas Van Goethem KW - 35J58 KW - 35Q74 KW - compatibility conditions KW - elasticity KW - Korn inequality KW - strain decomposition KW - subclass74B05 AB -In this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

VL - 38 UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450 ER - TY - JOUR T1 - Complexity of Control-Affine Motion Planning JF - SIAM Journal on Control and Optimization Y1 - 2015 A1 - Jean, F. A1 - Dario Prandi AB -In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

VL - 53 UR - https://doi.org/10.1137/130950793 ER - TY - JOUR T1 - Constrained BV functions on double coverings for Plateau's type problems JF - Adv. Calc. Var. Y1 - 2015 A1 - Stefano Amato A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

U1 - 7597 ER - TY - JOUR T1 - Convergence rate of the Glimm scheme JF - Bulletin of the Institute of Mathematics of Academia Sinica (New Series) Y1 - 2015 A1 - Stefano Modena A1 - Stefano Bianchini ER - TY - RPRT T1 - Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets Y1 - 2015 A1 - Dario Mazzoleni A1 - Davide Zucco AB - We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35140 U1 - 35378 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Cauchy-Laguerre two-matrix model and the Meijer-G random point field JF - Comm. Math. Phys. Y1 - 2014 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 326 UR - http://dx.doi.org/10.1007/s00220-013-1833-8 ER - TY - JOUR T1 - Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents JF - Communications in Mathematical Physics 331, nr. 2 (2014) 623-676 Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov's equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy. PB - SISSA UR - http://hdl.handle.net/1963/6979 N1 - 46 pages U1 - 6967 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Comparison between reduced basis and stochastic collocation methods for elliptic problems Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - The stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34727 U1 - 34916 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics JF - Annals of Nuclear Energy Y1 - 2014 A1 - Alberto Sartori A1 - Davide Baroli A1 - Antonio Cammi A1 - Davide Chiesa A1 - Lelio Luzzi A1 - Roberto R. Ponciroli A1 - Ezio Previtali A1 - Marco E. Ricotti A1 - Gianluigi Rozza A1 - Monica Sisti AB -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.

PB - Elsevier VL - 71 UR - http://urania.sissa.it/xmlui/handle/1963/35039 U1 - 35270 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription Y1 - 2014 A1 - Rod R. Gover A1 - Yaiza Canzani A1 - Dmitry Jakobson A1 - Raphaël Ponge A1 - Andrea Malchiodi AB - In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures. PB - Oxford University Press UR - http://urania.sissa.it/xmlui/handle/1963/35128 U1 - 35366 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - On conjugate times of LQ optimal control problems Y1 - 2014 A1 - Andrei A. Agrachev A1 - Luca Rizzi A1 - Pavel Silveira KW - Optimal control, Lagrange Grassmannian, Conjugate point AB - Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$. PB - Springer UR - http://hdl.handle.net/1963/7227 N1 - 14 pages, 1 figure U1 - 7261 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A correction and an extension of Stampacchia's work on the geometric BVP Y1 - 2014 A1 - Giovanni Vidossich AB - G. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results. PB - Advanced Nonlinear Studies UR - http://urania.sissa.it/xmlui/handle/1963/35023 U1 - 35263 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawling on directional surfaces JF - International Journal of Non-Linear Mechanics Y1 - 2014 A1 - Paolo Gidoni A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bio-mimetic micro-robots KW - Cell migration KW - Crawling motility KW - Directional surfaces KW - Self-propulsion AB -In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

VL - 61 UR - http://www.sciencedirect.com/science/article/pii/S0020746214000213 ER - TY - JOUR T1 - Critical points of the Moser-Trudinger functional on a disk Y1 - 2014 A1 - Andrea Malchiodi A1 - Luca Martinazzi AB - On the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe. PB - European Mathematical Society UR - http://hdl.handle.net/1963/6560 N1 - 16 pages U1 - 6487 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - The curvature of optimal control problems with applications to sub-Riemannian geometry Y1 - 2014 A1 - Luca Rizzi KW - Sub-Riemannian geometry AB - Optimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated. PB - SISSA UR - http://hdl.handle.net/1963/7321 N1 - The PhD thesis is composed of 211 pages and is recorded in PDF format U1 - 7367 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Curvature-adapted remeshing of CAD surfaces JF - Procedia Engineering Y1 - 2014 A1 - Franco Dassi A1 - Andrea Mola A1 - Hang Si AB -A common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

PB - Elsevier VL - 82 UR - https://doi.org/10.1016/j.proeng.2014.10.388 N1 - This is an open access article under the CC BY-NC-ND license U1 - 35220 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras JF - Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 Y1 - 2013 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations. PB - Springer UR - http://hdl.handle.net/1963/6978 N1 - 43 pages. Second version with minor editing and corrections U1 - 6966 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices JF - Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 Y1 - 2013 A1 - Denis Devaud A1 - Andrea Manzoni A1 - Gianluigi Rozza KW - Partial differential equations AB -We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

PB - Elsevier UR - http://hdl.handle.net/1963/7389 U1 - 7434 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons. JF - Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 Y1 - 2013 A1 - Giovanna De Palo A1 - Giuseppe Facchetti A1 - Monica Mazzolini A1 - Anna Menini A1 - Vincent Torre A1 - Claudio Altafini AB -Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

PB - SISSA U1 - 6453 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains JF - Journal of Differential Equations Y1 - 2013 A1 - Serena Dipierro KW - Finite-dimensional reductions KW - Local inversion KW - Singularly perturbed elliptic problems AB -We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

VL - 254 UR - http://www.sciencedirect.com/science/article/pii/S0022039612003312 ER - TY - JOUR T1 - The Conformal Willmore Functional: A Perturbative Approach JF - Journal of Geometric Analysis Y1 - 2013 A1 - Andrea Mondino AB -The conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ – where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

VL - 23 UR - https://doi.org/10.1007/s12220-011-9263-3 ER - TY - JOUR T1 - Connected Sum Construction for σk-Yamabe Metrics JF - Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 Y1 - 2013 A1 - Giovanni Catino A1 - Lorenzo Mazzieri AB - In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation. PB - Springer UR - http://hdl.handle.net/1963/6441 N1 - This article has not yet been published. U1 - 6366 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Crawlers in viscous environments: linear vs nonlinear rheology JF - International Journal of Non-Linear Mechanics 56, 142-147 (2013) Y1 - 2013 A1 - Antonio DeSimone A1 - Federica Guarnieri A1 - Giovanni Noselli A1 - Amabile Tatone AB - We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling. PB - Elsevier U1 - 34590 U2 - Mathematics ER - TY - RPRT T1 - On critical behaviour in systems of Hamiltonian partial differential equations Y1 - 2013 A1 - Boris Dubrovin A1 - Tamara Grava A1 - Christian Klein A1 - Antonio Moro AB -We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

PB - SISSA U1 - 7280 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - The curvature: a variational approach Y1 - 2013 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Luca Rizzi KW - Crurvature, subriemannian metric, optimal control problem AB - The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces. PB - SISSA UR - http://hdl.handle.net/1963/7226 N1 - 88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg group U1 - 7260 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Curved noncommutative torus and Gauss--Bonnet JF - Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 Y1 - 2013 A1 - Ludwik Dabrowski A1 - Andrzej Sitarz KW - Geometry AB - We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature. PB - American Institute of Physics UR - http://hdl.handle.net/1963/7376 N1 - The article is composed of 13 pages and is recorded in PDF format U1 - 7424 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - On a class of vector fields with discontinuity of divide-by-zero type and its applications JF - Journal of dynamical and control systems Y1 - 2012 A1 - Roberta Ghezzi A1 - Alexey O. Remizov AB -We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

PB - Springer VL - 18 IS - 1 U1 - 7038 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Classical double, R-operators, and negative flows of integrable hierarchies JF - Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 Y1 - 2012 A1 - Boris Dubrovin A1 - Taras V. Skrypnyk AB - Using the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U–V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations. PB - SISSA UR - http://hdl.handle.net/1963/6468 U1 - 6413 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. JF - Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 Y1 - 2012 A1 - Andrea Malchiodi A1 - Paul Yang A1 - Jih-Hsin Cheng A1 - JennFang Hwang AB - In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1 PB - SISSA UR - http://hdl.handle.net/1963/6556 U1 - 6490 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - CHAP T1 - Computing optimal strokes for low reynolds number swimmers T2 - Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, Y1 - 2012 A1 - Antonio DeSimone A1 - Luca Heltai A1 - François Alouges A1 - Lefebvre-Lepot Aline KW - Numerical analysis. AB -We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

JF - Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, PB - Springer SN - 9781461439967 UR - http://hdl.handle.net/1963/6445 U1 - 6381 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Concentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity JF - Communications in Contemporary Mathematics Y1 - 2012 A1 - Bonheure, Denis A1 - Di Cosmo, Jonathan A1 - Mercuri, Carlo AB -The present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

PB - World Scientific VL - 14 UR - https://doi.org/10.1142/S0219199712500095 ER - TY - JOUR T1 - Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids JF - Communications in Partial Differential Equations Y1 - 2012 A1 - Francesco Fanelli AB -In this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

PB - Taylor & Francis VL - 37 UR - https://doi.org/10.1080/03605302.2012.698343 ER - TY - JOUR T1 - Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density Y1 - 2012 A1 - Maria Giovanna Mora A1 - Lucia Scardia AB -The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

PB - Elsevier UR - http://hdl.handle.net/1963/3466 N1 - 21 pages U1 - 7112 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Convex pencils of real quadratic forms JF - Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 Y1 - 2012 A1 - Antonio Lerario AB - 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). PB - Springer UR - http://hdl.handle.net/1963/7099 N1 - Updated version to be published in DCG ; was published in : Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 U1 - 7097 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawling motility through the analysis of model locomotors: two case studies JF - The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 Y1 - 2012 A1 - Antonio DeSimone A1 - Amabile Tatone AB - We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility. PB - Springer UR - http://hdl.handle.net/1963/7017 U1 - 7014 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - On the critical behavior in nonlinear evolutionary PDEs with small viscocity JF - Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460 Y1 - 2012 A1 - Boris Dubrovin A1 - Maria Elaeva AB - We address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically. PB - SISSA UR - http://hdl.handle.net/1963/6465 U1 - 6409 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - A class of existence results for the singular Liouville equation JF - Comptes Rendus Mathematique 349 (2011) 161-166 Y1 - 2011 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional. PB - Elsevier UR - http://hdl.handle.net/1963/5793 U1 - 5648 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential JF - Rev. Mat. Iberoamericana Y1 - 2011 A1 - David Ruiz A1 - Giusi Vaira PB - Real Sociedad Matemática Española VL - 27 UR - https://projecteuclid.org:443/euclid.rmi/1296828834 ER - TY - RPRT T1 - Compactness by maximality Y1 - 2011 A1 - Sandro Zagatti AB - We derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$. UR - http://preprints.sissa.it/handle/1963/35317 U1 - 35626 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Computing global structural balance in large-scale signed social networks. JF - Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 Y1 - 2011 A1 - Giuseppe Facchetti A1 - Giovanni Iacono A1 - Claudio Altafini KW - Combinatorial optimization AB - Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\" PB - National Academy of Sciences UR - http://hdl.handle.net/1963/6426 N1 - Free fulltext article in Pubmed Central U1 - 6362 U2 - Physics U4 - -1 ER - TY - JOUR T1 - Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains JF - Annales de l'I.H.P. Analyse non linéaire Y1 - 2011 A1 - Serena Dipierro PB - Elsevier VL - 28 UR - http://www.numdam.org/item/AIHPC_2011__28_1_107_0 ER - TY - JOUR T1 - Cones of divisors of blow-ups of projective spaces JF - Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 Y1 - 2011 A1 - Alessio Lo Giudice A1 - Salvatore Cacciola A1 - M. Donten-Bury A1 - O. Dumitrescu A1 - J. Park KW - Mori dream space AB - 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. PB - Università degli Studi di Catania. Dipartimento di matematica UR - http://hdl.handle.net/1963/6613 U1 - 6462 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Covered by lines and Conic connected varieties JF - Le Matematiche 66 (2011) 137-151 Y1 - 2011 A1 - Simone Marchesi A1 - Alex Massarenti A1 - Saeed Tafazolian AB - We study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak. PB - Universita\\\' di Catania, Dipartimento di Matematica e Informatica UR - http://hdl.handle.net/1963/5788 U1 - 5641 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem JF - Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 Y1 - 2011 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3801 U1 - 526 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Crepant resolutions of weighted projective spaces and quantum deformations JF - This article will be published in 2011 in the \"Nagoya Mathematical Journal\" Volume 201, March 2011, Pages 1-22, under the title \"Computing certain Gromov-Witten invariants of the crepant resolution of P{double-strock}(1, 3, 4, 4) Y1 - 2011 A1 - Samuel Boissiere A1 - Etienne Mann A1 - Fabio Perroni AB - We compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity. PB - SISSA UR - http://hdl.handle.net/1963/6514 N1 - Exposition improved, new title, typos corrected. The section\r\n concerning the model for the orbifold Chow ring has been removed (appears now\r\n in our new preprint 0709.4559) U1 - 6463 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - Critical points of the Moser-Trudinger functional Y1 - 2011 A1 - Francesca De Marchis A1 - Andrea Malchiodi A1 - Luca Martinazzi KW - Moser-Trudinger inequality PB - SISSA UR - http://hdl.handle.net/1963/4592 U1 - 4353 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions JF - PNAS 108 (2011) 13978 Y1 - 2011 A1 - Luca Cardamone A1 - Alessandro Laio A1 - Rajesh Shahapure A1 - Antonio DeSimone PB - National Academy of Sciences UR - http://hdl.handle.net/1963/4358 U1 - 4066 U2 - Physics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Canonical k-Minkowski Spacetime Y1 - 2010 A1 - Gherardo Piacitelli A1 - Ludwik Dabrowski AB - A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime. UR - http://hdl.handle.net/1963/3863 U1 - 846 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Cauchy biorthogonal polynomials JF - J. Approx. Theory Y1 - 2010 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 162 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008 ER - TY - JOUR T1 - Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality JF - J. Geom. Phys. 60 (2010) 417-429 Y1 - 2010 A1 - Andrea Brini A1 - Luca Griguolo A1 - Domenico Seminara A1 - Alessandro Tanzini AB - We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting. UR - http://hdl.handle.net/1963/2938 U1 - 1762 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Cohomology of Skew-holomorphic lie algebroids Y1 - 2010 A1 - Ugo Bruzzo A1 - Vladimir Rubtsov AB - We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts. UR - http://hdl.handle.net/1963/3853 U1 - 856 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results JF - Arch. Ration. Mech. Anal. 196 (2010) 907-950 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero. UR - http://hdl.handle.net/1963/3406 U1 - 927 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in. UR - http://hdl.handle.net/1963/3409 U1 - 926 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Continuity of optimal control costs and its application to weak KAM theory JF - Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232 Y1 - 2010 A1 - Andrei A. Agrachev A1 - Paul Lee AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6459 N1 - 23 pages, 1 figures U1 - 6405 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - RPRT T1 - Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density Y1 - 2010 A1 - Elisa Davoli A1 - Maria Giovanna Mora AB - The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory. UR - http://hdl.handle.net/1963/4086 U1 - 317 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Cauchy two–matrix model JF - Comm. Math. Phys. Y1 - 2009 A1 - Marco Bertola A1 - M Gekhtman A1 - J Szmigielski VL - 287 ER - TY - JOUR T1 - Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity JF - BMC Research Notes (2009) 2:13 Y1 - 2009 A1 - Frederic D. Broccard A1 - Silvia Pegoraro A1 - Maria Elisabetta Ruaro A1 - Claudio Altafini A1 - Vincent Torre AB - BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison. PB - BioMed Central UR - http://hdl.handle.net/1963/3706 U1 - 599 U2 - Neuroscience U3 - Neurobiology ER - TY - JOUR T1 - Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights JF - Adv. Math. Y1 - 2009 A1 - Marco Bertola A1 - Mo, M. Y. VL - 220 ER - TY - JOUR T1 - A connection between viscous profiles and singular ODEs JF - Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Spinolo UR - http://hdl.handle.net/1963/2555 U1 - 1564 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds JF - Systems Control Lett. 58 (2009) 213-216 Y1 - 2009 A1 - Claudio Altafini AB - For isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field. PB - Elsevier UR - http://hdl.handle.net/1963/3523 U1 - 741 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability of the discrete-spectrum Schrodinger equation driven by an external field JF - Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 Y1 - 2009 A1 - Thomas Chambrion A1 - Paolo Mason A1 - Mario Sigalotti A1 - Ugo Boscain AB - We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials. UR - http://hdl.handle.net/1963/2547 U1 - 1572 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability on the group of diffeomorphisms JF - Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Marco Caponigro AB - Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M. UR - http://hdl.handle.net/1963/3396 U1 - 936 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence of viscous approximations after shock interactions JF - Discrete Contin. Dyn. Syst. 23 (2009) 29-48 Y1 - 2009 A1 - Alberto Bressan A1 - Carlotta Donadello AB - We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3412 U1 - 923 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Cubic string boundary value problems and Cauchy biorthogonal polynomials JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 42 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006 ER - TY - JOUR T1 - Cantor families of periodic solutions for completely resonant wave equations JF - Frontiers of Mathematics in China Y1 - 2008 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. © 2008 Higher Education Press. VL - 3 N1 - cited By (since 1996)0 ER - TY - JOUR T1 - Cantor families of periodic solutions for wave equations via a variational principle JF - Advances in Mathematics Y1 - 2008 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. © 2007 Elsevier Inc. All rights reserved. VL - 217 N1 - cited By (since 1996)6 ER - TY - JOUR T1 - Cantor families of periodic solutions of wave equations with C k nonlinearities JF - Nonlinear Differential Equations and Applications Y1 - 2008 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. © 2008 Birkhaueser. VL - 15 N1 - cited By (since 1996)10 ER - TY - JOUR T1 - Concentrating solutions of some singularly perturbed elliptic equations JF - Front. Math. China 3 (2008) 239-252 Y1 - 2008 A1 - Andrea Malchiodi AB - We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry. UR - http://hdl.handle.net/1963/2657 U1 - 1466 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On concentration of positive bound states for the Schrödinger-Poisson problem with potentials JF - Advanced nonlinear studies Y1 - 2008 A1 - Ianni, Isabella A1 - Giusi Vaira AB -We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

PB - Advanced Nonlinear Studies, Inc. VL - 8 ER - TY - JOUR T1 - Convergence of equilibria of three-dimensional thin elastic beams JF - Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 Y1 - 2008 A1 - Maria Giovanna Mora A1 - Stefan Müller AB - A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument. UR - http://hdl.handle.net/1963/1896 U1 - 2339 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Canonical structure and symmetries of the Schlesinger equations JF - Comm. Math. Phys. 271 (2007) 289-373 Y1 - 2007 A1 - Boris Dubrovin A1 - Marta Mazzocco AB - The Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates. UR - http://hdl.handle.net/1963/1997 U1 - 2199 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Chen-Ruan cohomology of ADE singularities JF - International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059 Y1 - 2007 A1 - Fabio Perroni KW - Chen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence AB - We study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism. PB - SISSA UR - http://hdl.handle.net/1963/6502 N1 - This is a short version of my Ph.D. Thesis math.AG/0510528. Version\r\n 2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a\r\n link with the classical McKay correpondence is given. International Journal\r\n of Mathematics (to appear) U1 - 6447 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - The cohomological crepant resolution conjecture for P(1,3,4,4) Y1 - 2007 A1 - Samuel Boissiere A1 - Fabio Perroni A1 - Etienne Mann AB - We prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results. PB - SISSA UR - http://hdl.handle.net/1963/6513 N1 - 11 pages, 1 figure U1 - 6464 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data JF - Bioinformatics 23 (2007) 1640-1647 Y1 - 2007 A1 - Nicola Soranzo A1 - Ginestra Bianconi A1 - Claudio Altafini AB - Motivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/ UR - http://hdl.handle.net/1963/2028 U1 - 2168 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - The complete one-loop spin chain for N=2 Super-Yang-Mills Y1 - 2007 A1 - Paolo Di Vecchia A1 - Alessandro Tanzini AB - We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap. UR - http://hdl.handle.net/1963/2309 N1 - Contributed to NATO Advanced Study Institute and EC Summer School on String Theory: From Gauge Interactions to Cosmology, Cargese, France, 7-19 Jun 2004. U1 - 1707 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Computing Amplitudes in topological M-theory Y1 - 2007 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants. JF - JHEP 03 (2007) 023 UR - http://hdl.handle.net/1963/1901 U1 - 2335 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Concentration on minimal submanifolds for a singularly perturbed Neumann problem JF - Adv. Math. 209 (2007) 460-525 Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $15. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence. JF - C. R. Math. Acad. Sci. Paris 342 (2006) 589-594 UR - http://hdl.handle.net/1963/1712 U1 - 2439 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Cantor families of periodic solutions for completely resonant nonlinear wave equations JF - Duke Math. J. 134 (2006) 359-419 Y1 - 2006 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity. UR - http://hdl.handle.net/1963/2161 U1 - 2083 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Classification of stable time-optimal controls on 2-manifolds JF - J. Math. Sci. 135 (2006) 3109-3124 Y1 - 2006 A1 - Ugo Boscain A1 - Igor Nikolaev A1 - Benedetto Piccoli UR - http://hdl.handle.net/1963/2196 U1 - 2048 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Common Polynomial Lyapunov Functions for Linear Switched Systems JF - SIAM J. Control Optim. 45 (2006) 226-245 Y1 - 2006 A1 - Paolo Mason A1 - Ugo Boscain A1 - Yacine Chitour AB - In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given. UR - http://hdl.handle.net/1963/2181 U1 - 2063 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Compactness of solutions to some geometric fourth-order equations JF - J. Reine Angew. Math. 594 (2006) 137-174 Y1 - 2006 A1 - Andrea Malchiodi AB - We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics. UR - http://hdl.handle.net/1963/2126 U1 - 2117 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem JF - Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 Y1 - 2006 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - We consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$. UR - http://hdl.handle.net/1963/2170 U1 - 2074 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Conservative Solutions to a Nonlinear Variational Wave Equation JF - Comm. Math. Phys. 266 (2006) 471-497 Y1 - 2006 A1 - Alberto Bressan A1 - Zheng Yuxi AB - We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values. UR - http://hdl.handle.net/1963/2184 U1 - 2060 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A cyclic integral on k-Minkowski noncommutative space-time JF - Int. J. Mod. Phys. A 21 (2006) 3133-3150 Y1 - 2006 A1 - Alessandra Agostini A1 - Giovanni Amelino-Camelia A1 - Michele Arzano A1 - Francesco D'Andrea AB - We examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this ``cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a ``canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators. UR - http://hdl.handle.net/1963/2158 U1 - 2086 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Commuting multiparty quantum observables and local compatibility JF - Phys. Rev. A 72 (2005) 012112 Y1 - 2005 A1 - Claudio Altafini AB - A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two ``fully nontrivial\\\'\\\' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the ``Bell Theorem without inequalities\\\'\\\'. UR - http://hdl.handle.net/1963/2228 U1 - 2016 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Complete systems of invariants for rank 1 curves in Lagrange Grassmannians T2 - Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 Y1 - 2005 A1 - Igor Zelenko AB - Curves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation. JF - Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 UR - http://hdl.handle.net/1963/2310 N1 - Proceedings of 9th Conference on Differential Geometry and its Applications, Prague 2004 U1 - 1706 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains JF - Geometric and Functional Analysis 15 (6) 1162-1222 (2005) Y1 - 2005 A1 - Andrea Malchiodi AB - We prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0. PB - Springer UR - http://hdl.handle.net/1963/4866 U1 - 4645 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Conservation laws with time dependent discontinuous coefficients JF - SIAM J. Math. Anal. 36 (2005) 1293-1309 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Nils Henrik Risebro AB - We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11]. PB - SISSA Library UR - http://hdl.handle.net/1963/1666 U1 - 2452 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals JF - J. Dyn. Control Syst. 11 (2005) 297-327 Y1 - 2005 A1 - Andrei A. Agrachev A1 - Natalia N. Chtcherbakova A1 - Igor Zelenko AB - Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem. UR - http://hdl.handle.net/1963/2254 U1 - 1993 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Calculation of impulsively started incompressible viscous flows JF - Int. J. Numer. Meth. Fluids Y1 - 2004 A1 - Marra, Andrea A1 - Andrea Mola A1 - Quartapelle, Luigi A1 - Riviello, Luca VL - 46 ER - TY - JOUR T1 - Coarse-grained models of materials with non-convex free-energy: two case studies JF - Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 Y1 - 2004 A1 - Antonio DeSimone AB - Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response. PB - Elsevier UR - http://hdl.handle.net/1963/4884 U1 - 4664 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Coherent control of open quantum dynamical systems JF - Phys. Rev. A 70 (2004) 062321 Y1 - 2004 A1 - Claudio Altafini AB - A systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via cohere nt controls are described. The analysis suggests to which extent (and how) it is possible to counteract the effect of dissipation. UR - http://hdl.handle.net/1963/2227 U1 - 2017 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence rate of vanishing viscosity approximations JF - Comm. Pure Appl. Math. 57 (2004) 1075-1109 Y1 - 2004 A1 - Alberto Bressan A1 - Tong Yang AB - Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves. PB - Wiley UR - http://hdl.handle.net/1963/2915 U1 - 1785 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The calibration method for the Mumford-Shah functional and free-discontinuity problems JF - Calc. Var. Partial Differential Equations 16 (2003) 299-333 Y1 - 2003 A1 - Giovanni Alberti A1 - Guy Bouchitte A1 - Gianni Dal Maso AB - We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results. PB - Springer UR - http://hdl.handle.net/1963/3051 U1 - 1282 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Control Problems for Systems of Conservation Laws Y1 - 2003 A1 - Giuseppe Maria Coclite KW - Asymptotic Stabilization PB - SISSA UR - http://hdl.handle.net/1963/5325 U1 - 5154 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Controllability properties for finite dimensional quantum Markovian master equations JF - J. Math. Phys. 44 (2003) 2357-2372 Y1 - 2003 A1 - Claudio Altafini AB - Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail. PB - American Institute of Physics UR - http://hdl.handle.net/1963/2909 U1 - 1791 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps JF - J. Convex Anal. 9 (2002) 1-29 Y1 - 2002 A1 - Maria Giovanna Mora AB - The calibration method is a classical minimality criterion, which has been recently adapted to functionals with free discontinuities by Alberti, Bouchitté, Dal Maso. In this paper we present a further generalization of this theory to functionals defined on vector-valued maps. PB - Heldermann Verlag UR - http://hdl.handle.net/1963/3049 U1 - 1284 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A center manifold technique for tracing viscous waves JF - Commun. Pure Appl. Anal. 1 (2002) 161-190 Y1 - 2002 A1 - Stefano Bianchini A1 - Alberto Bressan AB - In this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3075 U1 - 1258 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems JF - Nonlinear Anal. 48 (2002) 481-504 Y1 - 2002 A1 - Massimiliano Berti A1 - Carlo Carminati PB - Elsevier UR - http://hdl.handle.net/1963/1279 U1 - 3176 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Coherent state realizations of $\rm su(n+1)$ on the $n$-torus JF - J. Math. Phys. Y1 - 2002 A1 - de Guise, Hubert A1 - Marco Bertola VL - 43 ER - TY - JOUR T1 - Controllability of quantum mechanical systems by root space decomposition of su(N) JF - J.Math.Phys. 43(2002), no.5, 2051 Y1 - 2002 A1 - Claudio Altafini PB - SISSA Library UR - http://hdl.handle.net/1963/1613 U1 - 2505 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Curvature theory of boundary phases: the two-dimensional case JF - Interfaces Free Bound. 7 (2002) 345-370 Y1 - 2002 A1 - Andrea Braides A1 - Andrea Malchiodi AB - We describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted. PB - European Mathematical Society UR - http://hdl.handle.net/1963/3537 U1 - 1164 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A case study in vanishing viscosity JF - Discrete Cont. Dyn. Syst. 7 (2001) 449-476 Y1 - 2001 A1 - Stefano Bianchini A1 - Alberto Bressan PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3091 U1 - 1242 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Complex Lagrangian embeddings of moduli spaces of vector bundles JF - Differential Geom. Appl. 14 (2001) 151-156 Y1 - 2001 A1 - Ugo Bruzzo A1 - Fabio Pioli AB - By means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of special Lagrangian submanifolds. PB - Elsevier UR - http://hdl.handle.net/1963/2885 U1 - 1815 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Controllability for discrete systems with a finite control set JF - Math. Control Signals Systems 14 (2001) 173-193 Y1 - 2001 A1 - Yacine Chitour A1 - Benedetto Piccoli PB - Springer UR - http://hdl.handle.net/1963/3114 U1 - 1219 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Critical Behavior, the Connection Problem and the Elliptic Representation of a Painlevé VI Equation JF - Mathematical Physics, Analysis and Geometry 4: 293–377, 2001 Y1 - 2001 A1 - Davide Guzzetti KW - Painleve Equations, Isomonodromy deformations AB - In this paper we find a class of solutions of the sixth Painlevé equation appearing in\r\nthe theory of WDVV equations. This class covers almost all the monodromy data associated to\r\nthe equation, except one point in the space of the data. We describe the critical behavior close to\r\nthe critical points in terms of two parameters and we find the relation among the parameters at\r\nthe different critical points (connection problem). We also study the critical behavior of Painlevé\r\ntranscendents in the elliptic representation. PB - Kluwer Academic Publishers U1 - 6477 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - The Calibration Method for Free Discontinuity Problems JF - European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. Y1 - 2000 A1 - Gianni Dal Maso AB - The calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems. PB - SISSA Library UR - http://hdl.handle.net/1963/1496 U1 - 2667 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence of Godunov scheme for nonlinear hyperbolic systems JF - Chinese Ann. Math. B, 2000, 21, 269 Y1 - 2000 A1 - Alberto Bressan A1 - Helge Kristian Jenssen PB - SISSA Library UR - http://hdl.handle.net/1963/1473 U1 - 2690 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The calibration method for the Mumford-Shah functional JF - C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 Y1 - 1999 A1 - Giovanni Alberti A1 - Guy Bouchitte A1 - Gianni Dal Maso AB - In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3). PB - Elsevier UR - http://hdl.handle.net/1963/1235 U1 - 2708 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Categorial mirror symmetry for K3 surfaces JF - Comm. Math. Phys. 206 (1999) 265-272 Y1 - 1999 A1 - Claudio Bartocci A1 - Ugo Bruzzo A1 - Guido Sanguinetti AB - We study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$. PB - Springer UR - http://hdl.handle.net/1963/2887 U1 - 1813 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Correspondence between Minkowski and de Sitter quantum field theory JF - Phys. Lett. B Y1 - 1999 A1 - Marco Bertola A1 - Gorini, Vittorio A1 - Moschella, Ugo A1 - Schaeffer, Richard VL - 462 ER - TY - THES T1 - On the Cauchy Problem for the Whitham Equations Y1 - 1998 A1 - Tamara Grava KW - Korteweg de Vries equation PB - SISSA UR - http://hdl.handle.net/1963/5555 U1 - 5382 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Capacity theory for monotone operators JF - Potential Anal. 7 (1997), no. 4, 765-803 Y1 - 1997 A1 - Gianni Dal Maso A1 - Igor V. Skrypnik AB - If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$. PB - Springer UR - http://hdl.handle.net/1963/911 U1 - 2880 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Comportamento asintotico delle soluzioni di problemi di Dirichlet JF - Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 Y1 - 1997 A1 - Gianni Dal Maso UR - http://hdl.handle.net/1963/6438 N1 - This is the title of the conference which was delivered by prof. Dal Maso in Padova during the XV Congress of the \\\"Unione Mathematica Italiana\\\" (Padova, 11-16 settembre 1995) U1 - 6378 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A capacity method for the study of Dirichlet problems for elliptic systems in varying domains JF - Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 Y1 - 1996 A1 - Gianni Dal Maso A1 - Rodica Toader PB - SISSA Library UR - http://hdl.handle.net/1963/989 U1 - 2867 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Capacity and Dirichlet problems in varying domains Y1 - 1995 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/950 U1 - 3504 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Classical solutions for a perturbed N-body system JF - Topological nonlinear analysis, II (Frascati, 1995), 1--86, Progr. Nonlinear Differential Equations Appl., 27, Birkhauser Boston, Boston, MA, 1997 Y1 - 1995 A1 - Gianfausto Dell'Antonio PB - SISSA Library UR - http://hdl.handle.net/1963/126 U1 - 16 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - JOUR T1 - A class of absolute retracts of dwarf spheroidal galaxies JF - Proc.Amer.Math.Soc. 112 (1991), no.2, 413 Y1 - 1991 A1 - Alberto Bressan A1 - Arrigo Cellina A1 - Andrzej Fryszkowski PB - SISSA Library UR - http://hdl.handle.net/1963/837 U1 - 2954 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Chern-Simons forms on principal superfiber bundles JF - J.Math.Phys.31:45,1990 Y1 - 1990 A1 - Giovanni Landi A1 - Claudio Bartocci A1 - Ugo Bruzzo AB - 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 ``superextension\\\'\\\' of the Dirac monopole is discussed. PB - SISSA Library UR - http://hdl.handle.net/1963/590 U1 - 3314 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Correctors for the homogeneization of monotone operators JF - Differential Integral Equations 3 (1990), no.6, p.1151-1166. Y1 - 1990 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/812 U1 - 2979 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the continuous dependence of solutions of boundary value problems for ordinary differential equations (Revised version) JF - J. Differential Equations 82 (1989), no. 1, 1-14 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/666 U1 - 3260 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the continuous dependence of solutions of boundary value problems for ordinary differential equations JF - J. Differential Equations 82 (1989), no. 1, 1--14 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/633 U1 - 3820 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Convergence of unilateral problems for monotone operators JF - J. Analyse Math. 53 (1989), 269--289 Y1 - 1989 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/722 U1 - 3069 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984) JF - Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 Y1 - 1986 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/353 U1 - 3614 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A criterion for he existence of maximal solutions of strongly nonlinear elliptic problems Y1 - 1982 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/161 U1 - 3806 U2 - Mathematics U3 - Functional Analysis and Applications ER -