The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.

UR - http://www.sciencedirect.com/science/article/pii/S0723086918300975 ER - TY - CONF T1 - Efficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design T2 - VIII International Conference on Computational Methods in Marine Engineering Y1 - 2019 A1 - Andrea Mola A1 - Marco Tezzele A1 - Mahmoud Gadalla A1 - Valdenazzi, Federica A1 - Grassi, Davide A1 - Padovan, Roberta A1 - Gianluigi Rozza AB -In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

JF - VIII International Conference on Computational Methods in Marine Engineering ER - TY - RPRT T1 - Quasi-continuous vector fields on RCD spaces Y1 - 2019 A1 - Clément Debin A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - Reducibility of first order linear operators on tori via Moser's theorem JF - Journal of Functional Analysis Y1 - 2019 A1 - Roberto Feola A1 - Filippo Giuliani A1 - Riccardo Montalto A1 - Michela Procesi KW - Hyperbolic PDEs KW - KAM theory KW - Nash–Moser KW - Reducibility AB -In this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ⋅∂xu+a(ωt,x)⋅∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser's straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

VL - 276 UR - http://www.sciencedirect.com/science/article/pii/S0022123618303793 ER - TY - JOUR T1 - On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2019 A1 - Giovanni Bellettini A1 - Alaa Elshorbagy A1 - Maurizio Paolini A1 - Riccardo Scala AB -In this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to ``fill the hole'' in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

UR - https://doi.org/10.1007/s10231-019-00887-0 ER - TY - JOUR T1 - The Serre–Swan theorem for normed modules JF - Rendiconti del Circolo Matematico di Palermo Series 2 Y1 - 2019 A1 - Danka Lučić A1 - Enrico Pasqualetto VL - 68 UR - https://doi.org/10.1007/s12215-018-0366-6 ER - TY - JOUR T1 - Accelerating the iterative solution of convection-diffusion problems using singular value decomposition JF - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS Y1 - 2018 A1 - Giuseppe Pitton A1 - Luca Heltai UR - https://arxiv.org/abs/1807.09467 ER - TY - JOUR T1 - The deal.II Library, Version 9.0 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2018 A1 - Giovanni Alzetta A1 - Arndt, Daniel A1 - W. Bangerth A1 - Boddu, Vishal A1 - Brands, Benjamin A1 - Denis Davydov A1 - Gassmöller, Rene A1 - Timo Heister A1 - Luca Heltai A1 - Kormann, Katharina A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells UR - https://doi.org/10.1515/jnma-2018-0054 ER - TY - RPRT T1 - Differential of metric valued Sobolev maps Y1 - 2018 A1 - Nicola Gigli A1 - Enrico Pasqualetto A1 - Elefterios Soultanis ER - TY - RPRT T1 - On Geometric Quantum Confinement in Grushin-Like Manifolds Y1 - 2018 A1 - Matteo Gallone A1 - Alessandro Michelangeli A1 - Eugenio Pozzoli AB - We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator. UR - http://preprints.sissa.it/handle/1963/35322 N1 - 16 pages U1 - 35632 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments JF - ASTRONOMY & ASTROPHYSICS Y1 - 2018 A1 - Puglisi, Giuseppe A1 - Poletti, Davide A1 - Fabbian, Giulio A1 - Baccigalupi, Carlo A1 - Luca Heltai A1 - Stompor, Radek VL - 618 UR - https://arxiv.org/abs/1801.08937 ER - TY - RPRT T1 - Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis Y1 - 2018 A1 - Alessandro Michelangeli A1 - Giuseppe Pitton AB - We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. UR - http://preprints.sissa.it/handle/1963/35323 U1 - 35633 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - On the notion of parallel transport on RCD spaces Y1 - 2018 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2018 A1 - Tamara Grava A1 - Christian Klein A1 - Giuseppe Pitton AB -A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

VL - 474 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458 ER - TY - JOUR T1 - NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces JF - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Y1 - 2018 A1 - Giuseppe Pitton A1 - Luca Heltai VL - 338 UR - https://arxiv.org/abs/1804.08271 ER - TY - RPRT T1 - Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation Y1 - 2018 A1 - Roberto Feola A1 - Filippo Giuliani A1 - Michela Procesi ER - TY - JOUR T1 - On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics JF - Journal of Scientific Computing Y1 - 2017 A1 - Giuseppe Pitton A1 - Gianluigi Rozza AB -In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

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 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 - The deal.II Library, Version 8.5 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2017 A1 - Arndt, Daniel A1 - W. Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells VL - 25 UR - https://www.dealii.org/deal85-preprint.pdf ER - TY - RPRT T1 - Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires. UR - http://urania.sissa.it/xmlui/handle/1963/35269 U1 - 35575 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - On the effect of interactions beyond nearest neighbours on non-convex lattice systems Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation. UR - http://urania.sissa.it/xmlui/handle/1963/35268 U1 - 35574 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Linearisation of multiwell energies Y1 - 2017 A1 - Roberto Alicandro A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours. UR - http://preprints.sissa.it/handle/1963/35288 U1 - 35594 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Real topological string amplitudes JF - Journal of High Energy Physics Y1 - 2017 A1 - Narain, K. S. A1 - Nicolò Piazzalunga A1 - Alessandro Tanzini AB -We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'= −\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

VL - 2017 UR - https://doi.org/10.1007/JHEP03(2017)080 ER - TY - CHAP T1 - Reduced-order semi-implicit schemes for fluid-structure interaction problems T2 - Model Reduction of Parametrized Systems Y1 - 2017 A1 - Francesco Ballarin A1 - Gianluigi Rozza A1 - Yvon Maday ED - Peter Benner ED - Mario Ohlberger ED - Anthony Patera ED - Gianluigi Rozza ED - Karsten Urban AB -POD–Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

JF - Model Reduction of Parametrized Systems PB - Springer International Publishing ER - TY - JOUR T1 - Small Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators JF - Journal of Dynamical and Control Systems Y1 - 2017 A1 - Elisa Paoli AB -We compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

VL - 23 UR - https://doi.org/10.1007/s10883-016-9321-z ER - TY - JOUR T1 - Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth JF - J. Elast. Y1 - 2017 A1 - D. Ambrosi A1 - Pezzuto, S. A1 - Davide Riccobelli A1 - Stylianopoulos, T. A1 - Pasquale Ciarletta PB - Springer Netherlands VL - 129 ER - TY - CONF T1 - Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives T2 - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, Y1 - 2016 A1 - Filippo Salmoiraghi A1 - Francesco Ballarin A1 - Giovanni Corsi A1 - Andrea Mola A1 - Marco Tezzele A1 - Gianluigi Rozza ED - Papadrakakis, M. ED - Papadopoulos, V. ED - Stefanou, G. ED - Plevris, V. AB -Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

JF - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, PB - ECCOMAS CY - Crete, Greece U1 - 35466 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity JF - ESAIM: COCV Y1 - 2016 A1 - Giovanni Bellettini A1 - Lucia Tealdi A1 - Maurizio Paolini KW - Area functional AB -In this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html IS - 1 U1 - 7257 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - RPRT T1 - Behaviour of the reference measure on RCD spaces under charts Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto 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 - RPRT T1 - Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - RPRT T1 - Non-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics Y1 - 2016 A1 - Alessandro Michelangeli A1 - Giuseppe Pitton AB - We present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. UR - http://urania.sissa.it/xmlui/handle/1963/35266 U1 - 35572 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds JF - Communications in Partial Differential Equations Y1 - 2016 A1 - Ugo Boscain A1 - Dario Prandi A1 - M. Seri AB -We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

PB - Taylor & Francis VL - 41 UR - https://doi.org/10.1080/03605302.2015.1095766 ER - TY - JOUR T1 - Towards a gauge theory interpretation of the real topological string JF - Phys. Rev. D Y1 - 2016 A1 - Hayashi, Hirotaka A1 - Nicolò Piazzalunga A1 - Uranga, Angel M. AB -We consider the real topological string on certain noncompact toric Calabi-Yau three-folds $\mathbb{X}$, in its physical realization describing an orientifold of type IIA on $\mathbb{X}$ with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol’nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

PB - American Physical Society VL - 93 UR - https://link.aps.org/doi/10.1103/PhysRevD.93.066001 ER - TY - JOUR T1 - Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics JF - arXiv preprint arXiv:1602.08745 Y1 - 2016 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Elisa Paoli ER - TY - JOUR T1 - Z2 Invariants of Topological Insulators as Geometric Obstructions JF - Communications in Mathematical Physics Y1 - 2016 A1 - Domenico Fiorenza A1 - Domenico Monaco A1 - Gianluca Panati AB -We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a $\mathbb{Z}_2$-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.

VL - 343 UR - https://doi.org/10.1007/s00220-015-2552-0 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 - Model order reduction of parameterized systems (MoRePaS): Preface to the special issue of advances in computational mathematics JF - Advances in Computational Mathematics Y1 - 2015 A1 - Peter Benner A1 - Mario Ohlberger A1 - Anthony Patera A1 - Gianluigi Rozza A1 - Sorensen, D.C. A1 - Karsten Urban VL - 41 ER - TY - JOUR T1 - Reduced basis approximation of parametrized advection-diffusion PDEs with high Péclet number JF - Lecture Notes in Computational Science and Engineering Y1 - 2015 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

VL - 103 ER - TY - RPRT T1 - Results on the minimization of the Dirichlet functional among semicartesian parametrizations Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

UR - http://urania.sissa.it/xmlui/handle/1963/34488 N1 - The article is compsed of 18 pages and is recorded in PDF format U1 - 34671 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires Y1 - 2015 A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro A1 - Anja Schlomerkemper AB - In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7494 U1 - 7623 ER - TY - RPRT T1 - Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

UR - http://urania.sissa.it/xmlui/handle/1963/34483 N1 - The preprint is compsed of 37 pages and is recorded in PDF format U1 - 34670 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Stability of the (2+2)-fermionic system with zero-range interaction Y1 - 2015 A1 - Alessandro Michelangeli A1 - Paul Pfeiffer AB - We introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the the celebrated (and ubiquitous, in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system. UR - http://urania.sissa.it/xmlui/handle/1963/34474 N1 - This SISSA preprint has 17 pages and recorded in PDF format U1 - 34649 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry JF - Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203 Y1 - 2015 A1 - Domenico Monaco A1 - Gianluca Panati AB -We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The rôle of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34468 N1 - The article is composed of 23 pages and recorded in PDF format U1 - 34642 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - THES T1 - Volume variation and heat kernel for affine control problems Y1 - 2015 A1 - Elisa Paoli KW - Heat kernel asymptotics AB - In this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak Hörmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume. PB - SISSA U1 - 35290 U2 - Mathematics U4 - -1 U5 - MAT/05 ER - TY - JOUR T1 - An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds Y1 - 2014 A1 - Massimiliano Berti A1 - Livia Corsi A1 - Michela Procesi AB - We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34651 U1 - 34858 U2 - Mathematics 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 - An effective model for nematic liquid crystal composites with ferromagnetic inclusions Y1 - 2014 A1 - Maria Carme Calderer A1 - Antonio DeSimone A1 - Dmitry Golovaty A1 - Alexander Panchenko AB - Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature. PB - Society for Industrial and Applied Mathematics Publications UR - http://urania.sissa.it/xmlui/handle/1963/34940 U1 - 35194 U2 - Physics U4 - 1 ER - TY - THES T1 - Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution Y1 - 2014 A1 - Dario Prandi KW - control theory AB - This thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7474 U1 - 7576 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Hölder equivalence of the value function for control-affine systems JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2014 A1 - Dario Prandi PB - EDP Sciences VL - 20 ER - TY - JOUR T1 - KAM for Reversible Derivative Wave Equations JF - Arch. Ration. Mech. Anal. Y1 - 2014 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi AB -We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

PB - Springer VL - 212 UR - http://urania.sissa.it/xmlui/handle/1963/34646 IS - 3 U1 - 34850 U2 - Mathematics ER - TY - JOUR T1 - Local behavior of fractional p-minimizers Y1 - 2014 A1 - Agnese Di Castro A1 - Tuomo Kuusi A1 - Giampiero Palatucci KW - fractional Sobolev spaces AB -We extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

PB - SISSA U1 - 7301 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - M-theory interpretation of the real topological string JF - Journal of High Energy Physics Y1 - 2014 A1 - Nicolò Piazzalunga A1 - Uranga, Angel M. AB -We describe the type IIA physical realization of the unoriented topological string introduced by Walcher, describe its M-theory lift, and show that it allows to compute the open and unoriented topological amplitude in terms of one-loop diagram of BPS M2-brane states. This confirms and allows to generalize the conjectured BPS integer expansion of the topological amplitude. The M-theory lift of the orientifold is freely acting on the M-theory circle, so that integer multiplicities are a weighted version of the (equivariant subsector of the) original closed oriented Gopakumar-Vafa invariants. The M-theory lift also provides new perspective on the topological tadpole cancellation conditions. We finally comment on the M-theory version of other unoriented topological strings, and clarify certain misidentifications in earlier discussions in the literature.

VL - 2014 UR - https://doi.org/10.1007/JHEP08(2014)054 ER - TY - JOUR T1 - Pseudo-automorphisms of positive entropy on the blowups of products of projective spaces Y1 - 2014 A1 - Fabio Perroni A1 - Deqi Zhang AB - We use a concise method to construct pseudo-automorphisms fn of the first dynamical degree d1(fn) > 1 on the blowups of the projective n-space for all n ≥ 2 and more generally on the blowups of products of projective spaces. These fn, for n=3 have positive entropy, and for n≥ 4 seem to be the first examples of pseudo-automorphisms with d1(fn) > 1 (and of non-product type) on rational varieties of higher dimensions. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34714 U1 - 34921 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2014 A1 - Sara Daneri A1 - Aldo Pratelli AB -We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

VL - 31 UR - http://www.sciencedirect.com/science/article/pii/S0294144913000711 ER - TY - JOUR T1 - Stabilized reduced basis method for parametrized advection-diffusion PDEs JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2014 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -In this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

VL - 274 ER - TY - CONF T1 - Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts T2 - 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 Y1 - 2014 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -Advection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

JF - 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 UR - https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf ER - TY - JOUR T1 - Swelling-induced and controlled curving in layered gel beams Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Matteo Pezzulla AB - We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method. PB - Royal Society of London UR - http://urania.sissa.it/xmlui/handle/1963/34987 U1 - 35229 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Topological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene JF - J. Stat. Phys 155 (2014) 1027-1071 Y1 - 2014 A1 - Domenico Monaco A1 - Gianluca Panati KW - Wannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene AB -We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|≤const |x|^{−2} as |x|→∞, both in monolayer and bilayer graphene.

PB - Journal of Statistical Physics U1 - 7368 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting Y1 - 2013 A1 - Serena Dipierro A1 - Giampiero Palatucci A1 - Enrico Valdinoci KW - nonlocal Allen-Cahn equation AB - We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential. PB - SISSA UR - http://hdl.handle.net/1963/7124 U1 - 7124 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Existence and stability of quasi-periodic solutions for derivative wave equations JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni Y1 - 2013 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi KW - Constant coefficients KW - Dynamical systems KW - Existence and stability KW - Infinite dimensional KW - KAM for PDEs KW - Linearized equations KW - Lyapunov exponent KW - Lyapunov methods KW - Quasi-periodic solution KW - Small divisors KW - Wave equations AB - In this note we present the new KAM result in [3] which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. In turn, this result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems*. VL - 24 N1 - cited By (since 1996)0 ER - TY - JOUR T1 - Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian JF - Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 Y1 - 2013 A1 - Serena Dipierro A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

PB - University of Catania U1 - 7318 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Genus stabilization for moduli of curves with symmetries Y1 - 2013 A1 - Fabrizio Catanese A1 - Michael Lönne A1 - Fabio Perroni KW - group actions KW - mapping class group KW - Moduli space of curves KW - Teichmüller space AB - In a previous paper, arXiv:1206.5498, we introduced a new homological\r\ninvariant $\\e$ for the faithful action of a finite group G on an algebraic\r\ncurve.\r\n We show here that the moduli space of curves admitting a faithful action of a\r\nfinite group G with a fixed homological invariant $\\e$, if the genus g\' of the\r\nquotient curve is sufficiently large, is irreducible (and non empty iff the\r\nclass satisfies the condition which we define as \'admissibility\'). In the\r\nunramified case, a similar result had been proven by Dunfield and Thurston\r\nusing the classical invariant in the second homology group of G, H_2(G, \\ZZ).\r\n We achieve our result showing that the stable classes are in bijection with\r\nthe set of admissible classes $\\e$. PB - SISSA UR - http://hdl.handle.net/1963/6509 N1 - 21 pages, 2 figures U1 - 6461 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - KAM theory for the Hamiltonian derivative wave equation JF - Annales Scientifiques de l'Ecole Normale Superieure Y1 - 2013 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi AB -We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. © 2013 Société Mathématique de France.

VL - 46 N1 - cited By (since 1996)4 ER - TY - JOUR T1 - The nonlinear multidomain model: a new formal asymptotic analysis. JF - Geometry Partial Differential Equations – proceedings, CRM Series (15), 2013. Y1 - 2013 A1 - Stefano Amato A1 - Giovanni Bellettini A1 - Maurizio Paolini KW - bidomain model, anisotropic mean curvature, star-shaped combination AB -We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

SN - 8876424724 U1 - 7259 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces Y1 - 2013 A1 - Ugo Boscain A1 - Dario Prandi ER - TY - THES T1 - Semistability and Decorated Bundles Y1 - 2013 A1 - Andrea Pustetto KW - Decorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf AB - This thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we “enclose” the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition. PB - SISSA UR - http://hdl.handle.net/1963/7130 U1 - 7132 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes JF - J. Stat. Phys. Y1 - 2013 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 153 UR - http://dx.doi.org/10.1007/s10955-013-0845-2 ER - TY - JOUR T1 - Asymptotics of the s-perimeter as s →0 JF - Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 Y1 - 2012 A1 - Serena Dipierro A1 - Alessio Figalli A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

PB - American Institute of Mathematical Sciences U1 - 7317 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment JF - Nanoscale. 2012 Mar; 4(5):1734-41 Y1 - 2012 A1 - Alessandro Bosco A1 - Fouzia Bano A1 - Pietro Parisse A1 - Loredana Casalis A1 - Antonio DeSimone A1 - Cristian Micheletti AB - Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters. PB - Royal Society of Chemistry U1 - 6998 U2 - Physics U4 - -1 ER - TY - JOUR T1 - Nonlinear thin-walled beams with a rectangular cross-section-Part I JF - Math. Models Methods Appl. Sci. 22, 1150016 (2012) Y1 - 2012 A1 - Lorenzo Freddi A1 - Maria Giovanna Mora A1 - Roberto Paroni AB - Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results. PB - World Scientific UR - http://hdl.handle.net/1963/4104 U1 - 300 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes JF - J. Stat. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 146 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2 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 - 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 - D-branes, surface operators, and ADHM quiver representations Y1 - 2011 A1 - Ugo Bruzzo A1 - Duiliu-Emanuel Diaconescu A1 - M. Yardim A1 - G. Pan A1 - Yi Zhang A1 - Chuang Wu-yen AB - A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries. PB - SISSA UR - http://hdl.handle.net/1963/4133 N1 - 45 pages, v2: minor corrections U1 - 3873 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Infinitely many positive solutions for a Schrödinger–Poisson system JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2011 A1 - Pietro d’Avenia A1 - Alessio Pomponio A1 - Giusi Vaira KW - Non-autonomous Schrödinger–Poisson system KW - Perturbation method AB -We are interested in the existence of infinitely many positive solutions of the Schrödinger–Poisson system −Δu+u+V(|x|)ϕu=|u|p−1u,x∈R3,−Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<p<5 and V(r

VL - 74 UR - http://www.sciencedirect.com/science/article/pii/S0362546X11003518 ER - TY - JOUR T1 - Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations JF - Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290 Y1 - 2011 A1 - Boris Dubrovin A1 - M.V. Pavlov A1 - Sergei A. Zykov KW - Frobenius manifold AB - We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions. PB - Springer UR - http://hdl.handle.net/1963/6430 U1 - 6367 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells JF - Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050 Y1 - 2011 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces. PB - Springer UR - http://hdl.handle.net/1963/3392 U1 - 940 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Nonlinear thin-walled beams with a rectangular cross-section - Part II Y1 - 2011 A1 - Lorenzo Freddi A1 - Maria Giovanna Mora A1 - Roberto Paroni KW - Thin-walled cross-section beams AB - In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section.. PB - SISSA UR - http://hdl.handle.net/1963/4169 U1 - 3891 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces JF - Duke Mathematical Journal Y1 - 2011 A1 - Massimiliano Berti A1 - Michela Procesi AB - We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr¨odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions. VL - 159 IS - 3 ER - TY - RPRT T1 - A planar bi-Lipschitz extension Theorem Y1 - 2011 A1 - Sara Daneri A1 - Aldo Pratelli UR - http://arxiv.org/abs/1110.6124 ER - TY - JOUR T1 - Poincaré covariance and κ-Minkowski spacetime JF - Physics Letters A 375 (2011) 3496-3498 Y1 - 2011 A1 - Ludwik Dabrowski A1 - Gherardo Piacitelli AB - A fully Poincaré covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised á la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of \\\"Poincaré covariance\\\". PB - Elsevier UR - http://hdl.handle.net/1963/3893 U1 - 816 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Poincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces JF - Communications in Mathematical Physics 304 (2011) 395-409 Y1 - 2011 A1 - Ugo Bruzzo A1 - Rubik Poghossian A1 - Alessandro Tanzini AB -We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

PB - Springer VL - 304 UR - http://hdl.handle.net/1963/3738 IS - 2 U1 - 579 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators JF - Commun. Math. Phys. 308 (2011) 567-589 Y1 - 2011 A1 - Dorothea Bahns A1 - Sergio Doplicher A1 - Klaus Fredenhagen A1 - Gherardo Piacitelli AB - We develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out. PB - Springer UR - http://hdl.handle.net/1963/5203 U1 - 5025 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - An abstract Nash-Moser theorem with parameters and applications to PDEs JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis Y1 - 2010 A1 - Massimiliano Berti A1 - Philippe Bolle A1 - Michela Procesi KW - Abstracting KW - Aircraft engines KW - Finite dimensional KW - Hamiltonian PDEs KW - Implicit function theorem KW - Invariant tori KW - Iterative schemes KW - Linearized operators KW - Mathematical operators KW - Moser theorem KW - Non-Linearity KW - Nonlinear equations KW - Nonlinear wave equation KW - Periodic solution KW - Point of interest KW - Resonance phenomena KW - Small divisors KW - Sobolev KW - Wave equations AB - We prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. © 2009 Elsevier Masson SAS. All rights reserved. VL - 27 N1 - cited By (since 1996)9 ER - TY - Generic T1 - Aspects of Quantum Field Theory on Quantum Spacetime T2 - PoS CNCFG2010:027,2010 Y1 - 2010 A1 - Gherardo Piacitelli AB - We provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation. JF - PoS CNCFG2010:027,2010 PB - SISSA UR - http://hdl.handle.net/1963/4171 N1 - 25 pages, active hyperlinks. Corfu Summer Institute on Elementary\\r\\n Particles and Physics - Workshop on Non Commutative Field Theory and Gravity,\\r\\n September 8-12, 2010, Corfu Greece U1 - 3893 U2 - Mathematics U3 - Mathematical Physics 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 - 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 - 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 - On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system JF - Int. Math. Res. Not. (2010) 2010:279-296 Y1 - 2010 A1 - Claudio Bartocci A1 - Gregorio Falqui A1 - Igor Mencattini A1 - Giovanni Ortenzi A1 - Marco Pedroni AB - We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed. PB - Oxford University Press UR - http://hdl.handle.net/1963/3800 U1 - 8 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - RPRT T1 - The geometry emerging from the symmetries of a quantum system Y1 - 2010 A1 - Giuseppe De Nittis A1 - Gianluca Panati AB - We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result. UR - http://hdl.handle.net/1963/3834 U1 - 493 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Lorentz Covariant k-Minkowski Spacetime JF - Phys. Rev. D 81 (2010) 125024 Y1 - 2010 A1 - Ludwik Dabrowski A1 - Michal Godlinski A1 - Gherardo Piacitelli AB - In recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance. UR - http://hdl.handle.net/1963/3829 U1 - 498 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Quantum Spacetime: a Disambiguation Y1 - 2010 A1 - Gherardo Piacitelli AB - We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the \\\"canonical quantum spacetime\\\". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance. Some incorrect statements as \\\"universality of Planck scale conflicts with Lorentz-Fitzgerald contraction and requires a modification of covariance\\\", or \\\"stability of the geometric background requires an absolute lower bound of (\\\\Delta x^\\\\mu)\\\", or \\\"violations of unitarity are due to time/space non-commutativity\\\" are put in context, and discussed. UR - http://hdl.handle.net/1963/3864 U1 - 845 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 Y1 - 2010 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates. UR - http://hdl.handle.net/1963/2601 U1 - 1521 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Taming open/closed string duality with a Losev trick JF - JHEP 06(2010)063 Y1 - 2010 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini AB - A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual. UR - http://hdl.handle.net/1963/3855 U1 - 854 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - A three-dimensional model for the dynamics and hydrodynamics of rowing boats JF - Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology Y1 - 2010 A1 - L. Formaggia A1 - Andrea Mola A1 - N Parolini A1 - M Pischiutta AB -This paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

VL - 224 UR - https://doi.org/10.1243/17543371jset46 ER - TY - JOUR T1 - Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model JF - Comm. Math. Phys. 295 (2010) 701-729 Y1 - 2010 A1 - Gherardo Piacitelli AB - We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames. UR - http://hdl.handle.net/1963/3605 U1 - 696 U2 - Mathematics U3 - Mathematical Physics 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 - Decoupling A and B model in open string theory: topological adventures in the world of tadpoles JF - JHEP 06 (2009) 046 Y1 - 2009 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini A1 - Yang Jie AB - In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula. UR - http://hdl.handle.net/1963/3632 U1 - 672 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - Initial value problem of the Whitham equations for the Camassa-Holm equation JF - Physica D 238 (2009) 55-66 Y1 - 2009 A1 - Tamara Grava A1 - Virgil U. Pierce A1 - Fei-Ran Tian AB - We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp. PB - Elsevier UR - http://hdl.handle.net/1963/3429 U1 - 906 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A model for the orbifold Chow ring of weighted projective spaces JF - Comm. Algebra 37 (2009) 503-514 Y1 - 2009 A1 - Samuel Boissiere A1 - Etienne Mann A1 - Fabio Perroni AB - We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity. PB - Taylor and Francis UR - http://hdl.handle.net/1963/3589 U1 - 711 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A nonlinear theory for shells with slowly varying thickness JF - C. R. Math. 347 (2009) 211-216 Y1 - 2009 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface. UR - http://hdl.handle.net/1963/2632 U1 - 1491 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Twisted Covariance vs Weyl Quantisation Y1 - 2009 A1 - Gherardo Piacitelli AB - In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio \\\"why theta\\\"? UR - http://hdl.handle.net/1963/3451 U1 - 885 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions JF - Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 Y1 - 2009 A1 - Gianni Dal Maso A1 - Alessandro Giacomini A1 - Marcello Ponsiglione UR - http://hdl.handle.net/1963/2675 U1 - 1425 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fluid–structure interaction problems in free surface flows: Application to boat dynamics JF - International Journal for Numerical Methods in Fluids Y1 - 2008 A1 - L. Formaggia A1 - Edie Miglio A1 - Andrea Mola A1 - N Parolini PB - Wiley VL - 56 UR - https://doi.org/10.1002/fld.1583 ER - TY - JOUR T1 - Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices JF - Phys. Rev. B 77 (2008) 245105 Y1 - 2008 A1 - Matteo Rizzi A1 - Marco Polini A1 - Miguel A. Cazalilla A1 - M.R. Bakhtiari A1 - Mario P. Tosi A1 - Rosario Fazio AB -Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

UR - http://hdl.handle.net/1963/2694 U1 - 1406 U2 - Physics U3 - Condensed Matter Theory ER - TY - RPRT T1 - Instanton counting on Hirzebruch surfaces Y1 - 2008 A1 - Ugo Bruzzo A1 - Rubik Poghossian A1 - Alessandro Tanzini AB - We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa. UR - http://hdl.handle.net/1963/2852 U1 - 1848 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Noncommutative families of instantons JF - Int. Math. Res. Not. vol. 2008, Article ID rnn038 Y1 - 2008 A1 - Giovanni Landi A1 - Chiara Pagani A1 - Cesare Reina A1 - Walter van Suijlekom AB - We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$. PB - Oxford University Press UR - http://hdl.handle.net/1963/3417 U1 - 918 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Asymptotic variational wave equations JF - Arch. Ration. Mech. Anal. 183 (2007) 163-185 Y1 - 2007 A1 - Alberto Bressan A1 - Zhang Ping A1 - Zheng Yuxi AB - We investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data. UR - http://hdl.handle.net/1963/2182 U1 - 2062 U2 - Mathematics U3 - Functional Analysis and Applications 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 - Gaussian estimates for hypoelliptic operators via optimal control JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342 Y1 - 2007 A1 - Ugo Boscain A1 - Sergio Polidoro AB - We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem. UR - http://hdl.handle.net/1963/1994 U1 - 2202 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas JF - Phys. Rev. Lett. 98 (2007) 030404 Y1 - 2007 A1 - Gao Xianlong A1 - Matteo Rizzi A1 - Marco Polini A1 - Rosario Fazio A1 - Mario P. Tosi A1 - Vivaldo L. Jr. Campo A1 - Klaus Capelle AB -The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

UR - http://hdl.handle.net/1963/2056 U1 - 2140 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Time optimal swing-up of the planar pendulum JF - 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 Y1 - 2007 A1 - Mireille E. Broucke A1 - Paolo Mason A1 - Benedetto Piccoli AB - This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart. UR - http://hdl.handle.net/1963/1867 U1 - 2355 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 - A Hopf bundle over a quantum four-sphere from the symplectic group JF - Commun. Math. Phys. 263 (2006) 65-88 Y1 - 2006 A1 - Giovanni Landi A1 - Chiara Pagani A1 - Cesare Reina AB - We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$. UR - http://hdl.handle.net/1963/2179 U1 - 2065 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Infinite Horizon Noncooperative Differential Games Y1 - 2006 A1 - Alberto Bressan A1 - Fabio Simone Priuli AB - For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability. JF - J. Differential Equations 227 (2006) 230-257 UR - http://hdl.handle.net/1963/1720 U1 - 2431 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - N=1 superpotentials from multi-instanton calculus Y1 - 2006 A1 - Francesco Fucito A1 - Jose F. Morales A1 - Rubik Poghossian A1 - Alessandro Tanzini AB - In this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement. JF - JHEP01(2006)031 UR - http://hdl.handle.net/1963/1773 U1 - 2771 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Quasi-periodic solutions of completely resonant forced wave equations JF - Comm. Partial Differential Equations 31 (2006) 959 - 985 Y1 - 2006 A1 - Massimiliano Berti A1 - Michela Procesi AB - We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number. UR - http://hdl.handle.net/1963/2234 U1 - 2010 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Gel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited Y1 - 2005 A1 - Gregorio Falqui A1 - Marco Pedroni AB - In this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets. JF - Regul. Chaotic Dyn. 10 (2005) 399-412 UR - http://hdl.handle.net/1963/1689 U1 - 2444 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Hybrid necessary principle JF - SIAM J. Control Optim. 43 (2005) 1867-1887 Y1 - 2005 A1 - Mauro Garavello A1 - Benedetto Piccoli AB - We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature. PB - SIAM UR - http://hdl.handle.net/1963/1641 N1 - Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France U1 - 2477 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Orbifold Cohomology of ADE-singularities Y1 - 2005 A1 - Fabio Perroni KW - Orbifolds PB - SISSA UR - http://hdl.handle.net/1963/5298 U1 - 5126 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Quasi-periodic oscillations for wave equations under periodic forcing JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116 Y1 - 2005 A1 - Massimiliano Berti A1 - Michela Procesi PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/4583 U1 - 4350 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - CHAP T1 - A short introduction to optimal control T2 - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 Y1 - 2005 A1 - Ugo Boscain A1 - Benedetto Piccoli JF - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 SN - 2 7056 6511 0 UR - http://hdl.handle.net/1963/2257 U1 - 1990 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The spectral geometry of the equatorial Podles sphere JF - C. R. Math. 340 (2005) 819-822 Y1 - 2005 A1 - Ludwik Dabrowski A1 - Giovanni Landi A1 - Mario Paschke A1 - Andrzej Sitarz AB - We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties. UR - http://hdl.handle.net/1963/2275 U1 - 1972 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Traffic flow on a road network JF - SIAM J. Math. Anal. 36 (2005) 1862-1886 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Benedetto Piccoli A1 - Mauro Garavello AB - This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights. PB - SISSA Library UR - http://hdl.handle.net/1963/1584 U1 - 2534 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Energetics and switching of quasi-uniform states in small ferromagnetic particles JF - M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 Y1 - 2004 A1 - François Alouges A1 - Sergio Conti A1 - Antonio DeSimone A1 - Ivo Pokern AB - We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size. PB - EDP Sciences UR - http://hdl.handle.net/1963/2999 U1 - 1334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A geometric approach to the separability of the Neumann-Rosochatius system JF - Differential Geom. Appl. 21 (2004) 349-360 Y1 - 2004 A1 - Claudio Bartocci A1 - Gregorio Falqui A1 - Marco Pedroni AB - We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system. UR - http://hdl.handle.net/1963/2541 U1 - 1578 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Effective dynamics for Bloch electrons: Peierls substitution and beyond Y1 - 2003 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\\\\phi(\\\\epsi x)$, and vector potential $A(\\\\epsi x)$, with $x \\\\in \\\\R^d$ and $\\\\epsi \\\\ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\\\\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\\\\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics. PB - Springer UR - http://hdl.handle.net/1963/3040 U1 - 1293 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Hybrid optimal control: case study of a car with gears JF - Int. J. Control 76 (2003) 1272-1284 Y1 - 2003 A1 - Ciro D'Apice A1 - Mauro Garavello A1 - Rosanna Manzo A1 - Benedetto Piccoli AB - The purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis. PB - Taylor and Francis UR - http://hdl.handle.net/1963/3022 U1 - 1311 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Separation of variables for Bi-Hamiltonian systems JF - Math. Phys. Anal. Geom. 6 (2003) 139-179 Y1 - 2003 A1 - Gregorio Falqui A1 - Marco Pedroni AB - We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations. PB - SISSA Library UR - http://hdl.handle.net/1963/1598 U1 - 2520 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Space-adiabatic perturbation theory JF - Adv. Theor. Math. Phys. 7 (2003) 145-204 Y1 - 2003 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - We study approximate solutions to the Schr\\\\\\\"odinger equation $i\\\\epsi\\\\partial\\\\psi_t(x)/\\\\partial t = H(x,-i\\\\epsi\\\\nabla_x) \\\\psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space $\\\\Hi_{\\\\rm f}$ of fast ``internal\\\'\\\' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \\\\cite{NS} we prove that interband transitions are suppressed to any order in $\\\\epsi$. As a consequence, associated to that energy band there exists a subspace of $L^2(\\\\mathbb{R}^d,\\\\Hi _{\\\\rm f})$ almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory. PB - International Press UR - http://hdl.handle.net/1963/3041 U1 - 1292 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A stability result for nonlinear Neumann problems under boundary variations JF - J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 Y1 - 2003 A1 - Gianni Dal Maso A1 - Francois Ebobisse A1 - Marcello Ponsiglione AB - In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. PB - SISSA Library UR - http://hdl.handle.net/1963/1618 U1 - 2500 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type JF - J. Differ. Equations, 2002, 180, 395 Y1 - 2002 A1 - Jean-Marc Mercier A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1491 U1 - 2672 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Linearized elasticity as gamma-limit of finite elasticity JF - Set-Valued Anal. 10 (2002), p.165-183 Y1 - 2002 A1 - Gianni Dal Maso A1 - Matteo Negri A1 - Danilo Percivale PB - Springer UR - http://hdl.handle.net/1963/3052 U1 - 1281 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Poisson reduction for Gel\\\'fand-Zakharevich manifolds JF - Rep.Math.Phys.50 (2002), no.3, 395 Y1 - 2002 A1 - Gregorio Falqui A1 - Marco Pedroni PB - SISSA Library UR - http://hdl.handle.net/1963/1602 U1 - 2516 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On the reachability of quantized control systems JF - IEEE Trans. Automat. Contr. 47 (2002) 546-563 Y1 - 2002 A1 - Antonio Bicchi A1 - Alessia Marigo A1 - Benedetto Piccoli AB - In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed. PB - SISSA Library UR - http://hdl.handle.net/1963/1501 U1 - 2662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Space-adiabatic Decoupling in Quantum Dynamics Y1 - 2002 A1 - Gianluca Panati PB - SISSA UR - http://hdl.handle.net/1963/6360 U1 - 6292 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Space-adiabatic perturbation theory in quantum dynamics JF - Physical review letters. 2002 Jun; 88(25 Pt 1):250405 Y1 - 2002 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the g factor of the electron within nonrelativistic quantum electrodynamics. PB - American Physical Society UR - http://hdl.handle.net/1963/5985 U1 - 5841 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Bihamiltonian geometry and separation of variables for Toda lattices JF - J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127 Y1 - 2001 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni PB - SISSA Library UR - http://hdl.handle.net/1963/1354 U1 - 3101 U2 - Mathematics U3 - Mathematical Physics 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 - Dieletric breakdown: optimal bounds JF - Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 Y1 - 2001 A1 - Adriana Garroni A1 - Vincenzo Nesi A1 - Marcello Ponsiglione PB - SISSA Library UR - http://hdl.handle.net/1963/1569 U1 - 2549 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Extremal synthesis for generic planar systems JF - J. Dynam. Control Systems, 2001, 7, 209 Y1 - 2001 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1503 U1 - 2660 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Fourier transform for sheaves on real tori. I. The equivalence Sky(T)~ Loc (T) JF - J. Geom. Phys. 39 (2001), no. 2, 174--182 Y1 - 2001 A1 - Ugo Bruzzo A1 - Giovanni Marelli A1 - Fabio Pioli PB - SISSA Library UR - http://hdl.handle.net/1963/1526 U1 - 2637 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Global continuous Riemann solver for nonlinear elasticity JF - Arch. Ration. Mech. An., 2001, 156, 89 Y1 - 2001 A1 - Jean-Marc Mercier A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1493 U1 - 2670 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Morse properties for the minimum time function on 2-D manifolds JF - J. Dynam. Control Systems 7 (2001), no. 3, 385--423 Y1 - 2001 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1541 U1 - 2622 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Numerical minimization of the Mumford-Shah functional JF - Calcolo, 2001, 38, 67 Y1 - 2001 A1 - Matteo Negri A1 - Maurizio Paolini PB - SISSA Library UR - http://hdl.handle.net/1963/1461 U1 - 3079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems JF - J. Differential Equations 172 (2001) 59-82 Y1 - 2001 A1 - Paolo Baiti A1 - Philippe G. LeFloch A1 - Benedetto Piccoli PB - Elsevier UR - http://hdl.handle.net/1963/3113 U1 - 1220 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Abnormal extremals for minimum time on the plane Y1 - 2000 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1508 U1 - 2655 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A bi-Hamiltonian theory for stationary KDV flows and their separability JF - Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52 Y1 - 2000 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni A1 - Jorge P. Zubelli PB - SISSA Library UR - http://hdl.handle.net/1963/1352 U1 - 3103 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - An elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy JF - Theor. Math. Phys. 122 (2000) 17-28 Y1 - 2000 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni A1 - Jorge P. Zubelli AB - We give an elementary construction of the solutions of the KP hierarchy associated with polynomial τ-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a consequence, we establish a Wronskian formula for the polynomial τ-functions of the KP hierarchy. This formula, known in the literature, is obtained very directly. PB - Springer UR - http://hdl.handle.net/1963/3223 U1 - 1078 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Elliptic variational problems in $ R\\\\sp N$ with critical growth JF - J. Differential Equations 168 (2000), no. 1, 10--32 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1258 U1 - 3197 ER - TY - JOUR T1 - Existence and multiplicity results for some nonlinear elliptic equations: a survey. JF - Rend. Mat. Appl., 2000, 20, 167 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1462 U1 - 3078 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quantized control systems and discrete nonholonomy JF - Lagrangian and Hamiltonian Methods for Nonlinear Control : a proc. volume from the IFAC Workshop. Princeton, New Jersey, 16-18 March 2000 / ed. by N.E. Leonard, R. Ortega. - Oxford : Pergamon, 2000 Y1 - 2000 A1 - Alessia Marigo A1 - Benedetto Piccoli A1 - Antonio Bicchi PB - Elsevier SN - 0-08-043658-7 UR - http://hdl.handle.net/1963/1502 U1 - 2661 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Reachability Analysis for a Class of Quantized Control Systems T2 - Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 Y1 - 2000 A1 - Alessia Marigo A1 - Benedetto Piccoli A1 - Antonio Bicchi AB - We study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure. JF - Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 PB - IEEE UR - http://hdl.handle.net/1963/3518 U1 - 746 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Regular Synthesis and Sufficiency Conditions for Optimality JF - SIAM J. Control Optim. 39 (2000) 359-410 Y1 - 2000 A1 - Benedetto Piccoli A1 - Hector J. Sussmann AB - We propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side. PB - SIAM UR - http://hdl.handle.net/1963/3213 U1 - 1088 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - BOOK T1 - Well-posedness of the Cauchy problem for n x n systems of conservation laws T2 - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. Y1 - 2000 A1 - Alberto Bressan A1 - Graziano Crasta A1 - Benedetto Piccoli JF - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. PB - American Mathematical Society UR - http://hdl.handle.net/1963/3495 N1 - Chapter 1 and 2 U1 - 769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - A bihamiltonian approach to separation of variables in mechanics T2 - Proceedings of the workshop on nonlinearity, integrability and all that : twenty years after NEEDS \\\'79, Lecce, Italy, July 1 - 10, 1999 / ed. by M. Boiti. - Singapore : World Scientific, 2000. - p. 258-266 Y1 - 1999 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni AB - This paper is a report on a recent approach to the theory of separability of the Hamilton-Jacobi equations from the viewpoint of bihamiltonian geometry. JF - Proceedings of the workshop on nonlinearity, integrability and all that : twenty years after NEEDS \\\'79, Lecce, Italy, July 1 - 10, 1999 / ed. by M. Boiti. - Singapore : World Scientific, 2000. - p. 258-266 PB - World Scientific UR - http://hdl.handle.net/1963/3222 U1 - 1079 U2 - Mathematics U3 - Mathematical Physics ER - TY - CHAP T1 - The method of Poisson pairs in the theory of nonlinear PDEs T2 - Direct and inverse methods in nonlinear evolution equations : Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999 / Robert Conte ... ; Antonio M. Greco ed. - Berlin : Springer, 2003. - (Lecture Notes in Physics ; 632) Y1 - 1999 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni AB - The aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear partial differential equations. The prototype of these equations is the well-known Korteweg-de Vries (KdV) equation.\\nIn these lectures we touch the following subjects:\\ni) the birth and the role of the method of Poisson pairs inside the theory of the KdV equation;\\nii) the theoretical basis of the method of Poisson pairs;\\niii) the Gel\\\'fand-Zakharevich theory of integrable systems on bi-Hamiltonian manifolds;\\niv) the Hamiltonian interpretation of the Sato picture of the KdV flows and of its linearization on an infinite-dimensional Grassmannian manifold.\\nv) the reduction technique(s) and its use to construct classes of solutions;\\nvi) the role of the technique of separation of variables in the study of the reduced systems;\\nvii) some relations intertwining the method of Poisson pairs with the method of Lax pairs. JF - Direct and inverse methods in nonlinear evolution equations : Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999 / Robert Conte ... ; Antonio M. Greco ed. - Berlin : Springer, 2003. - (Lecture Notes in Physics ; 632) PB - Springer UR - http://hdl.handle.net/1963/1350 U1 - 3105 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws JF - J. Differential Equations 151 (1999) 345-372 Y1 - 1999 A1 - Debora Amadori A1 - Paolo Baiti A1 - Philippe G. LeFloch A1 - Benedetto Piccoli AB - The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality. PB - Elsevier UR - http://hdl.handle.net/1963/3312 U1 - 1018 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on fractional KDV hierarchies. II. The bihamiltonian approach Y1 - 1999 A1 - Paolo Casati A1 - Gregorio Falqui A1 - Marco Pedroni PB - SISSA Library UR - http://hdl.handle.net/1963/1220 U1 - 2723 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Perturbation of $\Delta u+u^(N+2)/(N-2)=0$, the scalar curvature problem in $R^N$, and related topics JF - J. Funct. Anal. 165 (1999) 117-149 Y1 - 1999 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral AB -Some nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

PB - Elsevier UR - http://hdl.handle.net/1963/3255 U1 - 1446 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Projection singularities of extremals for planar systems Y1 - 1999 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1304 U1 - 3151 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Renormalized solutions of elliptic equations with general measure data JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 Y1 - 1999 A1 - Gianni Dal Maso A1 - Francois Murat A1 - Luigi Orsina A1 - Alain Prignet PB - Scuola Normale Superiore di Pisa UR - http://hdl.handle.net/1963/1236 U1 - 2707 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A generic classification of time-optimal planar stabilizing feedbacks JF - SIAM J. Control Optim. 36 (1998) 12-32 Y1 - 1998 A1 - Alberto Bressan A1 - Benedetto Piccoli AB - Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto. PB - SISSA Library UR - http://hdl.handle.net/1963/998 U1 - 2858 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Geometric control approach to synthesis theory JF - Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001) Y1 - 1998 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1277 U1 - 3178 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Infinite time regular synthesis JF - ESAIM: COCV 3 (1998) 381-405 Y1 - 1998 A1 - Benedetto Piccoli AB - In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function. PB - EDP Sciences UR - http://hdl.handle.net/1963/3517 U1 - 747 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Structural stability for time-optimal planar sytheses JF - Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 Y1 - 1997 A1 - Alberto Bressan A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/997 U1 - 2859 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws JF - Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 Y1 - 1997 A1 - Graziano Crasta A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/969 U1 - 3485 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some control problems for the pendulum JF - Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318 Y1 - 1995 A1 - Benedetto Piccoli AB - The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems. PB - IEEE UR - http://hdl.handle.net/1963/982 U1 - 2874 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of obstacle problems for the area functional. JF - Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 Y1 - 1989 A1 - Gianni Dal Maso A1 - Michele Carriero A1 - Antonio Leaci A1 - Eduardo Pascali PB - SISSA Library UR - http://hdl.handle.net/1963/577 U1 - 3327 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Variational inequalities for the biharmonic operator with variable obstacles. JF - Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989) Y1 - 1988 A1 - Gianni Dal Maso A1 - Gabriella Paderni PB - SISSA Library UR - http://hdl.handle.net/1963/531 U1 - 3373 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Integral representation of some convex local functionals. JF - Ricerche Mat. 36 (1987), no. 2, 197-214 Y1 - 1987 A1 - Gianni Dal Maso A1 - Gabriella Paderni PB - SISSA Library UR - http://hdl.handle.net/1963/497 U1 - 3407 U2 - Mathematics U3 - Functional Analysis and Applications ER -