ingleseENG
Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo

 Seminari

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Prossimi Seminari

  • Deep Learning meets Parametric Partial Differential Equations
    Gitta Kutyniok, Institute of Mathematics, Technische Universität Berlin (DE)
    giovedì 16 luglio 2020 alle ore 14:00, Online seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1977&t=763724

Seminari Passati

  • Sistemi periodici di controllo e previsione
    S. Bittanti, Dip. Elettronica e Informazione
    venerdì 28 maggio 2004 alle ore 12:30, Aula B.21
  • Modelli d'urna con rinforzo aleatorio
    Dr. Anna Maria Paganoni, Politecnico di Milano
    giovedì 27 maggio 2004 alle ore 16:30, Aula Seminari, VI piano
    ABSTRACT
    Si affronta lo studio di modelli d'urna con rinforzo aleatorio, ed in particolare si concentra l'attenzione su un'urna a due colori che ad ogni estrazione viene rinforzata con un numero aleatorio di palline dello stesso
    colore della pallina estratta: la legge del numero di palline che vengono reinserite nell'urna dipende dal colore estratto. Si espongono risultati asintotici sul processo dei colori generati dall'urna e sul processo delle
    proporzioni di palline in essa contenuta. Questi schemi d'urna trovano applicazione nella formulazione di disegni clinici sequenziali e
    connessioni con la modellizzazione di disegni adattivi degli esperimenti in ambito Bayesiano.
  • Existence Results for a New Variational Problem in One Dimensional Segmentation Theory
    Tommaso Boccellari, Politecnico di Milano
    mercoledì 26 maggio 2004
  • Three body problems in quantum mechanics
    Wu-Yi Hsiang, Hong Kong University of Science and Technology (Hong Kong, Cina)
    mercoledì 26 maggio 2004 alle ore 17:00, Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza
    ABSTRACT
    In this talk, I shall describe the geometric approach to solve the Schrödinger equation for various physically meaningful three body systems such as He, H2+, H-, three bosons in R2 with d-function potential etc. The configuration space of the three body system in R3(resp. R2) (with center of gravity fixed at the origin) is an R6 (resp. R4) equipped with an SO(3) (resp. SO(2)) symmetric kinematic metric, while the potential function U is also SO(3) (resp. SO(2)) invariant. The first step is to fully utilize the SO(3) (resp. SO(2)) symmetry to reduce the Schrödinger equation to an equation solely defined at the level of the orbit space (i.e. R6/SO(3) (resp. R4/SO(2))) equipped with the orbital distance metric. One needs to make effective use of both group representation theory and equivariant differential geometry to achieve such a reduction. The orbit space of a three body system in R3 (resp. R2) equipped with the orbital distance metric is always isometric to the Riemannian cone over S2+ (1/2) (resp. S2(1/2))), namely the Euclidean hemisphere (resp. sphere) of radius 1/2. This remarkable fact (i.e. sphericality) enables us to bring in the spherical harmonics and their generalizations (namely, Jacobi polynomials and monopole harmonics) to greatly simplify the analysis of the angular part of the reduced equation. I will use the simpler case of the boson system to illustrate this step which enables us to further reduce the Schrödinger equation to an ODE solely in the radial direction. Such an ODE can be thoroughly analyzed and I will discuss the physical significance of these solutions so obtained for the three boson system. Bibliography Wu-Yi Hsiang. Kinematic geometry of mass-triangles and reduction of Schr¨odinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters. Proc. Nat. Acad. Sci. U.S.A., 94(17):8936–8938, 1997. Wu-Yi Hsiang. On the kinematic geometry of many body systems. Chinese Ann. Math. Ser. B, 20(1):11–28, 1999. A Chinese summary appears in Chinese Ann. Math. Ser. A 20 (1999), no. 1, 141.
  • Sistemi dinamici ed i fondamenti della termodinamica
    L. Galgani, Univ. di Milano
    venerdì 21 maggio 2004 alle ore 12:30, Aula B.21
  • Nonextensive statistical mechanics - Introduction and dynamical foundations
    Constantino Tsallis, Centro Brasileiro de Pesquisas Físicas (Rio de Janeiro, Brasile)
    venerdì 21 maggio 2004 alle ore 17:00, Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza
    ABSTRACT
    "Nonlinear dynamical systems that satisfy hypothesis such as ergodicity and exponentially quick mixing are well known to be adequately studied in terms of the Boltzmann-Gibbs entropy and its corresponding statistical mechanics. These simplifying hypothesis are however NOT satisfied in vast classes of systems such as the so called ""complex systems"", ubiquitously emerging in physics, mathematics, economics, linguistics, chemistry, astrophysics, geophysics, biology, computer networks, engineering and elsewhere. A nonextensive entropy (characterized by an entropic index q, which reproduces the Boltzmann-Gibbs expression for q = 1) and its corresponding statistical mechanics provide an answer for at least part of such anomalous systems. A brief introduction will be given to the subject, followed by a survey on its dynamical foundations, which enable in particular the calculation, from first principles, of the index q associated with specific systems. Recent bibliography: ""Nonextensive Entropy - Interdisciplinary Applications"", M. Gell-Mann and C. Tsallis, eds. (Oxford University Press, New York, 2004) Full bibliography"
  • Onde solitarie e campi elettromagnetici
    Donato Fortunato, Università di Bari
    mercoledì 19 maggio 2004 alle ore 11:30, Dipartimento di Matematica e Applicazioni - Università degli Studi di Milano Bicocca - Via Bicocca degli Arcimboldi, 8 - Aula Dottorato
  • Approximation of multi-scale elliptic problems using patches of finite elements
    Joel Wagner, iacs-epfl
    lunedì 17 maggio 2004 alle ore 14:30, Aula Seminari MOX-6° piano dip di matematica
    ABSTRACT
    The objective of this seminar is to present a new method to solve numerically
    elliptic problems such that a better precision on the solution is needed
    in certain regions of the domain wherein the equations
    are to be solved (C.R.Acad.Sci.Paris, Ser.I 337 (2003) 679--684).
    The approximation of this type of problems with multi-scale data can be approached using
    various methods. The technique we present uses multiple levels of not necessarily nested
    grids. It is a Schwarz type domain decomposition method with complete overlapping.
    The proposed algorithm consists in solving the problem on a domain wherein we consider
    patches of elements in the regions where we would like to obtain more accuracy.
    Thus we calculate successively corrections to the solution in the patches.
    The discretizations of the latter are not necessarily conforming.
    The method resembles the Fast Adaptive Composite grid method or possibly
    a hierarchical method with a mortar method. However it is of much more flexible use
    in comparison to the latter.

    The motivation for developing such a method is for example founded in air quality management.
    Pollution emission sources, and in particular point source plumes, give
    rise to models needing careful examination of the space-scale. Getting an accurate
    simulation on large scales is linked to a simulation in subregions around the
    pollution sources using finer grids. Such a method can straightforwardly be applied
    on boundary layer problems through the use of patches in critical regions.

    In this talk we present the algorithm and illustrate its efficiency through a model problem.
    We compare the speed of convergence on nested and non-nested, structured and unstructured grids.
    A spectral analysis of the iteration operator enables us to give a good estimate of the convergence
    rate for given grids. It also leads to a numerical method to evaluate the
    constant of the Cauchy-Buniakowski-Schwarz inequality in certain cases of approximation spaces.
    Finally we illustrate on several examples our \emph{a priori} estimate for
    the convergence in the grid-size.