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


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Prossimi Seminari

  • Nonintrusive reduced order models using physics informed neural networks
    Jan S. Hesthaven, Chair of Computational Mathematics and Simulation Science, EPFL, Lausanne, CH
    giovedì 29 ottobre 2020 alle ore 14:00 precise, Online seminar:

Seminari Passati

  • Multidomain simulation of flow in porous media
    Vincent Martin, MOX-Dip. Mate. Polimi
    lunedì 7 giugno 2004 alle ore 11:30, Aula Seminari MOX-6° piano. Dip. di Matematica
    I will present during this seminar the main results of my PhD thesis
    performed at Inria under the direction of Jean Roberts.

    It is mainly concerned with the multidomain simulations
    of flow in porous media. Three different themes are considered.
    First, I present a domain decomposition method with non-matching meshes
    using Robin type interface conditions, for the mixed finite
    elements. Second, this method was implemented in parallel
    using the parallel system OcamlP3l, written in Ocaml by
    computer scientists. In OcamlP3l, the user develops and
    debugs sequentially, and obtains the parallel code
    with a mere recompilation. A realistic 3D simulation is
    given to validate the procedure.
    Finally, we present a new model for flow in a porous medium containing
    large fractures that may have very large and/or very small permeabilities.
    In this model, the fractures are treated as interfaces between subdomains.
    Existence and uniqueness of the solution is proved and an error estimate is
    obtained. Some numerical experiments confirm the theorical results.

  • Chiacchierata sull'analisi non standard
    S. Salsa, Dip. di Matematica
    venerdì 4 giugno 2004 alle ore 12:30, aula T2.2
  • 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
    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
    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
    "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"