11 Febbraio, 2015 15:00

Seminari FDS

La galleria del vento del Politecnico di Milano: dalle grandi opere allo sport

Ferruccio Resta, Politecnico di Milano

Aula Consiglio, 7° piano, edificio 14 Nave – Via Bonardi, 9 – Milano

abstract

abstract

L'intervento vuole illustrare le potenzialità e i campi di applicazione della ricerca svolta presso la Galleria del Vento del Politecnico di Milano.
L'impianto, unico al mondo per le sue caratteristiche e dimensioni, nasce nel 2001 per rispondere a esigenze di progettazione dinamica delle grandi infrastrutture civili. Vengono provati in Galleria del Vento i grandi ponti sospesi, come l'attraversamento sul Bosforo, e i grandi grattacieli che hanno modificato la skyline di Milano. Ma l'ingegneria del vento non si ferma alle opere civili. Gli studi di aerodinamica e dinamica investono le più curiose applicazioni e i più innovativi settori tecnologici come quelli propri delle attività sportive. Sciatori, ciclisti e le imbarcazioni a vela da competizione sono solo alcuni esempi.

10 Febbraio, 2015 14:00

MOX Seminar

Isogeometric Analysis

Giancarlo Sangalli, Università degli Studi di Pavia

Aula Saleri VI Piano Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

N.A.

9 Febbraio, 2015 14:00 in punto

MOX Seminar

Hemodynamics of vascular access for hemodialysis

Andrea Remuzzi, Istituto M. Negri, Ranica (BG)

Aula Saleri 6° Piano Dipartimento di Matematica - Politecnico di Milano

abstract

abstract

Function and duration of vascular access for hemodialysis is the most important clinical problem in these patients. Arteriovenous fistula with native vessels is the most recommended strategy, but it is affected by early failure and short duration. Vascular access failure is predominantly related to development of intimal hyperplasia. We then studied the role of hemodynamics on development of initial hyperplasia in arteriovenous fistulas using idealized vascular models as well as patient-specific models.

referente: christian.vergara@unibg.it

5 Febbraio, 2015 11:00 in punto

MOX Seminar

High-Order Discontinuous Galerkin Time Stepping

Thomas Wihler, Universität Bern

Aula Saleri VI Piano - Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

The focus of this talk is to provide an analytical framework for arbitrary-order (hp-type) discontinuous Galerkin (dG) time discretizations.For this purpose, we will introduce and analyze a discrete dG time derivative operator within a general Hilbert space setting; this will turn out to be a crucial tool in the numerical analysis of the dG method.
Specifically, we will illustrate the general functionality of the dG operator in the context of existence proofs of discrete dG solutions for general nonlinear initial value problems (including blow-up problems) as well as in the derivation of a posteriori error estimates for linear parabolic problems.

5 Febbraio, 2015 11:00

Dipartimento di Matematica del Politecnico di Milano

Tactical vote in committes. Applications to law, teaching, business and sports

J. Freixas, UPC Manresa

DEIB - sala seminari - piano terreno

abstract

abstract

www.gametheory.polimi.it/

3 Febbraio, 2015 14:00

MOX Seminar

An overview of (Iso-geometric) Boundary Element Methods

Luca Heltai, SISSA, Trieste

Aula Saleri VI Piano Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

Isogeometric analysis (IGA) emerged as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis.

In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that describe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided when the partial differential equations to be solved admit a formulation in terms of boundary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM).

The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels.

In this talk I will address in detail the second point and present a nonsingular formulation of IGA-BEM, where Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the problem at hand are used to correct the resulting matrices.

contact: nicola.parolini@polimi.it

2 Febbraio, 2015 10:30 in punto

MOX Seminar

Mathematicians on Creativity

Peter Liljedahl, Simon Fraser University di Vancouver (Canada)

Aula Saleri VI Piano Dipartimento di Matematica - MOX -Politecnico di Milano

abstract

abstract

In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the École Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard,1945). In this talk I present a study that mirrors the work of Hadamard. Results both confirm and extend the work of Hadamard on the inventive process, mathematical creativity, and the phenomenon of the AHA! experience. The results also speak to the larger context of ‘doing’ and learning mathematics.

contact: chiara.andra@polimi.it

28 Gennaio, 2015 15:00

Seminari FDS

Matematica per vincere

Nicola Parolini, Politecnico di Milano

Aula Consiglio, 7° piano, edificio 14 Nave – Via Bonardi, 9 – Milano

abstract

abstract

Può la matematica aiutare a vincere una competizione sportiva? Cerchiamo di rispondere a questa domanda discutendo alcuni esempi nei quali i modelli matematici e numerici sono stati utilizzati nell'ambito di diversi sport per il design di attrezzature, l'analisi delle prestazioni e l'ottimizzazione dei gesti atletici.

27 Gennaio, 2015 15:00 in punto

MOX Seminar

A blended semi-implicit model for weakly compressible atmospheric dynamics

Tommaso Benacchio, UK Met Office, Exeter UK

Aula Saleri presso VI Piano Dipartimento di Matematica Ed. 14 -Politecnico di Milano

abstract

abstract

Physical processes in the atmosphere develop on a wide range of spatial and temporal scales. Meteorologically relevant phenomena move at speeds much lower than that of sound waves. Despite their unimportance in weather and climate studies, the latter enforce the use of very small time steps in explicit discretizations of the fully compressible equations. Traditionally, the problem has been tackled using reduced analytical formulations -- anelastic and pseudo-incompressible models on small scales, hydrostatic models on large scales -- that lack the terms that generate acoustics. Alternatively, fully compressible equations have been solved with split-explicit or semi-implicit numerical methods free of acoustic-dependent stability constraints. However, most existing numerical approaches resort to various forms of numerical filtering to achieve stability at the expense of accuracy. We present a semi-implicit fully compressible numerical model for the simulation of low-speed atmospheric flows. The second-order accurate finite volume scheme extends a projection method for the pseudo-incompressible model and agrees with it by construction in the small-scale limit. Quantities are advanced in time in an explicit advection step limited by a stability threshold independent of sound speed, with compressibility handled implicitly in a correction step. Well-balancing techniques are used to discretize buoyancy without reference to a hydrostatically balanced background state. Equations are then cast in a blended soundproof-compressible multimodel formulation allowing for controlled introduction of compressibility in the scheme in a unified and uniformly accurate framework. Convergence properties are evaluated on the advection of a smooth vortex, while the ability of the scheme to accurately simulate gravity-driven flows with large time steps is assessed on thermal benchmarks in neutrally and stably stratified atmospheres. Then, the blending feature is employed to filter acoustic perturbations in the initial stages of thermal simulations. The technique can find application in an atmospheric data assimilation context, enabling on-the-fly incorporation of unbalanced data in the numerical model.

Nota: seminario MOX (che vale anche come seminario del gruppo Fluids)

Contact: luca.bonaventura@polimi.it

27 Gennaio, 2015 17:00

Seminario Matematico e Fisico di Milano

LE RADICI CLASSICHE DELLA TEORIA QUANTISTICA

Luigi Accardi, Università di Roma Tor Vergata

Università di Milano, Dipartimento di Matematica, Via Saldini 50, Sala di rappresentanza

abstract

abstract

For several decades the mathematical model of Quantum Probability (QP) has been considered as a generalization of classical probability.
However some discoveries of the past 15 years show that the whole quantum theory, including quantum fields, is not a generalization,
but rather a deeper level of classical probability.

In fact, combining classical probability with the theory of
orthogonal polynomials in 1 or several real variables, it is possible to
prove that the canonical commutation relations, both Fermi and Bose
(and in fact even their $q$-deformations), arise canonically from the Bernoulli and Gaussian random variables respectively.


More generally one can prove that there is a one-to-one correspondence between Heisenberg-type commutation relations
and equivalence classes of probability measures on R with all moments.
The equivalence relation being defined, in the one-dimensional case,
by the fact that all measures in a class share the same principal
Jacobi sequence.

To each of these equivalence classes it is canonically associated a
free evolution, generalizing the classical harmonic oscillator evolution.

The characterization of the equilibrium states with respect to any such evolution naturally leads to a generalization of the Planck factor.
Similar arguments, applied to the recently introduced local
equilibrium states, lead to non-linear extensions of the Planck factor and non-linear Gibbs states.

Being functorial, the above construction also provides a generalization
of the second quantization procedure both at Hilbert space (Fock)
and $*$-algebra level and in some special cases (e.g. probability measures
on $R^d$ with compact support) even at $C^*$-algebra level.
However in general the class of morphisms will be much narrower than
in usual second quantization.

This fact supports the intuition that the new quantizations have a physical meaning in terms of non-linear completely integrable classical systems.

The present talk is concentrated on the goal to illustrate
the classical roots of quantum theory, however
if time allows it will be also mentioned how these new ideas have allowed
to solve a multiplicity of long standing open problems both in
classical probability and in the theory of orthogonal polynomials.