17 Maggio, 2006 12:30

Seminari di Cultura Matematica

Matematica e astronomia nel patrimonio culturale della cristianità medioevale di occidente

M. Incerti, Univ. di Ferrara

Aula B.21

16 Maggio, 2006 17:00

Seminario Matematico e Fisico di Milano

The Neumann problem for semilinear elliptic equations with critical Sobolev exponent

Jan Chabrowski, University of Queensland (Australia)

Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza

abstract

abstract

In my talk I give a survey of the existence results for the Neumann problem involving Sobolev and Sobolev - Hardy exponents. This also includes problems with the critical exponent on the boundary. A joint effect of the shape of the indefinite weight and the mean curvature on the existence will be discussed.

16 Maggio, 2006 

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Optimal pricing of transportation networks

Eugene Stepanov, Università di Pisa

In my talk I give a survey of the existence results for the Neumann problem involving Sobolev and Sobolev - Hardy exponents. This also includes problems with the critical exponent on the boundary. A joint effect of the shape of the indefinite weight and the mean curvature on the existence will be discussed.

15 Maggio, 2006 16:15

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Cellular traction as an inverse problem

Prof. Davide Ambrosi, Dipartimento di Matematica, Politecnico di Torino

Aula Seminari, VI piano Dipartimento

abstract

abstract

The evaluation of the traction exerted by a cell on a planar substrate is here considered as an inverse problem: shear stress is calculated on the basis of the measurement of the deformation of the underlying gel layer. The adjoint problem of the direct two-dimensional plain stress operator is derived by a suitable minimization requirement. The resulting coupled systems of elliptic partial differential equations (the direct and the adjoint problem) are solved by a finite element method and tested vs. experimental measures of displacement induced by a fibroblast cell traction.

12 Maggio, 2006 11:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Reduction techniques for the numerical solution to nonlinear stochastic PDEs

Clayton Webster, Department of Mathematics Florida State University

Aula Seminari, VI piano

abstract

abstract

The objective of this work is the development of novel, efficient and reliable reduction techniques, in both physical space-time and multi-dimensional probability spaces, for the numerical solution to various types of nonlinear Stochastic Partial Differential Equations (SPDEs).

This work proposes and analyzes a sparse grid stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms (input data of the model).
This method can be viewed as an extension of the Stochastic Collocation method proposed in [Babuska-Nobile-Tempone, Technical report, MOX, Dipartimento di Matematica, 2005] which consists of a Galerkin approximation in space and a collocation at the zeros of suitable tensor product orthogonal polynomials in probability space and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. The full tensor product spaces suffer from the curse of dimensionality since the dimension of the approximating space grows exponentially fast in the number of random variables. If the number of random variables is moderately large, this work proposes the use of sparse tensor product spaces utilizing either Clenshaw-Curtis or Gaussian abscissas. For both situations this work provides rigorous convergence analysis of the fully discrete problem and demonstrates algebraic convergence of the ``probability error'' with respect of the number of points in each direction of the probability space. The problem setting in which this procedure is recommended as well as suggestions for future enhancements to the method are discussed.

The complexity of such problems may also be decreased by means of reduced order modeling (ROM) in physical space-time. We also explore the use of ROMs for determining outputs that depend on solutions of nonlinear parabolic SPDEs driven by space-time white noise. In the context of proper orthogonal decomposition-based ROMs, we explore the effects on the accuracy of statistical information about outputs determined from ensembles of such solutions. The coupling of this technique with sparse approximation is a tool with which we plan to devote further investigation in a higher dimensional probability space.

Numerical examples demonstrate the analytic results and show the effectiveness of such methods.

11 Maggio, 2006 12:30

Seminari di Cultura Matematica

Matematica e letteratura, Hilbert e Queneau

A. Ferraro, Univ. di Udine

Aula B.21

The objective of this work is the development of novel, efficient and reliable reduction techniques, in both physical space-time and multi-dimensional probability spaces, for the numerical solution to various types of nonlinear Stochastic Partial Differential Equations (SPDEs).

This work proposes and analyzes a sparse grid stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms (input data of the model).
This method can be viewed as an extension of the Stochastic Collocation method proposed in [Babuska-Nobile-Tempone, Technical report, MOX, Dipartimento di Matematica, 2005] which consists of a Galerkin approximation in space and a collocation at the zeros of suitable tensor product orthogonal polynomials in probability space and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. The full tensor product spaces suffer from the curse of dimensionality since the dimension of the approximating space grows exponentially fast in the number of random variables. If the number of random variables is moderately large, this work proposes the use of sparse tensor product spaces utilizing either Clenshaw-Curtis or Gaussian abscissas. For both situations this work provides rigorous convergence analysis of the fully discrete problem and demonstrates algebraic convergence of the ``probability error'' with respect of the number of points in each direction of the probability space. The problem setting in which this procedure is recommended as well as suggestions for future enhancements to the method are discussed.

The complexity of such problems may also be decreased by means of reduced order modeling (ROM) in physical space-time. We also explore the use of ROMs for determining outputs that depend on solutions of nonlinear parabolic SPDEs driven by space-time white noise. In the context of proper orthogonal decomposition-based ROMs, we explore the effects on the accuracy of statistical information about outputs determined from ensembles of such solutions. The coupling of this technique with sparse approximation is a tool with which we plan to devote further investigation in a higher dimensional probability space.

Numerical examples demonstrate the analytic results and show the effectiveness of such methods.

9 Maggio, 2006 11:00

Sezione di Probabilità e Statistica Matematica

Modelli quantistici stocastici della meccanica statistica del nonequilibrio.

prof. Geoffrey Sewell, Department of Physics Queen Mary, Univ. of London

Aula seminari III piano

abstract

abstract

Costruirò un insieme di modelli stocastici quantistici che serve per lo studio della meccanica statistica del nonequilibrio. La costruzione porta ai due risultati seguenti:
(a) generalizza all'ambito quantistico
il programma classico di Jona-Lasinio et al;
(b) fornisce degli esempi concreti di modelli che verificano le ipotesi del mio trattamento
macrostatistico generale della termodinamica statistica del nonequilibrio
(Rev. Math. Phys. 2005).

8 Maggio, 2006 17:00

Seminario Matematico e Fisico di Milano

l trattamento numerico di problemi ellittici in domini aleatori

Claudio Canuto, Politecnico di Torino

Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza

abstract

abstract

"Le equazioni a derivate parziali stocastiche permettono di introdurre elementi di incertezza nella modellizzazione matematica: ciò può essere realizzato considerando come variabili aleatorie i coefficienti dell'equazione, i termini noti e lo stesso dominio in cui l'equazione è posta. Lo studio e la discretizzazione numerica di tali equazioni pone problemi interessanti e non banali. Focalizziamo l'attenzione sul trattamento dell'aleatorietà del dominio, che nasce ad esempio in certi processi tecnologici avanzati. Consideriamo due diversi approcci (""mapping"" e ""fictitious domain""): in entrambi i casi, il problema aleatorio viene trasformato in un problema deterministico attraverso l'uso di espansioni di Wiener (generalizzate), dette anche ""caos polinomiale"". La discretizzazione è effettuata attraverso metodi di proiezione di tipo Galerkin, eventualmente accompagnati da integrazione numerica (collocazione). Il confronto teorico e sperimentale con tecniche Monte Carlo mette in luce l'efficienza dei metodi proposti."

4 Maggio, 2006 09:00

Seminario Matematico e Fisico di Milano

MINI - WORKSHOP DI BIOSTATISTICA

Dottorandi XX ciclo in Bioingegneria, Dip.di Bioingegneria, Politecnico di Milano

Aula Seminari VI piano edificio Nave

abstract

abstract

Sono previsti i seguenti tre interventi:
Dr. Michele Butti,
(Dottorato in Biongegneria (XX ciclo), Dipartimento di Bioingegneria,
Politecnico di Milano) "Non-invasive Neuroimaging: analisi di serie
temporali da Near Infrared Spectroscopy"
Abstract:
L'attività cognitiva è associata a modifiche del flusso ematico locale
e delle caratteristiche di ossigenazione del sangue, fenomeni che
portano a differenze nelle proprietà ottiche del tessuto cerebrale. Con
la Near Infrared Spectroscopy (NIRS) è possibile risalire alle
caratteristiche emodinamiche per mezzo di misure ottiche. Si propone un
metodo di analisi per la visualizzazione di immagini di attivazione
cerebrale durante test cognitivi mediante l’utilizzo della teoria dei
Modelli Lineari.
Dr.ssa Katia Passera
(Dottorato in Biongegneria (XX ciclo), Dipartimento di Bioingegneria,
Politecnico di Milano) "Determinazione della volumetria delle neoplasie
delle fosse nasali e dei seni paranasali da indagini di risonanza
magnetica"
Abstract:
La segmentazione di lesioni neoplastiche su immagini di Risonanza
Magnetica fornisce informazioni sulle loro caratteristiche morfologiche
e di dimensione, indispensabili per pianificare e monitorare
l’efficacia di una terapia radiante o chirurgica. La forma irregolare e
frastagliata delle neoplasie delle fosse nasali e dei seni paranasali
rende inadatti molti algoritmi di segmentazione comunemente utilizzati.
Viene qui proposto un algoritmo di clustering semiautomatico EM
(Expectation Maximation).
Dr.ssa Valentina Corino
(Dottorato in Biongegneria (XX ciclo), Dipartimento di Bioingegneria,
Politecnico di Milano) "Valutazione della risposta ventricolare
all’esercizio e alla somministrazione di flecainide in pazienti affetti
da fibrillazione atriale"
Abstract:
La fibrillazione atriale è l'aritmia cardiaca più frequente nella
popolazione adulta e determina un ritmo altamente irregolare. Scopo di
questo studio è stato valutare la risposta ventricolare a riposo e
sotto sforzo con o senza la somministrazione di flecainide, un farmaco
antiaritmico, in un gruppo di pazienti affetti da fibrillazione
atriale.
Per evidenziare gli effetti combinati dell’esercizio e della
somministrazione del farmaco è stata utilizzata un’analisi della
varianza.
Tutti gli interessati sono cordialmente invitati a partecipare.

2 Maggio, 2006 14:30

Seminario Matematico e Fisico di Milano

Stabilized Pressure Segregation methods and their application to Fluid-Structure Interaction problems

Santiago Badia, Visitatore MOX

aula MOX VI piano ed. Nave

abstract

abstract

The numerical approximation of
the Navier-Stokes equations is a difficult task that has focused an
active research in the last decades. The velocity and pressure
interpolation spaces must satisfy a undesired compatibility
condition when using the Galerkin method. Another unrelated
complication is the numerical instability that arises for convective
dominated flows. About the computational cost, the incompressibility
constraint couples velocity and pressure computation, being its
numerical solution expensive.

In this seminar we consider some topics in order to facilitate the
finite element discretization of the Navier-Stokes equations. We
suggest the use of a stabilization technique in order to circumvent
the compatibility condition over the velocity and pressure discrete
spaces and be able to solve convective dominant flows. We introduce
some novel concepts for the stabilization of transient equations. In
order to reduce the computational cost, we explore some pressure
segregation methods motivated at the discrete level. We state and
analyze classical pressure correction methods and new velocity
correction methods motivated by the use of a discrete pressure
Poisson equation (where is the velocity instead of the pressure the
extrapolated variable).

The second part of the seminar tackles the fluid-structure
interaction problem. We apply the ALE framework in order for the
fluid governing equations to be formulated on moving domains. We
analyze the blend of the ALE framework and a stabilized finite
element method.For the interaction, we consider a coupling procedure
that profits from the ingredients previously introduced. The final
algorithm, using one loop, tends to the monolithic (fluid-structure)
system.

This method has been applied to the analysis of bridge aerodynamics,
obtaining a good convergence behavior. We end with the simulation of
wind turbines. The fact that we have a rotary body surrounded by the
fluid (air) has motivated the introduction of a selective remeshing
procedure.