16 Novembre, 2015 11:00

MOX Seminar

Fluidodinamica delle cavita' nasali

Maurizio Quadrio, Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano

Aula Seminari Saleri VI Piano Dipartimento di Matematica MOX, Politecnico di Milano

abstract

abstract

Le patologie che inducono difficolta' respiratorie nasali rappresentano una situazione molto comune, e comportano elevati costi sociali ed economici. Nonostante cio', la loro gestione eventualmente
anche chirurgica risente della difficolta' di correlare le anomalie anatomiche (e le loro eventuali correzioni chirurgiche) alle caratteristiche della corrente fluida all'interno delle cavita'
nasali. Negli ultimi anni la fluidodinamica computazionale (CFD) ha assunto un ruolo crescente nella descrizione della corrente fluida all'interno delle alte vie respiratorie.

Il seminario descrive i passi essenziali di una procedura patient-specific, basata sulla CFD, che stiamo sviluppando per supportare i chirurghi ORL nella loro pratica clinica quotidiana. La procedura parte da una scansione TAC del massiccio facciale del paziente, e produce un dettagliato campo fluidodinamico tridimensionale e dipendente dal tempo all'interno delle cavita' nasali. Requisiti essenziali della procedura sono:
i) la sua "economicita'" (nel senso piu' generale del termine), per poterla realisticamente utilizzare nella pratica clinica quotidiana;
ii) la robustezza e affidabilita' delle sue previsioni, relativamente non solo a quantita' globali (come la portata, o la resistenza nasale) ma anche ai dettagli della corrente fluida nelle aree in cui il chirurgo deve operare.

Dopo una breve descrizione dei passaggi procedurali che conducono dalla TAC al risultato fluidodinamico, verranno commentati i risultati di analisi fluidodinamiche ad alta fedelta' (DNS, LES) e le fasi
preparatorie di un esperimento di laboratorio. L'esperimento, i cui risultati saranno fondamentali per la taratura della procedura CFD, prevede la misura mediante tecniche PIV dell'intero campo di velocita'
in un modello in scala 2:1 anatomicamente realistico (derivato anch'esso da una TAC).

contatto: davide.ambrosi@polimi.it

13 Novembre, 2015 11:00 in punto

Sezione di Analisi

On the Dirichlet problem of mixed type for lower hybrid waves in axisymmetric cold plasmas

Dario D. Monticelli, Politecnico di Milano

Aula seminari III piano

abstract

abstract

In this talk we will describe some recent results concerning the Dirichlet problem for a class of second order differential equations of mixed elliptic-hyperbolic type on suitable bounded domains of R^2, which is used as a model to describe possible heating in axisymmetric cold plasmas subjected to high frequency electromagnetic waves near certain frequencies. The presence of hyperbolicity makes the problem overdetermined for classical solutions. We will show that the problem is well-posed for weak solutions belonging to a weighted version of the classical Sobolev space H^1_0, when the datum is chosen in a suitable weighted L^2 space. We will also provide a complete spectral theory for the Dirichlet problem in the setting of weighted Lebesgue and Sobolev spaces, with some applications to semilinear equations and to equations with lower order terms. Finally we will give a variational characterisation of weak solutions, which are shown to be saddle points of an associated strongly indefinite functional.

These results are joint work with D. Lupo (Politecnico di Milano) and K.R. Payne (Università degli Studi di Milano).

9 Novembre, 2015 17:00

MOX Seminar

Modeling climate change economics and policy

Massimo Tavoni, Politecnico di Milano Department of Management, Economics and Industrial Engineering

Aula Seminari "Saleri" VI piano MOX - Dipartimento di Matematica del Politecnico di Milano

abstract

abstract

Climate change is one of the great challenges which is confronting our society. This seminar will discuss how research can inform the debate surrounding climate change strategies. We will discuss the structure of numerical integrated assessment models of the economy and the climate, and their use in ex ante policy assessment. We will present applications with a focus on robust decision making under uncertainty. The seminar will conclude with new research topics and potential collaboration in
applied mathematics.

contact: piercesare.secchi@polimi.it

6 Novembre, 2015 10:30

MOX Seminar

Exploring Functional Data with Dynamic Models

Jim Ramsay, McGill University, Canada

l'Aula Seminari

abstract

abstract

Discrete observations of curves are often smoothed by attaching a penalty to the error sum of squares, and the most popular penalty is the integrated squared second derivative of the function that fits the data. But it has been known since the earliest days of smoothing splines that, if the linear differential operator D^2 is replaced by a more general differential operator L that annihilates most of the variation in the observed curves, then the resulting smooth has less bias and greatly reduced mean squared error.
This talk will show how we can use the data to estimate such an operator. The differential equation estimated in this way is already an interesting model for the data that represents the dynamics of the processes being estimated. But, in addition to the advantages in bias and MSE, it emerges that exciting new ways of representing the data emerge that use an orthogonal basis system defined by the estimated operator.

contact:laura.sangalli@polimi.it

6 Novembre, 2015 11:30

MOX Seminar

Data2PDE: an iterative scheme for obtaining data driven estimates of the parameters of PDEs defined over complex domains

Michelle Carey, McGill University, Canada

Aula Seminari "F. Saleri" VI piano - Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

Spatial data are abundant in many scientific fields, some examples include; satellite images of the earth, temperature readings from multiple weather stations and the spread of an infectious disease over a particular region. In many instances the spatial data are accompanied by mathematical models expressed in terms of partial differential equations (PDEs). These PDEs determine the theoretical aspects of the behaviour of the physical, chemical or biological phenomena considered. The parameters of the PDEs are typically unknown and must be inferred from expert knowledge of the phenomena considered. In this talk I will discuss extending the profiling with parameter cascading procedure outlined in Ramsay et al (2007) to incorporate PDE parameter estimation. Furthermore, following from Sangalli et al. (2013) the estimation procedure is extended to include finite element methods (FEMs). This allows the proposed method to account for attributes of the geometry of the physical problem such as irregular shaped domains, external and internal boundary features and strong concavities. Thus this talk introduces a methodology for data driven estimates of the parameters of PDEs defined over complex domains.

contact: laura.sangalli@polimi.it

5 Novembre, 2015 11:00

Sezione di Probabilità e Statistica Matematica

On random sequence comparison

Juri Lember, University of Tartu, Tartu, Estonia

Auletta Seminari III piano

abstract

abstract

Measuring the similarity of long strings like texts or DNA-sequences is an important subject in many fields. In computational molecular biology, for example, similar DNA sequences are deemed to have a common ancestor (homologous); in linguistics, the similarity of texts can indicate the same topic or author. Typically the similarity between two (finite length) sequences is measured via a similarity score. A commonly used score is the length of the longest common subsequence, but there are many other scores possible.
Often the sequences are modeled as random processes and then the score is a random variable, too. In order to distinguish related sequences from unrelated (independent) ones, one has to know the distribution of random score, at least asymptotically. It turns out that this is a very complicated task and has not yet been solved even for the simplest models.
In the talk, a brief overview of main sequence comparison ideas and methods is given. Moreover, some recent results concerning the rate of convergence of the moments of score are discussed as well.

4 Novembre, 2015 15:00

Seminari FDS

Il Metodo di Newton: dai Babilonesi ai giorni nostri passando per i pub londinesi

Marco Verani, Politecnico di Milano

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

abstract

abstract

Il "Metodo di Newton" è forse l'algoritmo piu' popolare per approssimare numericamente la soluzione di equazioni o sistemi di equazioni non lineari. La storia e le vicissitudini della sua ideazione e formalizzazione sono molto piu' articolate di quanto il nome non faccia pensare. Infatti alcuni semi dell'algoritmo possono essere ritrovati già presso la civiltà babilonese (1600 a.C. circa), mentre la sua moderna formulazione incrocia la vita e le vicissitudini di vari scienziati, tra cui Isaac Newton (1642 - 1727) stesso, ma anche Joseph Raphson (1648-1715) e Thomas Simpson (1710-1761). Il ruolo di quest'ultimo, personaggio poliedrico, dalla vita travagliata, è stato lungamente sottovalutato e relegato quasi completamente all'oblio.
In questo seminario si ripercorreranno le tappe di questa storia. Storia paradigmatica che mostra come in generale sia molto difficile, sovente impossibile, risalire all'origine delle idee matematiche che non sono patrimonio di un'unica civiltà e tantomeno di un solo uomo.

30 Ottobre, 2015 11:00 in punto

Sezione di Analisi

Shape sensitivity analysis for vibrating plates

Davide Buoso, Politecnico di Torino

Aula seminari III piano

abstract

abstract

In this talk we will consider the eigenvalues of the biharmonic operator subject to various boundary
conditions, namely Dirichlet, Neumann, Navier and Steklov ones. Note that such problems arise in the theory of linear elasticity, within the so-called Kirchhoff-Love model for the vibration of a plate. We will show that the eigenvalues of the Bilaplacian are analytic with respect to the shape, and compute Hadamard-type formulas for their differentials. Then, using the Lagrange Multiplier Theorem, we are able to show that the ball is a critical domain for any eigenvalue (under any of the boundary conditions considered). In the last part of the talk we will focus on eigenvalue shape optimization results for Neumann and Steklov problems. We will provide isoperimetric inequalities in quantitative form for the fundamental tones (i.e., the first non-trivial eigenvalues), and discuss the limiting cases.

22 Ottobre, 2015 11:00

MOX Seminar

Descriptors of arterial hemodynamics

Umberto Morbiducci, Politecnico di Torino

Aula Seminari Saleri VI piano MOX Dipartimento di Matematica Ed. 14 La Nave - Politecnico di Milano

abstract

abstract

Knowledge of blood flow mechanics is a critical issue (1) for an in depth understanding of the relationships between hemodynamic factors and arterial homeostasis and (2) for the identification of those flow features that lead to changes in the function and health of vessels. While from one side there is clear evidence that regions of disrupted flow are correlated to, e.g., the localization of atherosclerosis, the development of
neurysms and non-physiological transport of species, on the opposite cause-effect links still do not emerge clearly. To allow for a more effective and valuable understanding of blood flow structures and mechanisms in complex four-dimensional cardiovascular flows, in recent years a large number of hemodynamic parameters have surfaced in the literature, enabling the understanding of arterial hemodynamics and of the role of streaming blood in the development of pathological events. Here, a survey of recently proposed methods to characterize in! travascular fluid structures in arteries, in particular helical flow, is presented and their relationship with (1) widely adopted disturbed shear indicators as well as (2) emerging indicators of the relevance of wall shear stress multidirectionality in the distribution of vascular lesions, are discussed together with open questions on their clinical utility.

contact: christian.vergara@polimi.it

21 Ottobre, 2015 14:00

MOX Seminar

Optimized Schwarz methods for cilindrical interfaces

Christian Vergara, Politecnico di Milano Dipartimento di Matematica-MOX

Aula Semnari Saleri VI piano MOX - Dipartimento di Matematica Politecnico di Milano

abstract

abstract

We propose a unified convergence analysis of the generalized Schwarz method applied to a linear elliptic problem for a general interface (flat, cylindrical or spherical) in any dimension. In particular, we provide the exact convergence set of the interface symbols related to the operators involved in the transmission conditions. We also provide a general procedure to obtain estimates of the optimized interface symbols within the constants. We apply such general results to a simple fluid–structure
interaction model problem given by the interaction between an incompressible, inviscid
fluid and the wave equation, in the case of cylindrical interfaces.
Finally, we assess the effectiveness of the theoretical findings through three-dimensional numerical experiments in the haemodynamic context,obtained by solving the coupling between the Navier–Stokes equations and the linear infinitesimal elasticity.

contact: christian.vergara@polimi.it