28 Febbraio, 2018 16:30

Seminario Matematico e Fisico di Milano

How to eliminate\control flutter arising in flow structure interactions

Irena Lasiecka, University of Memphis

Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9

23 Febbraio, 2018 10:30 oclock

Seminario Matematico e Fisico di Milano

Sobolev and BV functions in infinite dimension

Alessandra Lunardi, Università di Parma

Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9

abstract

abstract

In Hilbert or Banach spaces $X$ endowed with a good probability measure $\mu$ there are a few "natural" definitions of Sobolev spaces and of spaces of bounded variation functions. The available theory deals mainly with Gaussian measures and Sobolev and BV functions defined in the whole $X$, while the study and Sobolev and BV spaces in domains, and/or with respect to non Gaussian measures, is largely to be developed.
As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular for PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an
infinite number of degrees of freedom, and in stochastic PDEs through Kolmogorov equations.
In this talk I will describe some of the main features and open problems concerning such function spaces.

22 Febbraio, 2018 14:00

MOX Colloquia

Models, Simulation, Uncertainty, and Medicine - Numerical Methods in Computational Biomechanics and Cardiology

Rolf Krause, Center for Computational Medicine in Cardiology, Università della Svizzera italiana,

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

The numerical simulation of physiological and biomechanics processes allows for a better understanding of many internal mechanism of the human body. For example stresses in joints or the activation sequence of the human heart can be computed “in silico”, thus providing the possibility to develop new therapies or to assist physician in diagnosis and therapy. In order to get close to realistic medical applications, or even to a clinical setting, several difficulties have to be addressed. These contain the efficient simulation of coupled and non-linear partial differential equations, the choice of the appropriate models, and, last but not least, the personalization of the simulation by means of, e.g., parameter fitting or uncertainty quantification. In this talk, we give an overview in numerical techniques in biomechanics and cardiology, including contact problems, the electro-mechanical activation of the human heart, and fluid-structure interaction in heart valves.

Contact: christian.vergara@polimi.it

Rolf Krause has has studied Mathematics in Berlin and did his PhD in Stuttgart and Berlin. In 2003, he became Professor for Scientific Computing at the University of Bonn and moved in 2009 to USI in Lugano as founding director of the ICS, the Institute of Computational Science of USI. He is working in the areas finite element methods, non-linear domain decomposition and multigrid methods, and parallel in time methods, with applications in geo-mechanics, cardiac and biomechanics.

21 Febbraio, 2018 15:15

Sezione di Analisi

Poincaré-Sobolev Inequalities and the p-Laplacian

Scott Rodney, Cape Breton University

Aula seminari 3° piano

abstract

abstract

It is well known that Poincar\'e-Sobolev inequalities play an important role in applications and in regularity theory for weak solutions of PDEs. In this talk I will discuss two new results connecting matrix weighted Poincar\'e-Sobolev estimates to the existence of regular weak solutions of Dirichlet and Neumann problems for a degenerate $p$-Laplacian:
\begin{eqnarray}
\Delta_{Q,p} \varphi(x) = \textrm{Div}\left(\big|Q(x)~\nabla \varphi(x)\big|^{p-2}~Q(x)~\nabla\varphi(x)\right).\nonumber
\end{eqnarray}
Degeneracy of $\Delta_{Q,p}$ is given by a measurable non-negative definite matrix-valued function $Q(x)$.

Rolf Krause has has studied Mathematics in Berlin and did his PhD in Stuttgart and Berlin. In 2003, he became Professor for Scientific Computing at the University of Bonn and moved in 2009 to USI in Lugano as founding director of the ICS, the Institute of Computational Science of USI. He is working in the areas finite element methods, non-linear domain decomposition and multigrid methods, and parallel in time methods, with applications in geo-mechanics, cardiac and biomechanics.

21 Febbraio, 2018 10:00

MOX Seminar

Numerical modelling of elliptic problems on octree-based meshes

Alice Raeli, IMAG Institut Montpelliérain Alexander Grothendiec, Montpellier

Aula Saleri VI Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The gradient of the solution can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure.Numerical illustrations are presented in two and three-dimensional configurations. Future perspectives will include the use of Hybrid High-Order methods to increase the approximation order.

Contact: luca.formaggia@polimi.it

Rolf Krause has has studied Mathematics in Berlin and did his PhD in Stuttgart and Berlin. In 2003, he became Professor for Scientific Computing at the University of Bonn and moved in 2009 to USI in Lugano as founding director of the ICS, the Institute of Computational Science of USI. He is working in the areas finite element methods, non-linear domain decomposition and multigrid methods, and parallel in time methods, with applications in geo-mechanics, cardiac and biomechanics.

20 Febbraio, 2018 12:15 oclock

Sezione di Finanza Quantitativa

Realized Peaks over Threshold: a Time-Varying Extreme Value Approach with High-Frequency based Measures

Luca Trapin, Scuola Normale Superiore

Aula seminari terzo piano

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The gradient of the solution can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure.Numerical illustrations are presented in two and three-dimensional configurations. Future perspectives will include the use of Hybrid High-Order methods to increase the approximation order.

Contact: luca.formaggia@polimi.it

Rolf Krause has has studied Mathematics in Berlin and did his PhD in Stuttgart and Berlin. In 2003, he became Professor for Scientific Computing at the University of Bonn and moved in 2009 to USI in Lugano as founding director of the ICS, the Institute of Computational Science of USI. He is working in the areas finite element methods, non-linear domain decomposition and multigrid methods, and parallel in time methods, with applications in geo-mechanics, cardiac and biomechanics.

19 Febbraio, 2018 14:00

MOX Seminar

Elastic Contact in Fluid-structure Interactions

Thomas Richter, Universität Magdeburg

Aula Saleri VI Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

In this talk we address the following fundamental question: what happens if an elastic ball is falling in a container with a viscous fluid towards a rigid wall on the bottom? Will it come to contact? Or will there always remain a thin fluid film between wall and bottom? Will the ball bounce off? Or will the ball come to rest and stick? We start by giving an overview on various results on this topic, computationally, analytically and experimentally. Then in a second part we numerically investigate this challenging problem.

The possible contact between ball and boundary is a fundamental difficulty for established discretization schemes as it involves topology changes in the domain. For describing the interaction problem between elastic solid and fluid we shortly introduce the ALE approach and discuss its shortcomings in terms of modeling contact. Then, we introduce an alternative Eulerian approach that is well suited for contact problems. This Eulerian approach however brings along new difficulties with respect to discretization.

Contact: christian.vergara@polimi.it

Rolf Krause has has studied Mathematics in Berlin and did his PhD in Stuttgart and Berlin. In 2003, he became Professor for Scientific Computing at the University of Bonn and moved in 2009 to USI in Lugano as founding director of the ICS, the Institute of Computational Science of USI. He is working in the areas finite element methods, non-linear domain decomposition and multigrid methods, and parallel in time methods, with applications in geo-mechanics, cardiac and biomechanics.

15 Febbraio, 2018 14:00

MOX Colloquia

Understanding Heart Tissue through Waves

D. Nordsletten, Biomedical Engineering Department, King’s College, London

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

Personalised models of cardiac mechanics have evolved into a powerful tool for studying the human heart in health and disease. Combining detailed information on the heart kinematics extracted from medical images, with mathematical models of cardiac function, patient-specific models provide a mathematical representation of individual hearts. As model parameters are linked to intrinsic tissue properties such as stiffness and contractility, unique and accurate parameter estimates are a prerequisite for the potential translation of personalised models to the clinic.

In parallel, magnetic resonance elastography (MRE) has evolved into a powerful tool for interrogating material stiffness. MRE has been exploited in the liver, breast, and brain using measured periodic waves to extract material stiffness properties. Transducing waves via external vibrations, MRE provides a more direct measure of the characteristics of tissues and their potential diseases. Integrating this work into the heart is complicated by a myriad of challenges including the inherent cardiac motion of the heart, evolving material properties due to the contractile state of the muscle, and the nonlinear effects of deformation on the apparent stiffness of the material.

In this talk, we discuss the merger of these two worlds, bridging between the nearly quasi-static model-based assessment of heart function and the high frequency wave-based assessment. In particular, we discuss the simple influence of deformation on apparent stiffness, explaining both from the realm of traditional wave mechanics and biomechanical theory.

Contact: christian.vergara@polimi.it


This seminar is organized within the Research project «An Integrated Heart Model for the simulation of the cardiac function - iHEART» Grant Agreement number 740132, funded by ERC (2016-ADG). Principal investigator: Prof. Alfio Maria Quarteroni

David Nordsletten is a Senior Lecturer at King's College London in the Division of Biomedical Engineering and Imaging Sciences. He graduated with a DPhil in Computer Science and Biomedical Engineering from the University of Oxford.

13 Febbraio, 2018 14:30 oclock

Sezione di Probabilità Quantistica

Macroscopic quantum systems & Measuring apparatuses

Caterina Foti, Università degli Studi di Firenze

Aula Seminari III piano

abstract

abstract

The emergence of classicality is the mechanism that makes us to observe a classical reality despite the fundamental laws of physics being quantum.
Apart from the neverending diatribe between different interpretations of Quantum Mechanics, what can be considered more or less accepted is that we experience a classical reality due to the continuos interaction between each microscopic component of any physical system and its environment, that can be regarded as the measuring apparatus and must be macroscopic since it contains us as observers. Among the various approaches proposed over the years by different authors to deal with the "quantum-to-classical" crossover, a useful tool is provided by the general method introduced by L. G. Yaffe in 1982 for finding the classical limits as large-N limits of arbitrary quantum theories with N dynamical variables. Such method isolates the minimal structure that any quantum theory should possess in order to have a classical limit. By using Yaffe's results in the framework of open quantum systems dynamics, one can show that whenever quantum environments have a sensible large-N limit, they evolve as if they were the same measuring apparatus in the classical limit.

David Nordsletten is a Senior Lecturer at King's College London in the Division of Biomedical Engineering and Imaging Sciences. He graduated with a DPhil in Computer Science and Biomedical Engineering from the University of Oxford.

8 Febbraio, 2018 14:00

MOX Colloquia

Regularization Theory and Applications to Photoacoustic Imaging

Otmar Scherzer, University of Vienna and Radon Institute of Computational and Applied Mathematics (Linz), Austria

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

In this talk we review recent results on regularization theory of variational regularization methods, such as Tikhonov regularization, which consists in finding the optimizer of a least functional which is perturbed by a convex functional. In particular we are reviewing new convergence rates results for solving Inverse Problemsin Hilbert Spaces.
Particular emphasize will be given to analyze and interpret the abstract results for photoacoustic imaging and inversion of the spherical mean operator.

Contact: elena.beretta@polimi.it

Otmar Scherzer received his PhD and Habilitation from the University of Linz (Austria) in 1990, 1995, respectively. He was a postdoc researcher at Texas A&M University and the University of Delaware. He held professorships at the Ludwig Maximilian University Munich, University of Bayreuth, University of Innsbruck before he became professor at the University of Vienna, where he is now the head of the Computational Science Center. In addition he is research group leader of the ``Imaging and Inverse Problems Group’’ of the Radon Institute of Computational and Applied Mathematics (RICAM) in Linz, which is an institute of the Austrian Academy of Sciences. Otmar Scherzer is an expert in regularization theory and mathematical imaging. He has about 200 publications in leading journals in these fields and is editor of about 10 journals and book series, including SIAM J. imaging Sciences. Moreover, he published two monographs, and edited several books, including the Handbook of Mathematical Imaging in three volumes. In 1991 he received the Theodor Körner Prize, the Prize of the Austrian Mathematical Society, the science prize of Tyrol, and in 1999 the START-prize of the Austrian Science Foundation, which is the highest award for young Austrian scientists in Austria. From 2010 to 2017 he has been Vice-president of the Inverse Problems International Association IPIA.