Dipartimento di Matematica – Politecnico di Milano

Prossimi Seminari

Models of living tissues, incompressible limit and free boundary
Benoit Perthame, Laboratoire J.-L. Lions, Université Pierre et Marie Curie, Paris
giovedì 28 settembre 2017 alle ore 11:15, Aula Consiglio VII Piano, Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

Tissue growth, as in solid tumors, can be described at a number of different scales from the individual cell to the organ. For a large number of cells, the ‘fluid mechanical’ approach has been advocated recently by many authors in mathematics, physics and biomecanics. Several levels of mathematical descriptions are commonly used, including elastic or visco-elastic effects, nutrients, active movement, surrounding tissue, vasculature remodeling and several other features.
We will focus on the links between two types of mathematical models. The `compressible’ description is at he cell population density level and a more macroscopic, description is based on a free boundary problem close to the classical Hele-Shaw equation. Asymptotic analysis is a tool to derive these Hele-Shaw free boundary problems from cell density systems in the stiff pressure limit. This modeling also opens other questions as circumstances in which instabilities develop and questions on the regularity of the interface between heathy and cancerous tissues.
This presentation follows collaborations with F. Quiros and J.-L. Vazquez (Universidad Autonoma Madrid), M. Tang (SJTU), N. Vauchelet (LJLL), A. Mellet (College Park), A. Lorz (LJLL) and T. Lorenzi (St Andrews).

contact: pasquale.ciarletta@polimi.it
On multi-curve models for the term structure of interest rates
Wolfgang J. Runggaldier, Università degli Studi di Padova
martedì 3 ottobre 2017 alle ore 14:00 precise, Seminar Room (6th Floor)
ABSTRACT

ABSTRACT

We discuss multi-curve extensions of classical short rate models, whereby the multi-curve quantities are obtained by adding a spread over the corresponding one-curve quantities. In particular, we consider factor-driven models for the short rate and the spreads, where the factors are of the exponentially quadratic class. For these models we furthermore discuss pricing of linear and optional derivatives (based on joint work with Zorana Grbac and Laura Meneghello).
Stabilized methods and inf-sup conditions
Tomas Chacon Rebollo, Instituto de Matematicas, Universidad de Sevilla
mercoledì 4 ottobre 2017 alle ore 14:00, Aula Seminari “F. Saleri”, MOX
ABSTRACT

ABSTRACT

Stabilized methods provide a procedure to stabilize the various sources of instabilities that arise in the numerical simulation of incompressible fluid flows with reduced computational cost. It consists in adding to the standard Galerkin formulation specific terms aiming at stabilizing the possible sources of instabilities (convection dominance, pressure discretization,…). We shall describe an analysis technique for Navier-Stokes equations, in which the stability of the pressure discretization is based upon the existence of an underlying inf-sup condition between an augmented velocity space and the pressure space. We will next apply this kind of techniques to the discretization of the Primitive Equations of the Ocean. We will end by presenting an application to reduced-order modeling of turbulence.
Contatto: luca.bonaventura@polimi.it
Il test del DNA per l’identificazione criminale: dalla biologia al calcolo delle probabilità
Marco Bramanti e dott. Giorgio Portera, Dipartimento di Matematica, Politecnico di Milano
mercoledì 4 ottobre 2017 alle ore 15:00, Aula Consiglio, 7° piano, edificio Nave, via Bonardi, 9 – Milano
Use of Routine Databases in the Design and Analysis of Surgical Trials
Linda Sharples, London School of Hygiene and Tropical Medicine
giovedì 5 ottobre 2017 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

A number of features of surgical interventions make their evaluation in randomised trials more difficult. For example, new procedures may be technically difficult to deliver so that surgical performance takes time to stabilise and outcomes may vary over time and between different surgeons. Moreover, there is a lack of trials culture among surgeons, so that efficient designs that are acceptable to the community are required. This talk will review some of the practical and technical issues involved in evaluations of surgical interventions, focusing on our work on the use of routine databases to explore learning curves, clustering between surgeons and the multiple component nature of the interventions. Some implications for design and analysis will be discussed and the limitations will be illustrated through the AMAZE trial in cardiac surgery patients who have a history of atrial fibrillation (irregular heart rhythm).

Contact: francesca.ieva@polimi.it
Spiralling solutions in limiting profiles of competition-diffusion systems
Susanna Terracini, Università di Torino
venerdì 6 ottobre 2017 alle ore 14:30 precise, Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9
Tettonica delle placche polarizzata e terremoti
Carlo Doglioni, Dipartimento di Scienze della Terra, Università La Sapienza, Roma
martedì 17 ottobre 2017 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

La tettonica delle placche e? il combinato di effetti secolari quali il raffreddamento della Terra e la dinamica astronomica. Quest’ultima appare il modulatore dei meccanismi e causa della polarizzazione del sistema caotico e auto-organizzato della geodinamica. Fenomeni di lungo periodo sia interni che esterni al pianeta determinano una deformazione stazionaria, intervallata da eventi semi-istantanei. Entrambe le tipologie di fenomeni rappresentano il rilascio di energia in zone dove si crea un gradiente, sia esso di pressione o temperatura. I margini di placca rappresentano l’espressione di gradienti di velocita? tra le placche, controllati da gradienti di viscosita? nel canale a bassa velocita? alla base della litosfera, a loro volta controllati da variazioni laterali della composizione chimica del mantello. Il canale a bassa velocita? e? il piano di scollamento fondamentale della tettonica delle placche e appare come la sede principale di sviluppo del magmatismo terrestre. La cinematica delle placche che possiamo ricostruire e? fortemente vincolata dalla profondita? del magmatismo. La parte pellicolare della litosfera, caratterizzata da una reologia fragile per fenomeni di alta frequenza, rilascia energia gravitazionale negli ambienti tettonici estensionali (gravimoti) e invece elastica negli ambienti trascorrenti e compressivi EelastomotiI. L’energia si accumula in volumi di crosta superiore e le faglie non sono altro che le guide d’onda lungo cui una parte di questa energia viene incanalata dai volumi e dissipata in forma elastica durante un terremoto.

Contact: edie.miglio@polimi.it
SPECTRAL THEORY, SUM RULES AND LARGE DEVIATIONS
Barry Simon, California Institute of Technology
lunedì 30 ottobre 2017 alle ore 16:30, Aula Chisini, via Saldini 50
RANDOMNESS IN PARTIAL DIFFERENTIAL EQUATIONS
Felix Otto, Max Plank Institute, Leipzig
lunedì 20 novembre 2017 alle ore 16:30, Aula Chisini, via Saldini 50
Multi-scale and multi-physics modeling of complex flow and transport processes for energy storage in the subsurface
Rainer Helmig, Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart
giovedì 23 novembre 2017 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

The subsurface is being increasingly utilised both as a resource and as an energy and waste repository. Historically, there have been few issues of concern related to competition between resources, with groundwater contamination being a notable exception. However, with increasing exploitation, resource conflicts are becoming increasingly common and complex. Current issues in this regard include, for example, the long-range impact of mechanical, chemical and thermal energy storage on groundwater resources, and the complex effects surrounding hydraulic fracturing in both geothermal and shale gas production.
To analyse and predict the mutual influence of subsurface projects and their impact on groundwater reservoirs, advanced numerical models are necessary. In general, these subsurface systems include processes of varying complexity occurring in different parts of the domain of interest. These processes mostly take place on different spatial and temporal scales. It is extremely challenging to model such systems in an adequate way, accounting for the spatially varying and scale-dependent character of these processes.
In this seminar, we will give an overview of possible utilisation conflicts in subsurface systems and of how the groundwater is affected and review several model coupling concepts with a focus on the lecturer’s work in this field. The concepts are divided into temporal and spatial coupling concepts, where the latter are sub-divided into multi-process, multi-scale, multi-dimensional, and multi-compartment coupling strategies. We will present a large-scale simulation showing the general applicability of the modelling concepts of such complicated natural systems, especially the impact on the groundwater of simultaneously using geothermal energy and storing chemical and thermal energy. At the same time, we will show that such real large-scale systems provide a good environment for balancing the efficiency potential and possible weaknesses of the approaches discussed.

Contact: anna.scotti@polimi.it
Numerical simulations of non-ideal compressible-fluid flows
Alberto Guardone, Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano
giovedì 30 novembre 2017 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

In the close proximity of the liquid-vapour saturation curve and critical point, well-known thermodynamic phenomena including large compressibility and critical point effects results in very unusual fluid dynamics features, including non-ideal or rarefaction shock waves, mixed and split waves. This unconventional behaviour, which cannot occur in the ideal flow of dilute gases, is referred to as Non-Ideal Compressible-Fluid Dynamics or NICFD. The focus of this short lecture is to review the theoretical background of NICFD and to discuss the impact of highly non-ideal conditions on the design and properties of numerical schemes for compressible flows. Exemplary flow fields will be presented and compared to available experimental data from the Test-Rig for Organic VApours (TROVA) of Politecnico di Milano, a unique facility in which supersonic flows in non-ideal conditions can be measured and observed. The present results are obtained within the framework of the ERC Consolidator Grant NSHOCK, of which the presenter is the PI.

contact: nicola.parolini@polimi.it
Five Decades of Time Parallel Time Integration: Best Current Methods for Parabolic and Hyperbolic Problems
Martin Gander, Section de Mathématiques, Université de Geneve
giovedì 14 dicembre 2017 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

Time parallel time integration methods have received renewed interest over the last decade because of the advent of massively parallel computers, due to the clock speed limit reached on today’s processors. When solving time dependent partial differential equations, the time direction is usually not used for parallelization. But when parallelization in space saturates, the time direction offers itself as a further direction for parallelization. The time direction is however special, and for evolution problems there is a causality principle: the solution later in time is determined by the solution earlier in time, so the flow of information is just into the direction forward in time. Algorithms trying to use the time direction for parallelization must therefore be special, and take this very different property of the time dimension into account.

I will show in this talk how time parallel time integration methods were invented over the past five decades, and give a classification into four different groups: methods based on multiple shooting,
space-time multigrid methods, methods based on domain decomposition and waveform relaxation, and direct time parallel methods. The performance of these methods depends on the nature of the underlying evolution problem, and it turns out that for the first two classes of methods, time parallelization is only really possible for parabolic problems, while the last two classes can also be used to parallelize
hyperbolic problems in time. I will also explain in more detail one of the methods from each class: the parareal algorithm and a space-time multigrid method, which are currently among the most promising methods for parabolic problems, and a Schwarz waveform relaxation method related to tent-pitching and a direct time parallel method based on diagonalization of the time stepping matrix, which are very effective for hyperbolic problems.

Contact: marco.verani@polimi.it
Combining in vitro and in silico approaches towards patient-specific cardiovascular investigations
Gabriele Dubini, Department of Chemistry, Materials and Chemical Engineering G. Natta, Politecnico di Milano
giovedì 18 gennaio 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

This seminar will outline the workflow developed at the Laboratory of Biological Structure Mechanics – LaBS, Politecnico di Milano. (www.labsmech.polimi.it) for the investigation of cardiovascular devices. The combined in vitro and in silico approach will be applied to the study of stenting procedures of peripheral arteries in idealized and patient-specific models as well as to the study of percutaneous aortic valves, where fluid-structure interaction simulations are required. Such examples will demonstrate the extent to which performances of minimally-invasive devices are related to their design, the materials and the applied loads.

contact: christian.vergara@polimi.it
Understanding Heart Tissue through Waves
D. Nordsletten, Biomedical Engineering Department, King’s College, London
giovedì 15 febbraio 2018 alle ore 14:00, 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
TBA
Rolf Krause, Center for Computational Medicine in Cardiology, Università della Svizzera italiana,
giovedì 22 febbraio 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

TBA

Contact: christian.vergara@polimi.it

Seminari Matematici Politecnico di Milano

Seminari Matematici Milano e dintorni

Archivio Seminari

Large-scale simulations with unfitted finite element techniques
Santiago Badia, Universitat Politècnica de Catalunya, Barcelona
giovedì 14 settembre 2017 alle ore 11:30, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
The use of unfitted finite element methods (FEMs) is an appealing approach for different reasons. They are interesting in coupled problems or to avoid the generation of body-fitted meshes. One of the bottlenecks of the simulation pipeline is the body-fitted mesh generation step and the unstructured mesh partition. The use of unfitted methods on background octree Cartesian meshes avoids the need to define body-fitted meshes, and can exploit efficient and scalable space-filling curve algorithms. In turn, such schemes complicate the numerical integration, imposition of Dirichlet boundary conditions, and the linear solver phase. The condition number of the resulting linear system does depend on the characteristic size of the cut elements, the so-called small cut cell problem.
In this work, we will present an parallel unfitted framework that relies on adaptive octree background meshes and space-filling curve partitioners. In order to solve the small cut cell problem, we will pursue two different lines. The first one is a re-definition of the finite element spaces that solves this issue, leading to condition number bounds as the ones for body-fitted schemes without any kind of perturbation/stabilization of the Galerkin formulation. Another approach will be to define appropriate iterative linear solvers based on domain decomposition preconditioning that are robust with respect to the small cut cell problem.
We will briefly present the linear solver machinery within out framework, based on highly scalable multilevel domain decomposition methods for the simulation of large scale finite element problems. Our motivation here is not only to show the excellent scalability results of the preconditioners resulting from the framework, but also to present its customization to challenging applications, e.g., space-time parallelism and heterogeneous problems. Finally, its application to challenging engineering problems, e.g., the simulation of superconductor devices or additive manufacturing will be considered.
Contatto: christian.vergara@polimi.it

contact:christian.vergara@polimi.it
ABSTRACT
The theory of quantum statistical comparison with some applications to quantum information science
Francesco Buscemi, Nagoya University
martedì 12 settembre 2017 alle ore 15:00, Aula Seminari III piano
ABSTRACT
In mathematical statistics a central role is played by the notion of statistical models (or, equivalently, statistical experiments). These objects, which can be imagined as families of probability distributions, are often used to describe the statistician’s state of knowledge about an unknown parameter. It is then natural to compare statistical models on the basis of their “information content.” This kind of problems led in the 1950s to the formulation of a whole new theory, sometimes named “statistical comparison theory,” which soon developed into a very deep field with many applications, ranging from mathematical statistics, to physics and economics. In this lecture I will present an overview of the basic ideas of statistical comparison, some possible generalizations to the quantum setting, and a few applications in quantum thermodynamics, entanglement theory, quantum measurement theory, and the theory of open quantum systems.
ABSTRACT
Modelling cell movement: from tissue organisation to disease
Kevin Painter, Heriot-Watt University, Edinburgh, UK
lunedì 4 settembre 2017 alle ore 14:30, Aula Seminari III piano
ABSTRACT
Cells move and position themselves according to various environmental cues, ranging from short range adhesive and repulsive interactions with other cells to long range guided responses due to chemicals.Cells move and position themselves according to various environmental cues, ranging from short range adhesive and repulsive interactions with other cells to long range guided responses due to chemicals. In this talk I will describe the modelling of these fundamental processes from both the individual and continuous scale, and discuss their application in areas ranging from developmental biology to cancer invasion. Along the way I will discuss the numerous modelling, numerical and analytical challenges posed. In this talk I will describe the modelling of these fundamental processes from both the individual and continuous scale, and discuss their application in areas ranging from developmental biology to cancer invasion. Along the way I will discuss the numerous modelling, numerical and analytical challenges posed.
ABSTRACT
Multivariate Splines and Their Applications
Ming-Jun Lai, Dept. of Math. University of Georgia, Athens, GA, USA
giovedì 20 luglio 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT
Multivariate splines are piecewise polynomial or rational functions over a collection of polygons. We shall explain some approximation properties of these splines and construction of locally supported basis functions. Then I will explain how to use them for numerical solution of linear and nonlinear partial differential equations and data fitting for statistical analysis. Our approach is based on barycentric coordinates (BB form) and generalized barycentric coordinates (GBC). The smoothness conditions, boundary conditions or interpolatory conditions will be set up as linear constraints when we minimize energy functional associated with the PDE to be solved or data to be fitted. Our approach enables us to use higher order polynomials and the smoothness higher than continuity easily. Several numerical examples of PDE and data fitting will be shown.
ABSTRACT
Doubly nonlocal Cahn-Hilliard equations
Ciprian G. Gal, Florida International University, Miami, USA
venerdì 14 luglio 2017 alle ore 11:00, Aula seminari 3° piano
ABSTRACT
We consider a doubly nonlocal nonlinear parabolic equation
which describes phase-segregation of a two-component material in a
bounded domain. This model is a more general version than the recent
nonlocal Cahn–Hilliard equation proposed by Giacomin and Lebowitz,
such that it reduces to the latter under certain conditions. It turns
out that there are four possible cases of double interaction in which
the nonlocality is reflected, we shall discuss some of them.
ABSTRACT
A Three-Field Formulation for Poroelasticity
Ricardo Ruiz Baier, Mathematical Institute, University of Oxford
mercoledì 12 luglio 2017 alle ore 11:30, MOX, Aula Saleri, Dipartimento di Matematica, VI piano
ABSTRACT
In this talk we present a stable and convergent conforming finite element method for the discretisation of the linear poroelasticity equations in a new formulation, where the volumetric contributions to the total stress are merged into an additional unknown. The resulting saddle point formulation can be analysed by means of a Fredholm alternative, after realizing that the problem is a compact perturbation of a Stokes-like invertible system. A generic Galerkin scheme is constructed, whose solvability properties follow closely those from the continuous variational form, and more importantly, given that specific finite dimensional spaces are chosen adequately, it is stable even in the incompressible limit.
Contatto: luca.formaggia@polimi.it
ABSTRACT
Quantum Markov Chains and Associated Open Quantum Random Walks
Ameur Dhahri, Chungbuk National University
martedì 11 luglio 2017 alle ore 14:00 precise, Aula Seminari III piano
ABSTRACT
We establish the connection between Open Quantum Random Walks and the Quantum Markov Chains. In particular, we construct tow kinds of Quantum Markov Chains associated with Open Quantum Random Walks. Finally, we study the recurrence, transience and the property of accessibility associated to these Quantum Markov Chains.
ABSTRACT
Glauber Dynamics on the Cycles: Spectral Distribution of the Generator
Hyun Jae Yoo, Hankyong National University
martedì 11 luglio 2017 alle ore 15:00 precise, Aula Seminari III piano
ABSTRACT
We consider Glauber dynamics on finite cycles. By introducing a vacuum state we consider an algebraic probability space for the generator of the dynamics. We obtain a quantum decomposition of the generator and construct an interacting Fock space. As a result we obtain a distribution of the generator in the vacuum state.

We also discuss the monotonicity of the moments of spectral measure as the couplings increase.

In particular, when the couplings are assumed to be uniform, as the cycle grows to an infinite chain, we show that the distribution (under suitable dilation and translation) converges to a Kesten distribution.
ABSTRACT