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

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

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

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

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

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

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

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

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

Abstract

TBA


Contact: christian.vergara@polimi.it