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«ABSTRACTS Scientific Committee David Arcoya Universidad de Granada, Spain Blanca Ayuso de Dios Centre de Recerca Matematica (CRM), Spain Nicola ...»

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SIMAI 2010

10th CONGRESS of SIMAI

ITALIAN SOCIETY for

APPLIED and INDUSTRIAL MATHEMATICS

in cooperation with

SEMA, Spanish Society for Applied Mathematics

Cagliari, June 21-25, 2010

ABSTRACTS

Scientific Committee

David Arcoya Universidad de Granada, Spain

Blanca Ayuso de Dios Centre de Recerca Matematica (CRM), Spain

Nicola Bellomo Politecnico di Torino, Italy

Michiel Bertsch CNR IAC, Roma, Italy Juan Casado Universidad de Sevilla, Spain Rosa Donat Universidad de Valencia, Spain Antonio Fasano Universit` di Firenze, Italy a Giorgio Fotia CRS4 Bioinformatica, Pula (Cagliari), Italy Alfio Quarteroni EPFL Lausanne and Politecnico di Milano, Italy Carlos V´zquez a Universidad de La Coru˜a, Spain n Organizing Committee Antonio Cazzani Universit` di Cagliari, Italy, a Alessandro Chessa Universit` di Cagliari, Italy a Gianmauro Cuccuru CRS4 Bioinformatica, Pula (Cagliari), Italy Elena De Angelis Politecnico di Torino, Italy Giorgio Fotia CRS4 Bioinformatica, Pula (Cagliari), Italy Chairman Roberto Natalini CNR IAC, Roma, Italy Simona Perotto Politecnico di Milano, Italy Luigia Puccio Universit` di Messina, Italy a Sebastiano Seatzu Universit` di Cagliari, Italy a

INVITED LECTURES

Luca Formaggia MOX Politecnico di Milano Numerical models for geological evolution Carlo Par´s e Universidad de Malaga

Numerical approximation of nonconservative hyperbolic systems:

applications and difficulties Benedetto Piccoli IAC, CNR, Roma From vehicular traffic to pedestrian motions and animal groups Luigi Preziosi Politecnico di Torino Multiphase and multiscale aspects of cancer modelling Peregrina Quintela Universidade de Santiago de Compostela Numerical simulation of nonsmooth mathematical models Anna Tramontano Sapienza University No protein is an island Juan Luis V´zquez a Universidad Autonoma de Madrid Porous medium ow with fractional diffusion Enrike Zuazua BCAM Basque Center for Applied Mathematics Waves and Numerics Invited Lectures 7 Numerical models for geological evolution Luca Formaggia

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The study of the evolution at geological scales is very important for oil exploration and exploitation, as well as for the study of the safety of sites for nuclear waste or CO2 sequestration. We here focus most on the first application, illustrating models for the evolution of sedimentary basins. A related aspect that we consider is the study of oil formation and expulsion. We will illustrate the main mathematical and numerical issues and present some numerical results.

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The design of high-order well-balanced shock-capturing numerical methods for nonconservative hyperbolic systems is a very active front of research, as PDE systems of this nature arises in many flow models. The approximated solutions are expected to be consistent with the physics of the real flows to be simulated: in particular (1) they should satisfy the conservation properties prescribed by the physics of the problem and (2) their discontinuities should satisfy some jump conditions consistent with the real phenomena to be simulated. In this presentation the difficulties related to the design of numerical schemes satisfying these two requirements will be discussed. Finally, some applications to real flows will be shown.

8 Invited Lectures

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The talk will be divided in two parts. In the first we illustrate some results of last five years for fluid dynamic modeling of vehicular traffic. In particular, focusing on conservation laws on graphs and data from mobile sensors. In the second part, looking at vehicular traffic from microscopic point of view, and thinking of it as a group of intelligent agents, we introduce a multiscale model using time evolving mesaures. The latter allows applications also to pedestrian motions and animal groups.

Multiphase and multiscale aspects of cancer modelling

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Resorting to a multiphase modelling framework, the lecture will be devoted to the description of some mechanical aspects influencing tumour growth. The starting point is the description of tumours as a mixture of tumour and host cells living in a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. Mechanical aspect can then play a role in the definition of the growth term and in the interactions of the growing tumour with the host tissue, and in the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental results at a cellular level, it is proposed that at a macroscopic level there exists a yield condition separating the elastic and dissipative regimes and determining when the cells stick to the ECM or move relatively to it. A method to upscale the microscopic information to the macroscopic scale is proposed. With a similar aim other multiscale aspects related to the need to insert particular signalling pathways in the model are dealt with.

Invited Lectures 9 Numerical simulation of nonsmooth mathematical models

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This talk reports joint work with M.T. Cao, C. Moreno and J. Paredes. Frequently, due to the coexistence of various materials, the irregularity of geometry, or discontinuities in data, nonsmooth models involving partial differential equations arise in the mathematical





modeling of problems in mechanics. We show two applications:

• in fluid mechanics, the numerical simulation of the motion of a gas bubble immersed in a liquid considering the surface tension effects. Using an Eulerian methodology to simulate the transport of the bubble, we propose a velocity–pressure mixed formulation to solve the hydrodynamic equations. When there is a severe discontinuity in the interface, the finite element space is enriched on the elements being cut by the interface.

• in Civil Engineering, it is of great interest the behavior of structures with discontinuous displacements and singular stresses coming from a cracked surface, in particular, when is submitted to non destructive tests by Rayleigh waves. The FEM is enriched by incorporating discontinuous functions near the crack border and the two–dimensional asymptotic displacement fields close to the tip.

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Life is brought about by a complex set of coordinated functions. Biology has gained an almost complete knowledge of the genetic material encoding for the components of many living organisms, and faces the unprecedented challenge to identify the encoded molecules and unravel their molecular and cellular function. However, after almost ten years of efforts, the number of genes in the human genome has not yet been established.

To make matters more complex, biological macromolecules interact and their physical and/or logical associations regulate nearly every living process. Determining the identity of the parts list of a living organism and their assembly instructions is a daunting challenge that will keep scientists busy for all this century and probably a good fraction of the next one. I will discuss the computational methods and strategies that can be used to face these challenges at a ”systems” level using interdisciplinary multi-layered approaches.

10 Invited Lectures

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We study a model for flow in porous media including nonlocal (long-range) diffusion effects. It is based on Darcy’s law and the pressure is related to the density by an inverse fractional Laplacian operator. We prove existence of solutions that propagate with finite speed, which is unexpected in fractional diffusion models. The model has also the very interesting property that mass-preserving selfsimilar solutions can be found by solving an elliptic obstacle problem with fractional Laplacian for the pair pressure-density. We use entropy methods to show that the asymptotic behaviour is describedafter rescaling by these solutions which play the role of the Barenblatt profiles of the standard porous medium model. Other related models will be presented.

This is a joint project with Luis Caffarelli, Univ. of Texas

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In this lecture we shall present some surprising numerical effects appearing when dealing with the numerical approximation of wave phenomena. These two issues, waves and numerics, enter and play a critical role in a number of relevant problems and applications including aeronautical optimal shape design, water waves, elastic structures, quantum dots, etc.

As we shall see, high frequency spurious numerical solutions may behave in an expected manner being compatible with the standard convergence analysis and properties of numerical schemes. The understanding of these issues requires of the combination of new tools combining Microlocal Analysis and classical numerical analysis. Some experiments and new analytical results will be provided making rigorous several asymptotic ansatzs.

FSP - Fausto Saleri 2008 Prize Recipient Lecture 11

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In this talk we present the mathematical modelling and the numerical simulation of the polymer extrusion process and its application to (hollow and non-hollow) synthetic yarns manufacturing. A crucial point in the extrusion process is that a non-Newtonian viscoelastic fluid (as the polymer melt) undergoes an increase in its cross-section when it is forced out of a die (a specialized tool in manufacturing to shape polymeric materials) into air. Such a phenomenon is known as “die swell ”. The mathematical modelling and numerical treatment of the die swell is of considerable importance both in the fundamental understanding of polymer flow behaviour and in the direct practical control of the manufacturing process of polymeric materials. In this talk we attempt to model and simulate the extrusion of hollow and non-hollow polymer yarns, and to develop a possible strategy for effective die design in profile extrusion. We numerically asses the validity of the model on both academic and real industrial test cases.

This talk is based on a joint work with N.A. Fadel and M. Verani (MOX, Politecnico di Milano).

MINISYMPOSIA

MSP01 - Advances and challenges in biomathematics and bioinformatics In the last years, mathematics is assuming a relevant role in supporting research in medicine and biology. Nowadays, the incresead computational capabilities allow long simulations at low cost and in controlled conditions. Mathematical modelling and computer simulation offer a useful tool in predicting dynamical patterns and in understanding the basic mechanism of many biological and biomedical processes.The fields of application range from theoretical analysis of physiological processes to numerical simulations of intracellular processes, from computational hemodynamics to simulation of cell structures and functions, from data mining to computational image analysis and geometrical reconstruction algorithms etc. This minisymposium offers an overview of the different models and techniques for biomedical applications and encourages the exchange of information between methodological and applicative fields, bringing together mathematicians, engineers, biologists, physicians, bioinformatics scientists, etc. Our goal is to provide a forum for discussion and exchange of ideas that can lead to the development of more realistic physiological models, and their future applications in biomedicine, biomathematics and bioinformatics.

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Bocci and Freguglia suggested a geometric model for a first order evolutionary theory in [1]. It is a first order since it does not consider any specific mechanism of reproduction, nor any environmental influence, but only the synthetic concept of perturbing action. In their theory Bocci and Freguglia define the notion of fertility factor as the main instrument for studying speciation. In this work we present an implementation of their geometric model and a discussion of its possible use for a quantitative understanding of the dependence of speciation on internal factors (fertility factor) and on external influences on the reproductive mechanism, which belong to the second level of evolution theories and are simulated in a compatible way with respect to the first level laws.



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