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Mechanisms of Cell Motion in Confined Geometries

R. J. Hawkins, R. Voituriez (2010)

Mathematical Modelling of Natural Phenomena

We present a simple mechanism of cell motility in a confined geometry, inspired by recent motility assays in microfabricated channels. This mechanism relies mainly on the coupling of actin polymerisation at the cell membrane to geometric confinement. We first show analytically using a minimal model of polymerising viscoelastic gel confined in a narrow channel that spontaneous motion occurs due to polymerisation alone. Interestingly, this mechanism...

Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...

Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...

Modeling, mathematical and numerical analysis of electrorheological fluids

Michael Růžička (2004)

Applications of Mathematics

Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.

Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects

G. Jouvet, M. Picasso, J. Rappaz, M. Huss, M. Funk (2011)

Mathematical Modelling of Natural Phenomena

A numerical model to compute the dynamics of glaciers is presented. Ice damage due to cracks or crevasses can be taken into account whenever needed. This model allows simulations of the past and future retreat of glaciers, the calving process or the break-off of hanging glaciers. All these phenomena are strongly affected by climate change.Ice is assumed to behave as an incompressible fluid with nonlinear viscosity, so that the velocity and pressure...

Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models

A. R.A. Anderson, K. A. Rejniak, P. Gerlee, V. Quaranta (2010)

Mathematical Modelling of Natural Phenomena

Since cancer is a complex phenomenon that incorporates events occurring on different length and time scales, therefore multiscale models are needed if we hope to adequately address cancer specific questions. In this paper we present three different multiscale individual-cell-based models, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular, cellular or subcellular, but also incorporating relevant information from other levels. We apply these hybrid...

Modelling of convective phenomena in forest fire.

M.ª Isabel Asensio, Luis Ferragut, Jacques Simon (2002)

RACSAM

We present a model coupling the fire propagation equations in a bidimensional domain representing the surface, and the air movement equations in a three dimensional domain representing an air layer. As the air layer thickness is small compared with its length, an asymptotic analysis gives a three dimensional convective model governed by a bidimensional equation verified by a stream function. We also present the numerical simulations of these equations.

Modelling of miscible liquids with the Korteweg stress

Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global existence...

Modelling of Miscible Liquids with the Korteweg Stress

Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global...

More pressure in the finite element discretization of the Stokes problem

Christine Bernardi, Frédéric Hecht (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

For the Stokes problem in a two- or three-dimensional bounded domain, we propose a new mixed finite element discretization which relies on a nonconforming approximation of the velocity and a more accurate approximation of the pressure. We prove that the velocity and pressure discrete spaces are compatible, in the sense that they satisfy an inf-sup condition of Babuška and Brezzi type, and we derive some error estimates.

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