Mathematical theory for the Ginzburg-Landau approximation in semilinear pattern forming systems with time-periodic forcing applied to electro-convection in nematic liquid crystals
Maximal regularity and viscous incompressible flows with free interface
We consider a free interface problem for the Navier-Stokes equations. We obtain local in time unique existence of solutions to this problem for any initial data and external forces, and global in time unique existence of solutions for sufficiently small initial data. Thanks to global in time maximal regularity of the linearized problem, we can prove a global in time existence and uniqueness theorem by the contraction mapping principle.
Maximal regularity of the spatially periodic Stokes operator and application to nematic liquid crystal flows
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal -regularity of the periodic Laplace and Stokes operators and a local-in-time existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group to obtain an -bound for the...
Mean field limit for the one dimensional Vlasov-Poisson equation
We consider systems of particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the Vlasov-Poisson equation. Actually a rigorous proof of that convergence was given by Trocheris in [Tro86]. Here we shall give a simpler proof of this result, and explain why it implies the so-called “Propagation of molecular chaos”. More precisely, both results will...
Measure attractors for stochastic Navier-Stokes equations.
Measure-valued solutions and asymptotic behavior of a multipolar model of a boundary layer
Mechanisms of Cell Motion in Confined Geometries
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
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
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...
Mémoire sur l'influence des frottements dans les mouvements réguliers des fluides.
Method of straight lines for a Bingham problem as a model for the flow of waxy crude oils.
Méthodes d'éléments finis quasilinéaires en déplacement pour l'étude de milieux incompressibles
Méthodes multipas pour des équations paraboliques non linéaires.
Méthodes numériques pour les équations de Navier-Stokes instationnaires des fluides visqueux incompressibles
Mixed Finite Element Approximation of the Vector Potential.
Mixed finite element in 3D in and
Modèles stratifiés en mécanique des fluides géophysiques
Modeling, mathematical and numerical analysis of electrorheological fluids
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
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
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...