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Kinetic equations with Maxwell boundary conditions

Stéphane Mischler (2010)

Annales scientifiques de l'École Normale Supérieure

We prove global stability results of DiPerna-Lionsrenormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which includes the so-called Maxwell boundary conditions, and we prove that it is realized (it is not only a boundary inequality condition as it has been established in previous works). We are able to deal with Boltzmann,...

Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions

S. Swaminathan, F. Ziebert, I. S. Aranson, D. Karpeev (2010)

Mathematical Modelling of Natural Phenomena

We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability...

Moving domain walls in magnetic nanowires

Katharina Kühn (2009)

Annales de l'I.H.P. Analyse non linéaire

New Results in Velocity Averaging

François Golse (2001/2002)

Séminaire Équations aux dérivées partielles

This paper discusses two new directions in velocity averaging. One is an improvement of the known velocity averaging results for $L^{1}$ functions. The other shows how to adapt some of the ideas of velocity averaging to a situation that is essentially a new formulation of the Vlasov-Maxwell system.

On the modified Enskog equation for elastic and inelastic collisions. Models with spin

Maria J. Esteban, Benoit Perthame (1991)

Annales de l'I.H.P. Analyse non linéaire

Quasichemical Models of Multicomponent Nonlinear Diffusion

A.N. Gorban, H.P. Sargsyan, H.A. Wahab (2011)

Mathematical Modelling of Natural Phenomena

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent...

The mean-field limit for the dynamics of large particle systems

François Golse (2003)

Journées équations aux dérivées partielles

This short course explains how the usual mean-field evolution PDEs in Statistical Physics - such as the Vlasov-Poisson, Schrödinger-Poisson or time-dependent Hartree-Fock equations - are rigorously derived from first principles, i.e. from the fundamental microscopic models that govern the evolution of large, interacting particle systems.