Grain size derived from transformation kinetic equations.

Moment systems derived from relativistic kinetic equations

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie alg...

Kinetic equations for grain boundary networks in two-dimensions

Chemotaxis: from kinetic equations to aggregate dynamics

The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-valued solutions and discontinuous velocities. An adaptation of the notion of duality solutions, introduced for linear equations with discontinuous coefficients, leads to an existence result. Uniqueness is obta...

Hamiltonian closures for two-moment fluid models derived from drift-kinetic equations

We derive the conditions under which the fluid models obtained from the first two moments of Hamiltonian drift-kinetic systems of interest to plasma physics, preserve a Hamiltonian structure. The adopted procedure consists of determining closure relations that allow to truncate the Poisson bracket of the drift-kinetic system, expressed in terms of the moments, in such a way that the resulting o...

Kinetic equations

Kinetic theory is a way of describing the time evolution of a system consisting of a large number of elementary objects which may be called particles. The mathematical study of such systems leads to a class of partial differential equations called kinetic equations. Equations of this type have many applications in physics and other sciences. The ’particles’ could for instance be electrons, star...