The kinetic Fokker–Planck equation with general force

Kinetic equation with exact charge conservation.

A kinetic master equation for multiplicity distributions is formulated for charged particles which are created or destroyed only in pairs due to the conservation of their Abelian charge. It allows one to study time evolution of the multiplicity distributions in a relativistic many-body system with arbitrary average particle multiplicities. It is shown to reproduce the equilibrium results for bo...

On general kinetic equation for many particle systems with interaction, fragmentation and coagulation

We deduce the most general kinetic equation that describe the low density limit of general Feller processes for the systems of random number of particles with interaction, collisions, fragmentation and coagulation. This is done by studying the limiting as ε → 0 evolution of Feller processes on ∪∞n Xn with X = Rd or X = Zd described by the generators of the form ε−1 ∑K k=0 ε kB(k), K ∈ N , where...

Comparison between solutions of the general dynamic equation and the kinetic equation for nucleation and droplet growth.

A comparison is made between two models of homogeneous nucleation and droplet growth. The first is a kinetic model yielding the master equations for the concentrations of molecular clusters. Such a model does not make an explicit distinction between nucleation and droplet growth. The second model treats nucleation and growth separately, fully ignoring stochastic effects, and leads to the contin...

A kinetic eikonal equation

We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit (t, x) → (t/ε, x/ε). We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small diffusivity. We prove well-posedness of the phase problem and convergence towards the viscosity sol...

The validity of the kinetic collection equation