The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special rela-tivistic physics, i.e. to model the dynamics of ne...

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to the experiment at JILA [1]. It shows the presence of Castaing’s instability of transverse spin polarization...

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic-and special relativistic physics, e.g. to model the dynamics of neutr...

Simultaneous reactions between solids and gases are very important in the chemical and metallurgical processes. In the modeling, the chemical reaction and diffusion of gases must be considered. Therefore, a set of coupled partial differential equations is found. When the kinetic is a function of solid concentration, there is not any analytical solution for these equations. Therefore, numerical ...

Starting from Enskog equation of hard spheres of mass m and diameter D under the gravity g, we first derive the exact equation of motion for the equilibrium density profile at a temperature T and examine its solutions via the gradient expansion. The solutions exist only when βμ ≤ μo ≈ 21.756 in 2 dimensions and μo ≈ 15.299 in 3 dimensions, where μ is the dimensionless initial layer thickness an...

We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. The full position and momentum dependence of the distribution function must then be retaine...

Interfacial thermal transport of multi-walled carbon nanotube is explored by using T-type sensor. Reliable signals of heat flow through an individual nanotube were obtained. Estimated thermal boundary resistances between the end of CNT and solid surfaces do not show the clear dependency on material that has been predicted by the diffuse mismatch model treating graphite. This discrepancy is main...

It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be mod-eled as classical systems of particles interacting with short range, repulsive forces. Here we give a brief introduction to those parts of chaos theory that are relevant for understanding some features of non-equilibrium processes in fluids. We introduce the n...