The present paper completes an earlier result by S. Ukai, T. Yang, and S.-H. Yu [Commun. Math. Phys. 236 (2003), 373−393] on weakly nonlinear half-space problems for the steady Boltzmann equation with hard-sphere potential. 1. Statement of the Problem & Main Result Boundary layers are an important class of flows in the kinetic theory of gases. One of the most significant problems in this contex...

A simplified version of a classical problem in thermodynamics--the adiabatic piston--is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained in the left and right chambers of the piston are always in equilibrium (that is, the molecules are uniformly distributed and their velocities obey the Maxwell-Boltz...

Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinet...

We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are derived through a modified version of the classical Boltzmann kinetic equation for monatomic gases. The free volumes around the gaseous molecules are introduced i...

In this paper, we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge of the homogeneous steady wealth distribution (the Maxwellian) of the underlying kinetic model. The ...

We numerically realize breather gas for the focusing nonlinear Schr\"odinger equation. This is done by building a random ensemble of N $\sim$ 50 breathers via Darboux transform recursive scheme in high precision arithmetics. Three types gases are synthesized according to three prototypical spectral configurations corresponding Akhmediev, Kuznetsov-Ma and Peregrine as elementary quasi-particles ...

The system of transport relaxation equations obtained from the linearized Waldmann-Snider equation is the starting point for the kinetic treatment of the heat conductivity for mixtures of linear diamagnetic molecules in an external homogeneous magnetic field. The connection of the occurring collision integrals with certain molecular cross sections is discussed and order of magnitude considerati...

In a recently developed simple particle mechanics model, in which a single particle represents the working fluid, (gas) in a heat engine, (exemplified by a piston engine) a new approach was outlined for the teaching of concepts to thermodynamic students. By mechanics reasoning, a model was developed that demonstrates the connection between the Carnot efficiency limitation of heat engines, and t...