Transport Theory and Statistical Physics 

About: Transport Theory and Statistical Physics is an academic journal. The journal publishes majorly in the area(s): Boltzmann equation & Boundary value problem. It has an ISSN identifier of 0041-1450. Over the lifetime, 1147 publications have been published receiving 12642 citations.

Invariant Variation Problems

Abstract: The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge for the corresponding differential equations find their most general expression in the theorems formulated in Section I and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of Lie's group theory. For special groups and problems in variation, this combination of methods is not new; I may cite Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker, Weyl and Klein)1 for special infinite groups. Especially Klein's second Note and the present developments have been mutually influenced by each other, in which regard I may ...

Kinetic models for gas-surface interactions

Abstract: The problem of a mathematical description of the relation between the distribution functions of impinging and emerging molecules at a solid wall is considered. Under suitable assumptions, of a rather general nature, certain properties of the acceptable models are set forth. These properties are then used to prove certain basic inequalities (including the one necessary to prove the H-theorem in presence of physical walls) as. well as constructing a specific model containing two disposable parameters. Preliminary comparisons of this model with experiment seem satisfactory.

On asymptotics of the Boltzmann equation when the collisions become grazing

Abstract: We deal in this work with an asymptotics of the Boltzmann equation leading to the Fokker-Planck-Landau equation. We prove its mathematical validity in the context of linearized equations and give an extension to the Ka[cbreve] equation.

A Fourier spectral method for homogeneous boltzmann equations

Abstract: A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.

The mode coupling theory of structural relaxations

Abstract: The basic ideas and approximations underlying the derivation of the mode coupling theory of structural relaxation in simple liquids are summarized. We explain why in disordered many particle systems the infinite set of density fluctuation products constitutes slow modes whose interactions lead to bifurcation singularities. The singularities are connected with the appearance of spontaneous arrest of particle distributions in ideal glass states. These constitute an almost frozen potential landscape for the phonon assisted transport processes, which restore ergodicity in strongly supercooled or super-compressed liquids. Some concepts needed for a description of structural relaxation are explained: glass transition singularities, non-ergodicity parameters, critical decay laws, separation parameters, critical temperature T c or density n c and α– and β–relaxation. It is emphasized that there are universality classes for the dynamics where the correlation functions within certain windows can be specifi...