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No description available.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1961. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1955. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 129-131).

[No abstract available] / Science, Faculty of / Chemistry, Department of / Graduate

Equations of change for the various hydrodynamic densities are derived for a dilute gas with degenerate internal states. To obtain a consistent set of hydrodynamic equations it is necessary to expand the collision term of the usual Waldmann-Snider Boltzmann equation (W-S equation) in position gradients of the distribution function [formula omitted]. In particular, the extension of the W-S equation to terms "linear" in the position gradients of [formula omitted] yields the correct form for the equation of change for the internal angular momentum density. Specifically, the production term in this equation of change is t he antisymmetric part of the pressure tensor, which is in accord with a hydrodynamic derivation. In addition, equations of change for the mass density, linear momentum density, and total energy density are also obtained. These results are shown to be similar to equations of change derived via a density-operator technique. Unfortunately, this " linear" extension of the W-S equation does not give a closed set of equations of change. However, a consistent set of equations is obtained if a restriction is placed on the form of the extended W-S equation. / Science, Faculty of / Chemistry, Department of / Graduate

A classical gas whose particles interact through a weak long range attraction and a strong short range repulsion is studied. The Liouville equation is solved as an infinite order perturbation expansion. The terms in this series are classified by Prigogine type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that., provided the range of the short range force is much less than the average interparticle distance which in turn is much less than the range of the long range forces the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from, the long range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations each of which is valid for a definite range of the parameters of the system. The short-time stability of the system is examined and a criterion for stability obtained. The equilibrium two-particle correlation function and an equation of state are determined, the latter being compared to the Van de Waals equation of state. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 128-136). Also available in electronic version.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

This work consists of three chapters. In the first chapter, a brief overview is made on the history of the modern kinetic theory of elastic and dilute gases since the early stages of Maxwell and Boltzmann. In addition, I short exposition on the complexities of the theory of granular media is presented. This chapter has the objectives of contextualize the problems that will be studied in the remainder of the document and, somehow, to exhibit the mathematical complications that may arise in the inelastic gases (not present in the elastic theory of gases). The rest of the work presents two self-contained chapters on different topics in the study of the Boltzmann equation. Chapter 2 focuses in studying and extending the propagation of regularity properties of solutions for the elastic and homogeneous Boltzmann equation following the techniques introduced by A. Bobylev in 1997 and Bobylev, Gamba and Panferov in 2002. Meanwhile, chapter 3 studies the existence and uniqueness of the inelastic and inhomogeneous Cauchy problem of the Boltzmann equation for small initial data. A new set of global in time estimates, proved for the gain part of the inelastic collision operator, are used to implement the scheme introduced by Kaniel and Shinbrot in the late 70’s. This scheme, known as Kaniel and Shinbrot iteration, produces a rather simple and beautiful proof of existence and uniqueness of global solutions for the Boltzmann equation with small initial data. / text