In this study, the unsteady velocity function of the ions and electrons in the collisional presheath and collisionless sheath of a plasma near a completely absorbing wall are determined from a kinetic analysis. The collisions in the presheath are modeled by a relaxtion time approximation (namely BGK model¡ABhatnagar-Gross-Krook ). The model and analysis from Emmert et al. are used to find the variation in electrostatic potential with position. Distribution functions of the ions and electrons in a collisionless presheath and sheath can be exactly obtained. Velocities of the ions in the presheath and sheath are highly non-Maxwell-Boltzmann distributions. The electrons in the presheath are close to Maxwell-Boltzmann distributions, but those in the sheath are non-Maxwell-Boltzmann distributions. The computed distribution functions for a completely absorbing surface agree with theoretical results provided in the literature.

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

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

There has been a long, but disparate discourse among those responsible for our built environment about the inevitability of change on the artifacts we inhabit and those social contracts that influence their making. At a basic level doors and operable windows are an indication of the various flows that move through buildings. Innumerable “passive” and “active” strategies have been devised to allow changes to building floor plans and sections, to control sunlight and wind, to change function, etc. Hundreds, or perhaps thousands, of prototypes have been proposed and developed that change shape or composition in response to various social and environmental pressures. Though not always done with the goals of sustainability in mind, these prototypes often sought to provide increased agency for users, improved energy-efficiency and cost-effectiveness, and other commonly understood goals of sustainability. A number of books, hundreds of articles, and dozens of patents beautifully illustrate many proposed and built examples from which to learn but the descriptive terms employed are greatly varied (i.e., adaptable, animated, collapsible, deployable, enabling, evolutionary, flexible, intelligent, kinetic, manipulable, mutable, open-system, portable, protean, reconfigurable, responsive, revolving, smart, and transformable, etc.) and are therefore difficult to find. By reviewing and synthesizing the existing literature, this study provides a starting point for future research that offers both insight into how these terms have been used over time and a critique of such concerns and the exclusion of the topic within sustainability rating criteria. / text

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