Please consider attending the following: MATERIALS ENGINEERING SEMINAR “The Statistical Mechanics of Interacting Particles (With Applications in Dislocation Dynamics)” By Joseph P. Anderson Purdue MSE Preliminary Exam Advisor: Professor Anter A. El-Azab ABSTRACT The dynamics of smooth density fields of discrete entities (e.g. electrons, fluid particles, dislocations) depend strongly on the short-range order of the underlying discrete entities considered. Statistical mechanics presents a means of determining this short-range order from the interaction potential. However, the means by which that is accomplished is not straightforward. In this presentation we will discuss the extension of statistical mechanics to interacting systems, and how this short-range order emerges in the equilibrium of such a system. This involves such topics as the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy of densities (of which the radial distribution function [cid:image002.png@01D5AEAE.52D8F370] is a special case) and closure approximations to this hierarchy. By means of a geometric interpretation of the ergodic theorem, we will examine under which regimes of interaction strength these methods may be applied, as well as the two-temperature models used to work around issues of ergodicity. Finally, we will discuss how dynamic theories which hold well beyond equilibrium may be formed from a description of short-range structures. This discussion will include projection operator approaches, as well as a formalism known as the General Equation for Non-Equilibrium Reversible Irreversible Coupling (GENERIC). Throughout, we will discuss the application of these ideas to the topic of dislocation dynamics, as well as the issues which arise in that application. . Date: Wednesday, December 13, 2019 Time: 8:00 A.M. Place: ARMS 1021
