Date of Award
Doctor of Philosophy (PhD)
Chair and Committee
The micro-structure of systems with competition often exhibits many universal features. In this thesis, we study certain aspects of these structural features as well as the microscopic interactions using disparate exact and approximate techniques. This thesis can be broadly divided into two parts. In the first part, we use statistical mechanics arguments to make general statements about length and timescales in systems with two-point interactions. We demonstrate that at high temperatures, the correlation function of general O(n) systems exhibits a universal form. This form enables the extraction of microscopic interaction potentials from the high temperature correlation functions. In systems with long range interactions, we find that the largest correlation length diverges in the limit of high temperatures. We derive an exact form for the correlation function in large-n systems with general two-point interactions at finite temperatures. From this, we obtain some features of the correlation and modulation lengths in general systems in the large-n limit. We derive a new exponent characterizing modulation lengths: or times) in systems in which the modulation length: or time) either diverges or becomes constant as a parameter, such as temperature exceeds a threshold value.
In the second part of this thesis, we study the micro-structure of a metallic glass system using molecular dynamics simulations. We use both classical and first principles simulation to obtain atomic configurations in the liquid as well as the glassy phase. We analyze these using standard methods of local structure analysis - calculation of pair correlation function and structure factor, Voronoi construction, calculation of bond orientational order parameters and calculation of Honeycutt indices. We show the enhancement of icosahedral order in the glassy phase. Apart from this, we also use the techniques of community detection to obtain the inherent structures
in the system using an algorithm which allows us to look at arbitrary length-scales.
Chakrabarty, Saurish, "Microstructure of Systems with Competition" (2012). All Theses and Dissertations (ETDs). 945.