Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Improving the Timeliness and Response to an Aerosolizedanthrax Attack in the Metropolitan Washington, D.C. Region

Our research was conducted to improve the timeliness, coordination, and communication during the detection, investigation and decision-making phases of the response to an aerosolized anthrax attack in the metropolitan Washington, DC, area with the goal of reducing casualties. Our research gathered information of the current response protocols through an extensive literature review and interviews with relevant officials and experts in order to identify potential problems that may exist in various steps of the detection, investigation, and response. Interviewing officials from private and government sector agencies allowed the development of a set of models of interactions and a communication network to identify discrepancies and redundancies that would elongate the delay time in initiating a public health response. In addition, we created a computer simulation designed to model an aerosol spread using weather patterns and population density to identify an estimated population of infected individuals within a target region depending on the virulence and dimensions of the weaponized spores. We developed conceptual models in order to design recommendations that would be presented to our collaborating contacts and agencies that would use such policy and analysis interventions to improve upon the overall response to an aerosolized anthrax attack, primarily through changes to emergency protocol functions and suggestions of technological detection and monitoring response to an aerosolized anthrax attack.