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.

The antioxidant glutathione in the fish cell lines EPC and BCF-2: response to model pro-oxidants as measured by three different fluorescent dyes

Reduced glutathione (GSH) protects cells against injury by oxidative stress and maintains a range of vital functions. In vitro cell cultures have been used as experimental models to study the role of GSH in chemical toxicity in mammals; however, this approach has been rarely used with fish cells to date. The present study aimed to evaluate sensitivity and specificity of three fluorescent dyes for measuring pro-oxidant-induced changes of GSH contents in fish cell lines: monochlorobimane (mBCl), 5-chloromethylfluorescein diacetate (CMFDA) and 7-amino-4-chloromethylcoumarin (CMAC-blue). Two cell lines were studied, the EPC line established from a skin tumour of carp Cyprinus carpio, and BF-2 cells established from fins of bluegill sunfish Lepomis macrochirus. The cells were exposed for 6 and 24 h to low cytotoxic concentrations of pro-oxidants including hydrogen peroxide, paraquat (PQ), copper and the GSH synthesis inhibitor, L-buthionine-SR-sulfoximine (BSO). The results indicate moderate differences in the GSH response between EPC and BF-2 cells, but distinct differences in the magnitude of the GSH response for the four pro-oxidants. Further, the choice of GSH dye can critically affect the results, with CMFDA appearing to be less specific for GSH than mBCl and CMAC-blue.

Model approach for estimating potato pesticide bioconcentration factor

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.