This thesis begins with a review on the topic of molecular electronics. The purpose of this review is to motivate the need for good theory to understand and predict molecular electronics behaviour. At present the most promising theoretical formalism for dealing with this problem is a combination of density functional theory and nonequilibrium Green's functions (NEGF-DFT). This formalism is especially attractive because it is an ab-initio technique, meaning that it is completely from first principles and does not require any empirical parameters. An implementation of this formalism has been developed by the research group of Hong Guo and is presented and explained here. A few other implementations which are similar but differ in some ways are also discussed briefly to highlight their various advantages and disadvantages. / One of the difficulties of ab-initio calculations is that they can be extremely costly in terms of the computing time and memory that they require. For this reason, in addition to using appropriate approximations, sophisticated numerical analysis tech niques need to be used. One of the bottlenecks in the NEGF-DFT method is solving the Poisson equation on a large real space grid. For studying systems incorporating a gate voltage it is required to be able to solve this problem with nonperiodic boundary conditions. In order to do this a technique called multigrid is used. This thesis examines the multigrid technique and develops an efficient implementation for the purpose of use in the NEGF-DFT formalism. For large systems, where it is necessary to use especially large real space grids, it is desirable to run simulations on parallel computing clusters to handle the memory requirements and make the code run faster. For this reason a parallel implementation of multigrid is developed and tested for performance. The multigrid tool is incorporated into the NEGF-DFT formalism and tested to ensure that it is properly implemented. A few calculations are made on a benzenedithiol system with gold leads to show the effect of an applied gate voltage.

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In this dissertation we study multiscale methods for slowly varying porous media, fluid and solid coupling, and application to geomechanics. The thesis consists of three closely connected results. We outline them and their relation. First, we derive a homogenization result for Stokes flow in slowly varying porous media. These results are important for homogenization in deformable porous media. Traditionally, these techniques are applied to periodic media, however, in the case of Fluid-Structure Interaction (FSI) slowly varying domains occur naturally. We then develop a computational methodology to compute effective quantities to construct homogenized equations for such media. Next, to extend traditional geomechanics models based primarily on the Biot equations, we use formal two-scale asymptotic techniques to homogenize the fully coupled FSI model. Prior models have assumed trivial pore scale deformation. Using the FSI model as a fine-scale model, we are able to incorporate non-trivial pore scale deformation into the macroscopic equations. The primary challenge here being the fluid and solid equations are represented in different coordinate frames. We reformulate the fluid equation in the fixed undeformed frame. This unified domain formulation is known as the Arbitrary Lagrange-Eulerian (ALE). Finally, we utilize the ALE formulation of the Stokes equations to develop an efficient multiscale finite element method. We use this method to compute the permeability tensor with much less computational cost. We build a dense hierarchy of macro-grids and a corresponding collection of nested approximation spaces. We solve local cell problems at dense macro-grids with low accuracy and use neighboring high accuracy solves to correct. With this method we obtain the same order of accuracy as we would if we computed all the local problems with highest accuracy.

This thesis reports a rock slope hazard investigation located in the Central Andes of Chile, where two significant rock mass wasting events were recognized. Dating using cosmogenic nuclide for ³⁶Cl showed that the deposits were post-glacial in age, corresponding to the Upper Pleistocene Portillo Rock Avalanche (PRA) and a Holocene rock slump and rockslide. The pre-historic landslide deposits underlie both a key transportation route between Chile and Argentina and an important ski resort. The purpose of this research was to investigate the likely failure mechanism and characterise the runout path and volume of the PRA. The insights gained on the back analysis of the slope were used in later stages to assess the hazard potential of a recurring major rockslide. The distinct element code UDEC was used to evaluate the failure mechanism. Elasto-plastic modelling results showed that sliding and shearing along the bedding planes together with brittle fracturing and shearing through the toe of the slope likely had occurred. Runout simulations were carried out using DAN3D. Combinations of rheologies were tested and ranked based on their ability to represent the current distribution of the debris by means of pre-failure topography reconstruction and volume estimates of the deposits. Results showed that the best basal rheological combination for the PRA was frictional during the rockslide and Voellmy when entrainment became important. In contrast, a constant frictional basal rheology best represented the Holocene rock slump. The performance of the present-day state of the slope was tested under different scenarios. Under static condition the slope proved to be stable indicating a stabilized geometrical profile with time. Also, the slope proved to be stable under increased pore water pressures at its toe. Finally the modelled slope was subjected to a seismic load (M=7.8) and its crest failed due to an outward rotation of blocks, probably aided by topographic amplification. The runout simulations showed that the leading edge of the flow could override part of the International Santiago-Mendoza Corridor with no direct impact to the Portillo Ski Resort. Overall, though, under this highly unlikely dynamic condition for the site, the hazard level is very low.

Thesis (M.S.)--University of Texas at El Paso, 2007. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.