Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Soft materials have a wide range of applications, which include the production of masks for nano–lithography, the separation of membranes with nano–pores, and the preparation of nano–size structures for electronic devices. Self–organization in soft matter is a primary mechanism for the formation of structure. Block copolymers are long chain molecules composed of several different polymer blocks covalently bonded into a single macromolecule, which belong to an important class of soft materials which can self–assemble into different nano–structures due to their natural ability to microphase separate. Experimental and theoretical studies of block copolymers are quite challenging and, without computer simulations, it is difficult and problematic to analyse modern experiments. The Cell Dynamics Simulation (CDS) technique is a fast and accurate computational technique, which has been used to investigate block copolymers. The stability has been analysed by making use of different discrete Laplacian operators using well–chosen time steps in CDS. This analysis offers stability conditions for phase–field, based on the Cahn–Hilliard Cook (CHC) equations of which CDS is the finite difference approximation. To overcome grid related artefacts (discretization errors) in the computational grid, the study has been done for employing an isotropic Laplacian operator in the CDS framework. Several 2D and 3D discrete Laplacians have been quantitatively compared for their isotropy. The novel 2D 9–point BV(D2Q9) isotropic stencil operators have been derived from the B.A.C. van Vlimmeren method and their isotropy measure has been determined optimally better than other exiting 2D 9–point discrete Laplacian operators. Overall, the stencils in 9–point family Laplacians in 2D and the 19–point stencil operators in 3D have been found to be optimal in terms of isotropy and time step stability. Considerable implementation of Laplacians with good isotropy has played an important role in achieving a proper structure factor in modelling methods of block copolymers. The novel models have been developed by implementing CDS via more stable implicit methods, including backward Euler, Crank–Nicolson (CN) and Alternating Direction Implicit (ADI) methods. The CN scheme were implemented for both one order and two order parameter systems in CDS and successful results were obtained compared to forward Euler method. Due to the implementation of implicit methods, the CDS has achieved second–order accuracy both in time and space and it has become stronger, robust and more stable technique for simulation of the phase–separation phenomena in soft materials.

We study a hydrodynamic evolution of a non-spherical core-collapse supernova in multidimensions. We begin our study from the moment of shock revival and continue for the first week after explosion when expansion of the supernova ejecta becomes homologous. We observe growth and interaction of Richtmyer-Meshkov, Rayleigh-Taylor, and Kelvin- Helmholtz instabilities resulting in an extensive mixing of the heavy elements throughout the ejecta. We obtain a series of models at progressively higher resolution and provide preliminary discussion of numerical convergence. Unlike in the previous studies, our computations are performed in a single domain. Periodic mesh mapping is avoided. This is made possible by employing an adaptive mesh refinement strategy in which computational workload (defined as a product of the total number of computational cells and the length of the time step) is monitored and, if necessary, limited. Our results are in overall good agreement with the simulations reported by Kifonidis et al. We demonstrate, however, that the amount of mixing and kinematic properties of radioactive species (i.e. 56Ni) is extremely anisotropic. In particular, we find that the model displays a strong tendency to expand laterally away from the equatorial plane toward the poles. Although this behavior is usually attributed to numerical artifacts characteristic of computations with assumed symmetry (axis-effect), the observed behavior can be attributed to a large heat content of the equatorial regions of the explosion model. Future studies are needed to verify that this explosion model property does not have a systematic character. / A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2009. / July 29, 2009. / Non-Spherical, Core-Collapse Supernova AMR / Includes bibliographical references. / Tomasz Plewa, Professor Directing Thesis; Peter Hoeflich, Committee Member; Gordon Erlebacher, Committee Member.

Heteroepitaxial thin films are essential components in many technological applications including optical, electronic and other functional devices. These films are also becoming important in the coating technologies for high-temperature materials applications. Typical heteroepitaxial systems involve one or more solid phases deposited on support structure called the substrate. Often the lattice and thermal mismatch in these systems results in significant elastic strains that, under the appropriate temperature conditions, drive mass transport by diffusion. Surface diffusion in these systems is usually a dominant mass transport mechanism that leads to morphological evolution of the surface. This evolution is called stress-driven morphological growth, and it has received much attention by materials modelers. In the current work, the problem of stress-driven morphological evolution in strained thin films is revisited; we develop a generalized formulation of this problem in the non-linear regime based upon a curvilinear coordinate formalism and finite element solution of the elastic sub-problem. This combination of methods facilitates the analysis of the onset of the instability and the early stage temporal evolution of the film surface. We apply our numerical scheme to surface wave, dot, pit, and ring morphologies and demonstrate the effects of model parameters on the incipient instabilities. / A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science. / Summer Semester, 2010. / June 28, 2010. / Thin Films, Instability, Epitaxy / Includes bibliographical references. / Anter El-Azab, Professor Directing Thesis; Gordon Erlebacher, Committee Member.

The primary hydrodynamic flow feature of early explosion phases of a core-collapse supernova is a spherical shock. This shock is born deep in the central regions of the collapsing stellar core, stalls shortly afterward, and in case of a successful explosion is revived and becomes the supernova shock. The revival process involves a standing accretion shock instability, SASI. This shock instability is considered the key processes aiding the core-collapse supernova (ccSN) explosion. The aim of our study is to identify feasible conditions and parameters for an experimental system that is able to capture the essential characteristics of SASI. We use analytic methods and high-resolution hydrodynamic simulations in multidimensions to investigate a possible experimental design on the National Ignition Facility. The experimental configuration involves a steady, spherical shock. We explore a viable region of parameters and obtain limits on the shocked flow geometry. We study the stability properties of the shock and its post-shock region. We discuss key differences between the experimental setup and astrophysical environment. The obtained flowfield closely resembles conveging nozzle flow. The post-shock region, in contrast to the supernova setting, is found to be stably stratified and insensitive to perturbations upstream of the shock. We conclude that it is not possible to capture the characteristics of the supernova SASI for the converging shocked flow configuration considered here. However, such configuration offers a very stable setting for precision studies of shocked, dense, high temperature plasmas requiring finely-controlled conditions. / A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2011. / October 21, 2011. / hydrodynamics, laboratory astrophysics, shockwaves, supernovae / Includes bibliographical references. / Tomasz Plewa, Professor Directing Thesis; Gordon Erlebacher, Committee Member; Michael Navon, Committee Member.

Advances in computational power have lead to many developments in science and en- tertainment. Powerful simulations which required expensive supercomputers can now be carried out on a consumer personal computer and many children and young adults spend countless hours playing sophisticated computer games. The focus of this research is the development of tools which can help bring the entertaining and appealing traits of video games to scientific education. Video game developers use many tools and programming languages to build their games, for example the Blender 3D content creation suite. Blender includes a Game Engine that can be used to design and develop sophisticated interactive experiences. One important tool in computer graphics and animation is the particle system, which makes simulated effects such as fire, smoke and fluids possible. The particle system available in Blender is unfortunately not available in the Blender Game Engine because it is not fast enough to run in real-time. One of the main factors contributing to the rise in computational power and the increas- ing sophistication of video games is the Graphics Processing Unit (GPU). Many consumer personal computers are equipped with powerful GPUs which can be harnassed for general purpose computation. This thesis presents a particle system library is accelerated by the GPU using the OpenCL programming language. The library integrated into the Blender Game Engine providing an interactive platform for exploring fluid dynamics and creating video games with realistic water effects. The primary system implemented in this research is a fluid sim- ulator using the Smoothed Particle Hydrodynamics technique for simulating incompressible fluids such as water. The library created for this thesis can simulate water using SPH at 40fps with upwards x  of 100,000 particles on an NVIDIA GTX480 GPU. The fluid system has interactive features such as object collision, and the ability to add and remove particles dynamically. These features as well as phsyical properties of the simulation can be controlled intuitively from the user interface of Blender. / A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2011. / August 24, 2011. / Game Design, GPU, OpenCL, SPH / Includes bibliographical references. / Gordon Erlebacher, Professor Directing Thesis; Tomasz Plewa, Committee Member; Anter El-Azab, Committee Member.

This thesis explores possible improvements in the construction of Delaunay Triangulations on the Sphere by designing and implementing a parallel alternative to the software package STRIPACK. First, it gives an introduction to Delaunay Triangulations on the plane and presents current methods available for their construction. Then, these concepts are mapped to the spherical case: Spherical Delaunay Triangulation (SDT). To provide a better understanding of the design choices, this document includes a brief overview of parallel programming, that is followed by the details of the implementation of the SDT generation code. In addition, it provides examples of resulting SDTs as well as benchmarks to analyze its performance. This project was inspired by the concepts presented in Robert Renka's work and was implemented in C++ using MPI. / A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science. / Spring Semester, 2011. / April 1, 2011. / Delaunay Triangulation, Spherical Delaunay Triangulation, Parallel Programming, Software Package / Includes bibliographical references. / Max Gunzburger, Professor Directing Thesis; Anke Meyer-Baese, Committee Member; Janet Peterson, Committee Member; Jim Wilgenbusch, Committee Member.

In response to potential increasing rate of sea-level rise, planners and engineers are making accommodations in their management plans for protection of coastal infrastructure and natural resources. Dunes and barrier islands are important for coastal protection and restoration, because they absorb storm energy and play an essential role in sediment transportation. Most of traditional coastal models do not simulate joint evolution of dunes and barrier islands and do not explicitly address sea-level rise. A new model was developed in this study that represents basic barrier island processes under sea-level rise and links dynamics of different components of barrier islands. The model was used to evaluate near-future (100 years) responses of a semi-synthetic island, with the characteristics of Santa Rosa Island of Florida, USA, to five rates of sea-level rise. The new model is capable of representing considerable practical information about effects of different sea level rise scenarios on the test island. The modeling results show that different areas and components of the island have different responses to sea-level rise. Depending on the rate of sea level rise and overwash sediment supply, evolution of dunes and barrier islands is important to habitat suitable for coastal birds or to backbarrier salt marshes. The modeling results are inherently uncertain due to unknown storm variability and sea-level rise scenarios. The storm uncertainty, characterized as parametric uncertainty, and its propagation to the modeling results, were assessed using the Monte Carlo (MC) method for the synthetic barrier island. A total of 1000 realizations of storm magnitude, frequency, and track through a barrier island were generated and used for the MC simulation. To address the scenario uncertainty, five sea-level rise scenarios were considered using the current rate and four additional rates that lead to sea-level rise of to 0.5m, 1.0m, 1.5m, and 2.0m in the next 100 years. Parametric uncertainty in the simulated beach dune heights and the backshore positions was assessed for the individual scenarios. For a given scenario, the parametric uncertainty varies with time, becoming larger when time increases. For different sea-level rise scenarios, the parametric uncertainty is different, being larger for more severe sea-level rise. The method of scenario averaging was used to quantify the scenario uncertainty. The scenario averaging results are between the results of smallest and largest sea-level rise scenarios. The results of uncertainty analysis provide guidelines for coastal management and protection of coastal ecology. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2011. / November 3, 2011. / barrier island, morphology, sea-level rise, storm / Includes bibliographical references. / Ming Ye, Professor Directing Thesis; Dennis Slice, Committee Member; Tomasz Plewa, Committee Member.

Heat is transfered in crystalline semiconductor materials via lattice vibrations. Lattice vibrations are treated with a wave-particle duality just like photons are quantum mechanical representations of electro-magnetic waves. The quanta of energy of these lattice waves are called phonons. The Boltzmann Transport Equation (BTE) has proved to be a powerful tool in modeling the phonon heat conduction in crystalline solids. The BTE tracks the phonon number density function as it evolves according to the drift of all phonons and to the phonon-phonon interactions (or collisions). Unlike Fourier's law which is limited to describing diffusive energy transport, the BTE can accurately predict energy transport in both ballistic (virtually no collisions) and diffuse regimes. Motivated by the need to understand thermal transport in irradiated Uranium Dioxide at the mesoscale, this work investigates phonon transport in UO2 using Monte Carlo simulation. The simulation scheme aims to solve the Boltzmann transport equation for phonons within a relaxation time approximation. In this approximation the Boltzmann transport equation is simplified by assigning time scales to each scattering mechanism associated with phonon interactions. The Monte Carlo method is first benchmarked by comparing to similar models for silicon. Unlike most previous works on solving this equation by Monte Carlo method, the momentum and energy conservation laws for phonon-phonon interactions in UO2 are treated exactly; in doing so, the magnitude of possible wave vectors and frequency space are all discretized and a numerical routine is then implemented which considers all possible phonon-phonon interactions and chooses those interactions which obey the conservation laws. The simulation scheme accounts for the acoustic and optical branches of the dispersion relationships of UO2. The six lowest energy branches in the [001] direction are tracked within the Monte Carlo. Because of their predicted low group velocities, the three remaining, high-energy branches are simply treated as a reservoir of phonons at constant energy in K-space. These phonons contribute to the thermal conductivity only by scattering with the six lower energy branches and not by their group velocities. Using periodic boundary conditions, this work presents results illustrating the diffusion limit of phonon transport in UO2 single crystals, and computes the thermal conductivity of the material in the diffusion limit based on the detailed phonon dynamics. The temperature effect on conductivity is predicted and the results are compared with experimental data available in the literature. / A Thesis submitted to the Department of ScientifiC Conmputing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2011. / November 7, 2011. / Boltzmann, Carlo, Monte, Phonon, Thermal, Transport / Includes bibliographical references. / Anter El-Azab, Professor Directing Thesis; Tomasz Plewa, Committee Member; Xiaoqiang Wang, Committee Member.

In this dissertation, the recently developed peridynamic nonlocal continuum model for solid mechanics is extensively studied, specifically, the numerical methods for the deterministic and stochastic steady-state peridynamics models. In contrast to the classical partial differential equation models, peridynamic model is an integro-differential equation that does not involve spatial derivatives of the displacement field. As a result, the peridynamic model admits solutions having jump discontinuities so that it has been successfully applied to the fracture problems. This dissentation consists of three major parts. The first part focuses on the one-dimensional steady-state peridynamics model. Based on a variational formulation, continuous and discontinuous Galerkin finite element methods are developed for the peridynamic model. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. A strategy for identifying the discontinuities of the solution is developed and implemented. The convergence of peridynamics model to classical elasticity model is studied. Some relevant nonlocal problems are also considered. In the second part, we focus on the two-dimensional steady-state peridynamics model. Based on the numerical strategies and results from the one-dimensional peridynamics model, we developed and implemented the corresponding approaches for the two-dimensional case. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. In the third part, we study the stochastic peridynamics model. We focus on a version of peridynamics model whose forcing terms are described by a finite-dimensional random vector, which is often called the finite-dimensional noise assumption. Monte Carlo methods, stochastic collocation with full tensor product and sparse grid methods based on this stochastic peridynamics model are implemented and compared. / A Dissertation submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester, 2012. / June 22, 2012. / DISCONTINUOUS GALEKIN METHODS, FINITE ELEMENT METHODS, INTEGRAL DIFFERENTIAL EQUATIONS, NONLOCAL DIFFUSION PROBLEM, PERIDYNAMICS, STOCHASTIC / Includes bibliographical references. / Max Gunzburger, Professor Directing Dissertation; Xiaoming Wang, University Representative; Janet Peterson, Committee Member; Xiaoqiang Wang, Committee Member; Ming Ye, Committee Member; John Burkardt, Committee Member.