Thesis (Ph. D.)--Georg-Augustus-Universitat, 1902.

Thesis (M. Sc.) -- University of the Western Cape. / Includes bibliographic references (leaves 80-89).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1961. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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.

An odd or even continuous function on a symmetric interval [-a,a] can be evaluated in two different ways, each using only one uniform polynomial approximation. It is of practical importance to know which method of evaluation takes fewer arithmetic operations. This is a special case of a more general problem, which is concerned with the optimal subdivision of the interval of evaluation of a function f into sub-intervals, on each of which f has a uniform polynomial approximation. In the first three chapters a method of computing the number of arithmetic operations for evaluation is developed. Expansions in Chebyshev polynomials are studied, with emphasis on the practical problem of computing coefficients, and then it is shown how the expansion in Chebyshev polynomials may be used to obtain truncation error bounds for the uniform polynomial approximation. From these bounds the required degree for the approximation and the required number of multiplications for evaluation may be easily determined. Tables of computed results are given. In Chapter 4 theoretical results are developed from the theory of Lagrange interpolation and these results are in agreement with the computed results obtained previously. In the problem of evaluation of even and odd functions on [-a,a] , use of the uniform polynomial approximation on [-a,a] is advantageous unless the rate of increase of the derivative of f is rapid. In the general case of evaluation of a continuous function, use of approximations on sub-intervals becomes more advantageous the more rapidly the derivatives of f increase. / Science, Faculty of / Mathematics, Department of / Graduate

Romberg's quadrature is investigated with special emphasis on its use in automatic integration. Section 1 reproduces many of the facts known about Romberg's method and investigates the selection of stepsize. Section 2 discusses the integration of singular integrands, with emphasis on detecting algebraic endpoint singularities and the reliability of methods used for handling them. Section 3 looks at CADRE, the first automatic integration routine published based on the adaptive use of Romberg's method. It is adapted for use on the IBM 360 and is compared to SQUANK, an adaptive Simpson routine already available in the U.B.C. program library. / Science, Faculty of / Computer Science, Department of / Graduate

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.