Physical Sciences and Mathematics Commons^™

Energy Functional For Nuclear Masses, Michael Giovanni Bertolli

Doctoral Dissertations

An energy functional is formulated for mass calculations of nuclei across the nuclear chart with major-shell occupations as the relevant degrees of freedom. The functional is based on Hohenberg-Kohn theory. Motivation for its form comes from both phenomenology and relevant microscopic systems, such as the three-level Lipkin Model. A global fit of the 17-parameter functional to nuclear masses yields a root- mean-square deviation of χ[chi] = 1.31 MeV, on the order of other mass models. The construction of the energy functional includes the development of a systematic method for selecting and testing possible functional terms. Nuclear radii are computed within …

Electronic Excitations In Ytio3 Using Tddft And Electronic Structure Using A Multiresolution Framework, William Scott Thornton

Doctoral Dissertations

We performed ab initio studies of the electronic excitation spectra of the ferro- magnetic, Mott-insulator YTiO3 using density functional theory (DFT) and time- dependent density functional theory (TDDFT). In the ground state description, we included a Hubbard U to account for the strong correlations present within the d states on the cation. The excitation spectra was calculated using TDDFT linear response formalism in both the optical limit and the limit of large wavevector transfer. In order to identify the local d-d transitions in the response, we also computed the density response of YTiO3 using a novel technique where the basis …

A Time-And-Space Parallelized Algorithm For The Cable Equation, Chuan Li

Doctoral Dissertations

Electrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a nonlinear diffusion-reaction parabolic partial differential equation for the transmembrane voltage $V(x,t)$, known as the cable equation. This equation involves a highly nonlinear source term, representing the total ionic current across the membrane, governed by a Hodgkin-Huxley type ionic model, and requires the solution of a system of ordinary differential equations. Thus, the model consists of a PDE (in 1-, 2- or 3-dimensions) coupled to a system of ODEs, and it is very expensive to solve, especially in 2 and 3 dimensions.

In order to …

Adaptive Discontinuous Galerkin Finite Element Methods For A Diffuse Interface Model Of Biological Growth, Andreas C Aristotelous

Doctoral Dissertations

This PhD dissertation concentrates on the development and application of adaptive Discontinuous Galerkin Finite Element (DG-FE) methods for the numerical solution of a Cahn-Hilliard-type diffuse interface model for biological growth. Models of this type have become popular for studying cancerous tumor progression in vivo. The work in this dissertation advances the state-of-the-art in the following ways: To our knowledge the work here contains the first primitive-variable, completely discontinuous numerical implementations of a 2D scheme for the Cahn-Hilliard equation as well as a diffuse interface model of cancer growth. We provide numerical evidence that the schemes above are convergent, with the …

Optimal Theory Applied In Integrodifference Equation Models And In A Cholera Differential Equation Model, Peng Zhong

Doctoral Dissertations

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior.

Cholera remains a public health threat in many parts of the world and improved …

Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, Lisa M. Kuhn

Doctoral Dissertations

In recent years, much research has been motivated by the idea of biologically-inspired flight. It is a conjecture of the United States Air Force that incorporating characteristics of biological flight into air vehicles will significantly improve the maneuverability and performance of modern aircraft. Although there are studies which involve the aerodynamics, structural dynamics, modeling, and control of flexible wing micro aerial vehicles (MAVs), issues of control and vehicular modeling as a whole are largely unexplored. Modeling with such dynamics lends itself to systems of partial differential equations (PDEs) with nonlinearities, and limited control theory is available for such systems.

In …

A Numerical Method For Studying Thermal Deformation In 3d Double-Layered Thin Films With Imperfect Interfacial Thermal Contact Exposed To Ultrashort-Pulsed Lasers, Runzhou Liu

Doctoral Dissertations

Micro heat transfer induced by Ultrashort-pulsed lasers is an important research topic in mechanical engineering and material science. In order to apply ultrashort-pulsed lasers successfully, studying the thermal deformation in double-layered thin films with imperfect thermal interfacial contact induced by ultrashort-pulsed lasers is important for preventing thermal damage. For the ultrashort-pulsed laser, the thermal damage is different from that caused by the long-pulsed lasers, and ultrafast cracks occur after heating.

This dissertation presents a new finite difference method for investigating the thermal deformation in a 3D gold-chromium thin film with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers. The method …

Improving The Accuracy Of The Generalized Fdtd-Q Scheme For Solving The Linear Time-Dependent Schrödinger Equation, James John Elliot Iii

Doctoral Dissertations

This dissertation improves the accuracy of the Generalized Finite Difference Time Domain (FDTD) scheme by determining a differential operator that is capable of achieving reasonable accuracy when used to obtain even-order derivatives up to order fourteen. The Generalized FDTD scheme is an explicit, scheme used to solve the time-dependent Schrödinger equation, and being an explicit scheme, it must utilize a carefully devised ratio of the temporal step to the spatial step to maintain numerical stability. This ratio is called the mesh ratio, and the Generalized FDTD scheme allows this ratio to be significantly relaxed. As the mesh ratio increases, the …

Dynamics Of Mushy Layers On A Finite Domain, Nicholas Ray Gewecke

Doctoral Dissertations

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Mushy layers are regions of intermixed liquid and solid which can arise during the solidification of binary alloys, generally consisting of dendritic solids with solute-rich liquid in the interstices. They occur due to an instability resulting from the buildup of rejected solute along the solidification front. Liquid ahead of the front becomes supercooled, so disturbances to the interface grow more rapidly than the interface itself. A simple experiment has a tank filled with a uniform solution at uniform temperature being placed upon a cold surface. Early on, a small solid layer forms at the …

Shape Reconstruction And Classification Using The Response Matrix, Wei Wang

Doctoral Dissertations

This dissertation presents a novel method for the inverse scattering problem for extended target. The acoustic or electromagnetic wave is scattered by the target and received by all the transducers around the target. The scattered field on all the transducers forms the response matrix which contains the information of the geometry of the target. The objective of the inverse scattering problem is to reconstruct the shape of the scatter using the Response Matrix.

There are two types of numerical methods for solving the inverse problem: the direct imaging method and the iterative method. Two direct imaging methods, MUSIC method and …

A Numerical Method For Solving The Elliptic And Elasticity Interface Problems, Liqun Wang

Doctoral Dissertations

Interface problems arise when dealing with physical problems composed of different materials or of the same material at different states. Because of the irregularity along interfaces, many common numerical methods do not work, or work poorly, for interface problems. Matrix-coefficient elliptic and elasticity equations with oscillatory solutions and sharp-edged interfaces are especially complicated and challenging for most existing methods. An accurate and efficient method is desired.

In 1999, the boundary condition capturing method was proposed to deal with Poisson equations with interfaces whose variable coefficients and solutions may be discontinuous. In 2003, a weak formulation was derived. Built on previous …

Results In Lattices, Ortholattices, And Graphs, Jianning Su

Doctoral Dissertations

This dissertation contains two parts: lattice theory and graph theory. In the lattice theory part, we have two main subjects. First, the class of all distributive lattices is one of the most familiar classes of lattices. We introduce "π-versions" of five familiar equivalent conditions for distributivity by applying the various conditions to 3-element antichains only. We prove that they are inequivalent concepts, and characterize them via exclusion systems. A lattice L satisfies D0π, if a ✶ (b ✶ c) ≤ (a ✶ b) ✶ c for all 3-element antichains { a, b, c}. We consider …

Vascular Countercurrent Network For 3d Triple-Layered Skin Structure With Radiation Heating, Xiaoqi Zeng

Doctoral Dissertations

Heat transfer in living tissue has become more and more attention for researchers, because high thermal radiation produced by intense fire, such as wild fires, chemical fires, accidents, warfare, terrorism, etc, is often encountered in human's daily life. Living tissue is a heterogeneous organ consisting of cellular tissue and blood vessels, and heat transfer in cellular tissue and blood vessel is quite different, because the blood vessels provide channels for fast heat transfer. The metabolic heat generation, heat conduction and blood perfusion in soft tissue, convection and perfusion of the arterial-venous blood through the capillary, and interaction with the environment …