Physical Sciences and Mathematics Commons^™

The Reasonable Effectiveness Of Mathematics In The Natural Sciences, Nicolas Fillion

Electronic Thesis and Dissertation Repository

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed.

I distinguish three forms of the …

Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman

Masters Theses

Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …

Stability And Convergence For Nonlinear Partial Differential Equations, Oday Mohammed Waheeb

Boise State University Theses and Dissertations

If used cautiously, numerical methods can be powerful tools to produce solutions to partial differential equations with or without known analytic solutions. The resulting numerical solutions may, with luck, produce stable and accurate solutions to the problem in question, or may produce solutions with no resemblance to the problem in question at all. More such numerical computations give no hope of solving this troublesome feature and one needs to resort to investing time in a theoretical approach. This thesis is devoted not solely to computations, but also to a theoretical analysis of the numerical methods used to generate computationally the …

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility …

Hard And Soft Error Resilience For One-Sided Dense Linear Algebra Algorithms, Peng Du

Doctoral Dissertations

Dense matrix factorizations, such as LU, Cholesky and QR, are widely used by scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This dissertation develops fault tolerance algorithms for one-sided dense matrix factorizations, which handles Both hard and soft errors.

For hard errors, we propose methods based on diskless checkpointing and Algorithm Based Fault Tolerance (ABFT) to provide full matrix protection, including the left and right factor that are normally seen in …

Degree Constrained Triangulation, Roshan Gyawali

UNLV Theses, Dissertations, Professional Papers, and Capstones

Triangulation of simple polygons or sets of points in two dimensions is a widely investigated problem in computational geometry. Some researchers have considered variations of triangulation problems that include minimum weight triangulation, de-launay triangulation and triangulation refinement. In this thesis we consider a constrained version of the triangulation problem that asks for triangulating a given domain (polygon or point sites) so that the resulting triangulation has an increased number of even degree vertices. This problem is called Degree Constrained Triangulation (DCT). We propose four algorithms to solve DCT problems. We also present experimental results based on the implementation of the …

Numerical Analysis Of First And Second Order Unconditional Energy Stable Schemes For Nonlocal Cahn-Hilliard And Allen-Cahn Equations, Zhen Guan

Doctoral Dissertations

This PhD dissertation concentrates on the numerical analysis of a family of fully discrete, energy stable schemes for nonlocal Cahn-Hilliard and Allen-Cahn type equations, which are integro-partial differential equations (IPDEs). These two IPDEs -- along with the evolution equation from dynamical density functional theory (DDFT), which is a generalization of the nonlocal Cahn-Hilliard equation -- are used to model a variety of physical and biological processes such as crystallization, phase transformations, and tumor growth. This dissertation advances the computational state-of-the-art related to this field in the following main contributions: (I) We propose and analyze a family of two-dimensional unconditionally energy …

Analysis Of Solvability And Applications Of Stochastic Optimal Control Problems Through Systems Of Forward-Backward Stochastic Differential Equations., Kirill Yevgenyevich Yakovlev

Doctoral Dissertations

A stochastic metapopulation model is investigated. The model is motivated by a deterministic model previously presented to model the black bear population of the Great Smoky Mountains in east Tennessee. The new model involves randomness and the associated methods and results differ greatly from the deterministic analogue. A stochastic differential equation is studied and the associated results are stated and proved. Connections between a parabolic partial differential equation and a system of forward-backward stochastic differential equations is analyzed.

A "four-step" numerical scheme and a Markovian type iterative numerical scheme are implemented. Algorithms and programs in the programming languages C and …

Pointwise Schauder Estimates Of Parabolic Equations In Carnot Groups, Heather Arielle Griffin

Graduate Theses and Dissertations

Schauder estimates were a historical stepping stone for establishing uniqueness and smoothness of solutions for certain classes of partial differential equations. Since that time, they have remained an essential tool in the field. Roughly speaking, the estimates state that the Holder continuity of the coefficient functions and inhomogeneous term implies the Holder continuity of the solution and its derivatives. This document establishes pointwise Schauder estimates for second order parabolic equations where the traditional role of derivatives are played by vector fields generated by the first layer of the Lie algebra stratification for a Carnot group. The Schauder estimates are shown …

A Local Radial Basis Function Method For The Numerical Solution Of Partial Differential Equations, Maggie Elizabeth Chenoweth

Theses, Dissertations and Capstones

Most traditional numerical methods for approximating the solutions of problems in science, engineering, and mathematics require the data to be arranged in a structured pattern and to be contained in a simply shaped region, such as a rectangle or circle. In many important applications, this severe restriction on structure cannot be met, and traditional numerical methods cannot be applied. In the 1970s, radial basis function (RBF) methods were developed to overcome the structure requirements of existing numerical methods. RBF methods are applicable with scattered data locations. As a result, the shape of the domain may be determined by the application …