Browsing by Department "Mathematics"
Now showing items 120 of 237

A Computational Approach to Classifying Low Rank Modular Tensor Categories
(20180807)The dissertation introduces a computational approach to classifying low rank modular categories up to their modular data. The modular data of a modular category is a pair of matrices, (S; T). Virtually all the numerical ... 
A Continuum Mechanics Model of Stress Mediated Arterial Growth during Hypertension Using an Eulerian Frame
(20150728)Hypertension is a medical condition in which persistent high blood pressure causes the heart to exert more energy to circulate blood through the blood vessels and can lead to life threatening conditions including stroke, ... 
A Local Minimax Method Using the Generalized Nehari Manifold for Finding Differential Saddles
(20171130)In order to find the first few unconstrained saddles of functionals with different types of variational structures, a new local minimax method (LMM), based on a dynamics of points on virtual geometric objects such as curves, ... 
A Novel Methodology for Creating Auto Generated SpringBased Truss Problems Through Mechanix
(20181128)Software that provides automated teaching assistance and instantaneous feedback for students has revolutionized the modern classroom. In addition to helping instructors manage large classes, the interactive experience can ... 
ADiscriminant Varieties and Amoebae
(20130515)The motivating question behind this body of research is Smale’s 17th problem: Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average, in polynomial time with a uniform algorithm? While ... 
Adaptive Generalized Multiscale Model Reduction Techniques for Problems in Perforated Domains
(20180524)Multiscale modeling of complex physical phenomena in many areas, including hydrogeology, material science, chemistry and biology, consists of solving problems in highly heterogeneous porous media. In many of these applications, ... 
Adaptivity and Online Basis Construction for Generalized Multiscale Finite Element Methods
(20170718)Many problems in application involve media with multiple scale, for example, in composite materials, porous media. These problems are usually computationally challenging since fine grid computation is extremely expensive. ... 
The Amalgamated Free Product of Hyperfinite von Neumann Algebras
(20120716)We examine the amalgamated free product of hyperfinite von Neumann algebras. First we describe the amalgamated free product of hyperfinite von Neumann algebras over finite dimensional subalgebras. In this case the result ... 
An Energy Formulation of Surface Tension or Willmore Force For TwoPhase Flow
(20170712)The motion of a biological cell in liquid is a rich subject for modeling. In the early 1970’s, it was realized by Canham that biological vesicles with lipid bilayer membranes reach a steady state shape that minimizes ... 
Analysis and computation of multiple unstable solutions to nonlinear elliptic systems
(20090515)We study computational theory and methods for finding multiple unstable solutions (corresponding to saddle points) to three types of nonlinear variational elliptic systems: cooperative, noncooperative, and Hamiltonian. We ... 
Analysis of a PML method applied to computation to resonances in open systems and acoustic scattering problems
(20100114)We consider computation of resonances in open systems and acoustic scattering problems. These problems are posed on an unbounded domain and domain truncation is required for the numerical computation. In this paper, a ... 
Analysis of Avian Migration using Scheper's Model
(20140429)Many species of birds migrate nocturnally. In nocturnally migrating birds, endogenous circadian and circannual rhythms serve as biological pacemakers (clocks). They are responsible for an individual’s migratory behavioral ... 
Analysis of finite element approximation and iterative methods for timedependent Maxwell problems
(Texas A&M University, 20040930)In this dissertation we are concerned with the analysis of the finite element method for the timedependent Maxwell interface problem when Nedelec and RaviartThomas finite elements are employed and preconditioning ... 
Analysis of the Threedimensional Superradiance Problem and Some Generalizations
(20111021)We study the integral equation related to the three and higher dimensional superradiance problem. Collective radiation phenomena has attracted the attention of many physicists and chemists since the pioneering work of R. ... 
Application of L1 Minimization Technique to Image SuperResolution and Surface Reconstruction
(20130506)A surface reconstruction and image enhancement nonlinear finite element technique based on minimization of L1 norm of the total variation of the gradient is introduced. Since minimization in the L1 norm is computationally ... 
Applications of algebraic geometry to object/image recognition
(20090602)In recent years, new approaches to the problem of Automated Target Recognition using techniques of shape theory and algebraic geometry have been explored. The power of this shape theoretic approach is that it allows one ... 
Applications of Potential Theory to the Analysis of Property (P_(q))
(20140707)In the dissertation, we apply classical potential theory to study Property (P_(q)) and its relation with the compactness of the ∂ ̅Neumann operator N_(q). The main results in the dissertation consist of four parts. In ... 
Approximation and interpolation employing divergencefree radial basis functions with applications
(Texas A&M University, 20040930)Approximation and interpolation employing radial basis functions has found important applications since the early 1980's in areas such as signal processing, medical imaging, as well as neural networks. Several ... 
Approximation of linear partial differential equations on spheres
(Texas A&M University, 20040930)The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as ... 
Approximation Techniques for Incompressible Flows with Heterogeneous Properties
(20111021)We study approximation techniques for incompressible flows with heterogeneous properties. Speci cally, we study two types of phenomena. The first is the flow of a viscous incompressible fluid through a rigid porous ...