Browsing Dissertations & Theses by Title
Now showing items 46-65 of 173
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From Discrete To Continuous Models Of Cell Movement: An Application To Medical Implants
(Mathematics, 2013-03-20)Mathematical modeling of cell movement is needed to aid in the deeper understanding of vital processes such as embryogenesis, angiogenesis, tumor metastasis, and immune reactions to foreign bodies. In this work, cell ... -
A Generalized Approach To Darboux Transformations For Differential Equations
(Mathematics, 2014-07-14)A Darboux transformation is a mathematical procedure to produce a solution to a differential equation when the solution to a related differential equation is known. The basic idea behind a Darboux transformation is to ... -
Generalized Inverse Scattering Transform For The Nonlinear Schrödinger Equation
(Mathematics, 2008-08-08)The nonlinear Schrödinger (NLS) equation describes wave propagation in optical fibers, and it is one of the most well-known nonlinear partial differential equations. In 1972 Zakharov and Shabat introduced a powerful method ... -
The Generalized Two-component Hunter-Saxton System
(Mathematics, 2013-07-22)This thesis is concerned with the generalized two-component Hunter-Saxton system. In the periodic setting, we study the wave-breaking phenomenon and global existence for the generalized two-component Hunter-Saxton system. ... -
A Globally Convergent Numerical Method For Coefficient Inverse Problems
(Mathematics, 2009-09-16)In our terminology "globally convergent numerical method" means a numerical method, whose convergence to a good approximation for the correct solution is independent of the initial approximation. A new numerical imaging ... -
Haplotype-based Statistical Inference For Case-control Genetic Association Studies With Complex Sampling
(Mathematics, 2014-09-17)With the advances in human genome research, it is now believed that the risks of many complex diseases are triggered by the interplay of genetic susceptibilities and environmental exposures. The population-based case-control ... -
High Order Compact Scheme For Discontinuous Differential Equations
(Mathematics, 2011-07-14)A high order implicit second derivative compact method is given which is similar the Adams-Moulton method, but requiring only two steps for sixth order. This method is used in both predictor-corrector and Newton's method ... -
High Order DNS For Late Flow Transition
(Mathematics, 2012-07-25)In this report, a new high order scheme for boundary points is introduced when calculating the derivative of smooth functions by Compact Scheme. The primitive function reconstruction method of ENO schemes is applied to ... -
HIGH ORDER DNS FOR VORTEX STRUCTURE IN LATE FLOW TRANSITION
(2017-08-02)Turbulence is still a world puzzle after over one hundred years research, and the current and classical theories brim with self-contradictions. C. Liu proposed a new theory on turbulence generation and structure after 28 ... -
High Order LES For Supersonic Ramp Flow Control With MVG
(Mathematics, 2012-07-25)An implicitly implemented large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with and without control at Mach 2.5 and Re=5760. Flow control ... -
High Order Numerical Schemes For PDEs And Applications To CFD
(Mathematics, 2014-03-12)In the past two decades, many efforts have been made in developing high-order schemes with high resolution, such as compact scheme, essentially non-oscillatory scheme (ENO), weighted essentially non-oscillatory scheme ... -
High Order Weighted Compact Boundary Condition
(Mathematics, 2008-09-17)In multi-dimension flows, we expect to have problems at the boundaries when a shock hits or reflects at the boundary wall the remedy to this would be to develop weighted boundary conditions similar to the Weighted Compact ... -
High-order Numerical Schemes For High-speed Flows
(Mathematics, 2009-09-16)A numerical scheme with high order of accuracy is necessary to resolve small length scales in flow transition and turbulence processes. However, numerical simulation for shock-boundary layer interaction, shock-acoustic ... -
HIGHER-ORDER NONSTANDARD FINITE DIFFERENCE METHODS FOR AUTONOMOUS DIFFERENTIAL EQUATIONS WITH APPLICATIONS IN MATHEMATICAL ECOLOGY
(2022-08-08)Nonstandard finite difference (NSFD) methods have been widely used to numerically solve various problems in biology. In recent years, NSFD methods have been proposed that preserve essential properties of the solutions of ... -
Image Analysis Based on Differential Operators with Applications to Brain MRIs
(2019-07-25)In differential geometry, computational diffeomorphism (smooth and invertible mapping) has become a fast-growing field in developing the theoretical frameworks and computational toolboxes for the tasks such as computer ... -
Image Reconstruction from Incomplete Radon Data and Generalized Principal Component Analysis
(2017-08-11)Image reconstruction in various types of tomography requires inversion of the Radon transform and its generalizations. While there are many stable and robust algorithms for such inversions from reasonably well sampled data, ... -
Impact of domestic animals on prevalence of vector-borne diseases in humans
(2020-06-05)Vector-borne infectious diseases are one of the leading problems for public health worldwide, particularly in underdeveloped and developing countries. These diseases infect humans through the bite of infected vectors. The ... -
The Impact Of Vaccination And Multiple Types Of HPV On Cervical Cancer
(Mathematics, 2008-09-17)Understanding the relationship between multiple strains of human papillomavirus and cervical cancer may play a key role in vaccination strategies for the virus. In this article we formulate a model with two strains of ... -
The Influence Of Dynamic Visualization On Undergraduate Calculus Learning
The urgent need in the United States to produce an additional one million graduates in the areas of science, technology, engineering and mathematics and previous research into why students choose to abandon their quest to ... -
INVERSE PROBLEMS AND FORWARD PROPAGATION OF OPTICAL FLOW
(2020-08-24)Optical flow is a concept originally introduced in computer vision that quantifies, and aids in the presentation of, motion (flow field) between two or more images. In essence, it is a solution of an inverse problem ...