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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
Most of the data encountered is bounded nonlinear data. The Universe is bounded, planets are sphere like shaped objects, and life growing on Earth comes in various shapes and colors that can hardly be represented as points on a linear...
Two numerical methods are developed and analyzed for studying two-phase jet flows. The first numerical method solves the eigenvalue problem for the matrix system that is constructed from the pseudo-spectral discretization of the 3D...
Standard spatial discretization schemes for dynamical system (DS), usually lead to large-scale, high-dimensional, and in general, nonlinear systems of ordinary differential equations.Due to limited computational and storage capabilities, ...
The motion of vortices in a Type II superconductor destroys the material's superconductivity because it dissipates energy and causes resistance. When a transport current is applied to a clean Type-II superconductor in the mixed state, ...
The objective of this dissertation is to study impulse control problems in situations where the volatility of the underlying process is not constant. First, we explore the case where the dynamics of the underlying process are modified...
In 2001, the discovery of the intermetallic compound superconductor MgB2 having a critical temperature of 39K stirred up great interest in using a generalization of the Ginzburg-Landau model, namely the two-band time-dependent Ginzburg...
This thesis investigates nonlinear systems that are dispersive and conservative in nature and well-approximated by the nonlinear Schrödinger (NLS) equation. The NLS equation is the prototypical equation for describing such phenomena and...
A Computational Aeroacoustics [CAA] cascade model has been built to study the generation and propagation mechanisms of noise resulting from the interaction of the fan and outlet guide vanes in a high-bypass ratio turbofan engine. Also...
No-Reference Natural Image/Video Quality Assessment of Noisy, Blurry, or Compressed Images/Videos Based on Hybrid Curvelet, Wavelet and Cosine Transforms
In this thesis, we first propose a new Image Quality Assessment (IQA) method based on a hybrid of curvelet, wavelet, and cosine transforms, called the Hybrid No-reference (HNR) model. From the properties of natural scene statistics, the...
In this dissertation we look at a stochastic volatility model with coupled additive and multiplicative noise. We begin by explaining the suitability of the model for the logarithm of volatility by looking at the skewness and kurtosis. We...
A finite dimensional amplitude equation model of 2-dimensional double-diffusive convection near a quadruple-zero (codimension 4) bifurcation point is derived using center manifold reduction. The derivation employs small perturbation...
In this manuscript, we propose space-time spectral element methods to solve problems arising from fluid dynamics and materials science. Many engineering applications require one to solve complex problems, such as flows containing multi...
A unified, asymptotically-preserving method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated Semi-Lagrangian advection algorithm is presented. The new algorithm uses a semi-implicit...
This dissertation considers optimization problems on a Riemannian matrix manifold ℳ⊆ℝ[superscript m x n] with an additional rank inequality constraint. A novel technique for building new rank-related geometric objects from known...
Neurons and endocrine cells display various patterns of electrical activity, including periodic bursting. Bursting oscillations are characterized by the alternation between periods of fast spiking (the active phase) and quiescent periods...
We develop partial differential equation methods with well-posed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space...
We develop a spectral element method to price European options under the Black-Scholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre...
Karst aquifers are vulnerable to contamination, as conduits and fractures in the aquifers are preferential flow paths where contaminants move fast. On the other hand, the presence of conduits and fractures make groundwater modeling for...
Mesh generation in regions in Euclidean space is a central task in computational science, especially for commonly used numerical methods for the solution of partial differential equations (PDEs), e.g., finite element and finite volume...
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