Facial recognition has become increasingly important in recent years, due to the wide range of applications it has in fields such as security, surveillance, and human-computer interaction. Three popular methods for facial recognition are the Principal Component Analysis (PCA), Karhunen-Loeve Expansions, which is fundamentally a continuous form of PCA but...
In this paper, we discuss two possible modifications to a numerical solution method for a model of microbiologically induced calcite precipitation (MICP). MICP provides a means to seal cracks in the surfaces of geological structures. From a mathematical and computational point of view MICP has very interesting features which make...
In previous papers by Awrejcewicz in 1986 and Narayanan and Jayaraman in 1991, it was claimed that the nonlinear oscillator with dry friction exhibited chaos for several forcing frequencies. The chaos determination was achieved using the characteristic exponent of Lyapunov which requires the right-hand side of the differential equation to...
This thesis explores student understanding of divergence in physics settings. The various uses of divergence in physics are detailed. Textbook approaches to divergence are categorized as geometric, curvilinear coordinate, discussion-based, and algebraic statement. Textbook approaches to the divergence theorem are categorized as geometric, equivalent integrals, mathematical statement with explanation, and...
The growing need for cleaner fuels requires the development of better deep fuel desulfurization methods. The current study presents a reaction model for the mechanism of dibenzothiophene oxidization by dissolved oxygen occurring in a corona discharge microreactor. In the present work, a Finite Volume Method model of the reactor is...
In this work, we consider a convexity splitting scheme for a coupled phase field and energy equation, a modification of Stefan problem. The Stefan problem is a free boundary value problem that models the temperature in a homogeneous multiphase medium. Each phase is modeled using a heat diffusion parabolic partial...
Simulations of combustion and reacting flows often encounter stiffness in the equations governing chemical kinetics. Explicit solvers for these ordinary differential equations offer low computational expense, but typically cannot efficiently handle stiff systems. In contrast, implicit methods demand greater expense but offer unconditional stability—as a result, most reactive-flow solvers rely...
Wachspress rational functions are ratios of polynomials having certain properties which make them good candidates for basis functions in finite element methods. In addition. it had been theorized that Wachspress rational weight functions should Provide a full-resolution discretization of the neutral particle transport equation in thick diffusive regions, but this...
In source-detector radiation transport simulations, pulse height distributions are a useful metric in assessing the effectiveness of nuclear instrumentation. In the area of spectroscopy, pulse height distributions are used to identify an unknown source. It is widely believed that pulse height distributions cannot be created using deterministic methods. This quantity...
