Physical Sciences and Mathematics Commons^™

Nonlocal Boundary Value Problems For Linear Hyperbolic Systems With Two Independent Variables, Afrah Almutairi

Theses and Dissertations

Nonlocal boundary value problems in a characteristic rectangle for second order linear hyperbolic systems are considered. There are established: (i) Unimprovable sufficient conditions for general boundary value problems to possess the Fredholm property; (ii) Optimal sufficient conditions of unique solvability of general boundary value problems; (iii) Effective sufficient conditions for doubly periodic problems to possess the Fredholm property; (iv) Unimprovable sufficient conditions of unique solvability of doubly periodic problems; (v) Effective sufficient conditions for boundary value problems of periodic type to possess the Fredholm property; (vi) Unimprovable sufficient conditions of unique solvability of boundary value problems of periodic type; (vii) …

Stability Analysis Of Neutral Functional Differential Equations Arising In Partial Element Equivalent Circuit Models, Howard Michael Allison

Theses and Dissertations

Neutral Functional Differential Equations (NFDEs) arise in the study of the Partial Element Equivalent Circuit (PEEC) model with time delays. We present sufficient conditions for asymptotic stability and global stability in the delays of the PEEC NFDE’s, using Lyapunov-Razumikhin function methods.. We develop, for the first time, a standard mixing-type nonlinearity for the PEEC NFDEs. Introducing time invariant and time varying nonlinear perturbation to the PEEC NFDEs, we develop sufficient conditions for stability of the nonlinear perturbed PEEC NFDEs and convergence of the nonlinear system to the original stable linear autonomous system. We also develop sufficient conditions for stability and …

Some Free Boundary Problems For The Nonlinear Degenerate Multidimensional Parabolic Equations Modeling Reaction-Diffusion Processes, Amna Abu Weden

Theses and Dissertations

This dissertation presents a full classification of the short-time behavior of the interfaces or free boundaries for the nonlinear second order degenerate multidimensional parabolic partial differential equation (PDE) ut −∆u m +buβ = 0, x ∈ R N ,0 < t < T (1) with m > 0, β > 0,b ∈ R, arising in various applications in fluid mechanics, filtration of oil or gas in a porous media, plasma physics, reaction-diffusion equations in chemical kinetics, population dynamics in mathematical biology etc. as a mathematical model of nonlinear diffusion phenomena in the presence of the absorption or release of energy. Cauchy problem with compactly supported and nonnegative initial function …

Computational Models For Biological Locomotion In Gels, Hashim Mohammed Alshehri

Theses and Dissertations

We investigated Low Reynold’s Number Locomotion in two-phase biological gels. The gel is composed of two materials: a viscous fluid solvent phase and a viscoelastic polymer network phase. A novel Two-phase Immersed Boundary Method (IBM) is developed to simulate the complicated interactions between an elastic boundary and a mixture of two fluids with very different physical properties. A further extension of the method is developed for the case where fluids satisfy partial-slip and free-slip conditions on the elastic boundary. Our major conclusions are summarized as following: (i) Our numerical scheme is proved to be robust and efficient. It can successfully …

Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen

Dissertations

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.

In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic. …

Dynamical Modeling In Cell Biology With Ordinary Differential Equations, Renee Marie Dale

LSU Doctoral Dissertations

Dynamical systems have been of interest to biologists and mathematicians alike. Many processes in biology lend themselves to dynamical study. Movement, change, and response to stimuli are dynamical characteristics that define what is 'alive'. A scientific relationship between these two fields is therefore natural. In this thesis, I describe how my PhD research variously related to biological, mathematical, and computational problems in cell biology. In chapter 1 I introduce some of the current problems in the field. In chapter 2, my mathematical model of firefly luciferase in vivo shows the importance of dynamical models to understand systems. Data originally collected …

Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

Mathematics & Statistics ETDs

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension and …

Planck's And Callendar's Blackbody Radiation Formulas And Their Fitness To Experimental Data, Max Tran

Publications and Research

In this paper, we compare the blackbody radiation density formula obtained with classical physics by Hugh L Callendar and the formula obtained by Max Planck using quantization of energy. We use R and Maxima to analyze their fitness on coordinating experimental data and indicate some limitations with experiments in this area.

Deep Learning (Partly) Demystified, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Successes of deep learning are partly due to appropriate selection of activation function, pooling functions, etc. Most of these choices have been made based on empirical comparison and heuristic ideas. In this paper, we show that many of these choices -- and the surprising success of deep learning in the first place -- can be explained by reasonably simple and natural mathematics.

The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.

Properly Handling Negative Values In The Calculation Of Binding Constants By Physicochemical Modeling Of Spectroscopic Titration Data, Nathanael P. Kazmierczak, Douglas A. Vander Griend

University Faculty Publications and Creative Works

To implement equilibrium hard-modeling of spectroscopic titration data, the analyst must make a variety of crucial data processing choices that address negative absorbance and molar absorptivity values. The efficacy of three such methodological options is evaluated via high-throughput Monte Carlo simulations, root-mean-square error surface mapping, and two mathematical theorems. Accuracy of the calculated binding constant values constitutes the key figure of merit used to compare different data analysis approaches. First, using singular value decomposition to filter the raw absorbance data prior to modeling often reduces the number of negative values involved but has little effect on the calculated binding constant …

How Can We Explain Different Number Systems?, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At present, we mostly use decimal (base-10) number system, but in the past, many other systems were used: base-20, base-60 -- which is still reflected in how we divide an hour into minutes and a minute into seconds -- and many others. There is a known explanation for the base-60 system: 60 is the smallest number that can be divided by 2, by 3, by 4, by 5, and by 6. Because of this, e.g., half an hour, one-third of an hour, all the way to one-sixth of an hour all correspond to a whole number of minutes. In this …

On The Sparre-Andersen Risk Models, Ruixi Zhang

Electronic Thesis and Dissertation Repository

This thesis develops several strategies for calculating ruin-related quantities for a variety of extended risk models. We focus on the Sparre-Andersen risk model, also known as the renewal risk model. The idea of arbitrary distribution for the waiting time between claim payments arose in the 1950’s from the collective risk theory, and received many extensions and modifications in recent years. Our goal is to tackle model assumptions that are either too relaxed for traditional methods to apply, or so complicated that elaborate algebraic tools are needed to obtain explicit solutions.

In Chapter 2, we consider a Lévy risk process and …

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Facuty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

Why Does Ramanujan, The Man Who Knew Infinity, Matter?, Ken Ono

Dalrymple Lecture Series

Dr. Ken Ono is the Thomas Jefferson Professor of Mathematics at the University of Virginia, the Asa Griggs Candler Professor of Mathematics at Emory University, and the vice president of the American Mathematical Society.He is an associate producer of the film The Man Who Knew Infinity starring Dev Patel and Jeremy Irons about Srinivasa Ramanujan, a self-trained two-time college dropout who left behind three notebooks filled with equations that mathematicians are still trying to figure out today. Ramanujan claimed that his ideas came to him as visions from an Indian goddess. This lecture is about why Ramanujan matters. The answers …

Mathematics Saves Lives: Models And Signals Enabling Medicine And Biology, Raina Robeva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analyzing Student Loan Debt Using Seir Compartmental Model Of Epidemiology, Kavya Ravishankar, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effects Of Excess Nutrients On Tri-Trophic Food Chains In The Aquatic Ecosystem, Lale Asik, Ming Chen, Angela Peace

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Applying Methods Of The Theory Of Heterogeneous Populations To The Problem Of Pathogen Co-Existence, Eric Sarfo Amponsah

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Evaluation Of Age- And Risk-Based Mass Drug Administration Policies To Control Soil-Transmitted Helminths: A Mathematical Modeling Study Of Ghana, Mugdha Thakur

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Agent-Based Ecological Model Of West Nile Virus For Classroom Use, Stuart Thiel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Agent-Based Modeling Approach For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Joey Gaudy, Craig Garzella

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Sperm Motility In Groups, Julie Simons

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Estimation Within An Sir Model Of Chestnut Blight In North America, Anita Davelos Baines, Hope B. Anderson, John S. Mcalister, Robert F. Allen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling And Analysis Of American Chestnut Blight In North America, Robert F. Allen, Anita D. Baines, Hope B. Anderson, John S. Mcalister, Tatum D. Rask, Maia Richards-Dinger

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring Modeling By Programming: Insights From Numerical Experimentation, Sean Laverty, Brittany E. Bannish

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Distribution In Carbon Uptake Across A Global Measurement Network Of Terrestrial Ecosystems, John Zobitz, Madeline Oswood

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Seasonal Dynamics Of Swimmer's Itch And The Efficacy Of Potential Treatment Options, James Peirce

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.