Applied Mathematics Commons^™

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Pulses And Snakes In Ginzburg-Landau Equation, S.C. Mancas, Roy S. Choudhury

Publications

Using a variational formulation for partial differential equations combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the dependence of both their shape and stability on the physical parameters of the cubic-quintic Ginzburg–Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the CGLE …

A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids, Adrian Constantin, Rossen Ivanov

Articles

We provide a Hamiltonian formulation for the governing equations describing the two-dimensional nonlinear interaction between coupled surfacewaves, internalwaves, and an underlying current with piecewise constant vorticity, in a two-layered fluid overlying a flat bed. This Hamiltonian structure is a starting point for the derivation of simpler models, which can be obtained systematically by expanding the Hamiltonian in dimensionless parameters. These enable an in-depth study of the coupling between the surface and internal waves, and how both these wave systems interact with the background current.

Blurring And Deblurring Digital Images Using The Dihedral Group, Husein Hadi Abbas Jassim, Zahir M. Hussain, Hind R.M. Shaaban, Kawther B.R. Al-Dbag

Research outputs 2014 to 2021

A new method of blurring and deblurring digital images is presented. The approach is based on using new filters generating from average filter and H-filters using the action of the dihedral group. These filters are called HB-filters; used to cause a motion blur and then deblurring affected images. Also, enhancing images using HB-filters is presented as compared to other methods like Average, Gaussian, and Motion. Results and analysis show that the HB-filters are better in peak signal to noise ratio (PSNR) and RMSE.

Process Design, Dynamics, And Techno-Economic Analysis Of A Sustainable Coal, Wind, And Small Modular Nuclear Reactor Hybrid Energy System, Kyle Lee Buchheit

Doctoral Dissertations

"The availability of cheap electricity is one of the biggest factors for improving quality of life. With the debate on the effects of carbon dioxide emissions continuing, several countries have either implemented or are considering the reduction of emissions through various economic means. The inclusion of a monetary penalty on carbon emissions would increase the prices of electricity produced by carbon-based sources. The push for large-scale renewable sources of energy has met problems with regards to energy storage and availability. The proposed coal, wind, and nuclear hybrid energy system would combine a renewable energy source, wind, with traditional and stable …

Increasing Student Engagement In The Secondary Math Classroom, Chantell Holloway Walker

LSU Master's Theses

This thesis reports on a professional development package developed by the author to help three teachers increase the level of student engagement in their math classrooms. There were three phases: 1) initial presentation of strategies and sample lessons, 2) classroom implementation, 3) reflection and evaluation. As a result of the professional development, the Louisiana Compass Teacher Evaluation Rubric scores of the teachers improved in the area of student engagement. This thesis can be used as a guide for principals or instructional specialists who wish to provide professional development for small groups of teachers, with a focus on increasing student engagement.

The Interplay Between Wnt Mediated Expansion And Negative Regulation Of Growth Promotes Robust Intestinal Crypt Structure And Homeostasis, Huijing Du, Qing Nie, William R. Holmes

Department of Mathematics: Faculty Publications

The epithelium of the small intestinal crypt, which has a vital role in protecting the underlying tissue from the harsh intestinal environment, is completely renewed every 4–5 days by a small pool of stem cells at the base of each crypt. How is this renewal controlled and homeostasis maintained, particularly given the rapid nature of this process? Here, based on the recent observations from in vitro “mini gut” studies, we use a hybrid stochastic model of the crypt to investigate how exogenous niche signaling (from Wnt and BMP) combines with auto-regulation to promote homeostasis. This model builds on the sub-cellular …

Application Of Loglinear Models To Claims Triangle Runoff Data, Netanya Lee Martin

Masters Theses

"In this thesis, we presented in detail different aspects of Verrall's chain ladder method and their advantages and disadvantages. Insurance companies must ensure there are enough reserves to cover future claims. To that end, it is useful to estimate mean expected losses. The chain ladder technique under a general linear model is the most widely used method for such estimation in property and casualty insurance. Verrall's chain ladder technique develops estimators for loss development ratios, mean expected ultimate claims, Bayesian premiums, and Bühlmann credibility premiums. The chain ladder technique can be used to estimate loss development in cases where data …

Exploring A Generalized Partial Borda Count Voting System, Christiane Koffi

Senior Projects Spring 2015

The main purpose of an election is to generate a fair end result in which everyone's opinion is gathered into a collective decision. This project focuses on Voting Theory, the mathematical study of voting systems. Because different voting systems yield different end results, the challenge begins with finding a voting system that will result in a fair election. Although there are many different voting systems, in this project we focus on the Partial Borda Count Voting System, which uses partially ordered sets (posets), instead of the linearly ordered ballots used in traditional elections, to rank its candidates. We introduce the …

A Mathematical Model Of The Effect Of Aspirin On Blood Clotting, Breeana J. Johng

Scripps Senior Theses

In this paper, we provide a mathematical model of the effect of aspirin on blood clotting. The model tracks the enzyme prostaglandin H synthase and an important blood clotting factor, thromboxane A₂, in the form of thromboxane B₂. Through model analysis, we determine conditions under which the reactions of prostaglandin H synthase are self-sustaining. Lastly, through numerical simulations, we demonstrate that the model accurately captures the steady-state chemical concentrations of interest in blood, both with and without aspirin treatment.

Modeling Contagion In The Eurozone Crisis Via Dynamical Systems, Giuseppe Castellacci, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We recently (Castellacci and Choi, 2013) formulated a theoretical framework for the modeling of financial instability contagion using the theories of dynamical systems. Here, our main goal is to model the Eurozone financial crisis within that framework. The underlying system comprises many economic agents that belong to several subsystems. In each instantiation of this framework, the hierarchy and nesting of the subsystems is dictated by the nature of the problem at hand. We describe in great detail how a suitable model can be set up for the Eurozone crisis. The dynamical system is defined by the evolution of the wealths …

The Coupled Within- And Between-Host Dynamics In The Evolution Of Hiv/Aids In China, Jie Lou, Hongna Zhou, Dong Liang, Zhen Jin, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this work, we develop and analyze mathematical models for the coupled within-host and between-host dynamics caricaturing the evolution of HIV/AIDS. The host population is divided into susceptible, the infected without receiving treatment and the infected receiving ART treatment in accordance with China’s Four-Free-One-Care Policy. The within-host model is a typical ODE model adopted from literatures. The between-host model incorporates age-since-infection described by a system of integrodifferential equations. The two models are coupled via the viral load and number of CD4+ T cells of within the hosts. For the between-host model with an arbitrarily selected HIV infected individual, we focus …

The Krylov Subspace Methods For The Computation Of Matrix Exponentials, Hao Wang

Theses and Dissertations--Mathematics

The problem of computing the matrix exponential e^tA arises in many theoretical and practical problems. Many methods have been developed to accurately and efficiently compute this matrix function or its product with a vector, i.e., e^tAv. In the past few decades, with the increasing need of the computation for large sparse matrices, iterative methods such as the Krylov subspace methods have proved to be a powerful class of methods in dealing with many linear algebra problems. The Krylov subspace methods have been introduced for computing matrix exponentials by Gallopoulos and Saad, and the corresponding error bounds …

Analysis And Constructions Of Subspace Codes, Carolyn E. Troha

Theses and Dissertations--Mathematics

Random network coding is the most effcient way to send data across a network, but it is very susceptible to errors and erasures. In 2008, Kotter and Kschischang introduced subspace codes as an algebraic approach to error correcting in random network coding. Since this paper, there has been much work in constructing large subspace codes, as well as exploring the properties of such codes. This dissertation explores properties of one particular construction and introduces a new construction for subspace codes. We begin by exploring properties of irreducible cyclic orbit codes, which were introduced in 2011 by Rosenthal et al. As …

Spread And Interaction Of Epidemics And Information On Adaptive Social Networks, Yunhan Long

Dissertations, Theses, and Masters Projects

The spread of diseases and opinions has profoundly affected the development of human societies. The structure of the underlying social network may change as a result of individuals changing their social connections in response to an ongoing epidemic or opinion spreading, either for self protection or as an expression of personal values. The interaction of spreading processes and the underlying network structure has been a focus of many recent studies. In this dissertation, we construct models to better incorporate heterogeneous responses to disease spread and attempted opinion spread.;We first model the simultaneous spread of an epidemic and awareness about the …

One-Bit Compressive Sensing With Partial Support Information, Phillip North

CMC Senior Theses

This work develops novel algorithms for incorporating prior-support information into the field of One-Bit Compressed Sensing. Traditionally, Compressed Sensing is used for acquiring high-dimensional signals from few linear measurements. In applications, it is often the case that we have some knowledge of the structure of our signal(s) beforehand, and thus we would like to leverage it to attain more accurate and efficient recovery. Additionally, the Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization. Indeed, the field of One-Bit Compressive Sensing aims to recover a signal from measurements reduced to only their sign-bit. This …

An Exposition And Calibration Of The Ho-Lee Model Of Interest Rates, Benjamin I. Lawson

CMC Senior Theses

The purpose of this paper is to create an easily understandable version of the Ho-Lee interest rate model. The first part analyzes the model in detail, and the second part calibrates it to demonstrate how it can be applied to real market data.

An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper

Theses and Dissertations

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.

First, we create a …

Applications Of Stability Analysis To Nonlinear Discrete Dynamical Systems Modeling Interactions, Jonathan L. Hughes

Theses and Dissertations

Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model …

Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan

Theses and Dissertations

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.

We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation …