Applied Mathematics Commons^™

Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

Articles

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion …

Management Of Invasive Allee Species, David Chan, C. M. Kent, D. M. Johnson

Mathematics and Applied Mathematics Publications

In this study, we use a discrete, two-patch population model of an Allee species to examine different methods in managing invasions. We first analytically examine the model to show the presence of the strong Allee effect, and then we numerically explore the model to test the effectiveness of different management strategies. As expected invasion is facilitated by lower Allee thresholds, greater carrying capacities and greater proportions of dispersers. These effects are interacting, however, and moderated by population growth rate. Using the gypsy moth as an example species, we demonstrate that the effectiveness of different invasion management strategies is context-dependent, combining …

Code For "Noise-Enhanced Coding In Phasic Neuron Spike Trains", Cheng Ly, Brent D. Doiron

Statistical Sciences and Operations Research Data

This zip file contains Matlab scripts and ode (XPP) files to calculate the statistics of the models in "Noise-Enhanced Coding in Phasic Neuron Spike Trains". This article is published in PLoS ONE.

Dynamics And Clustering In Locust Hopper Bands, Jialun Zhang

HMC Senior Theses

In recent years, technological advances in animal tracking have renewed interests in collective animal behavior, and in particular, locust swarms. These swarms pose a major threat to agriculture in northern Africa, the Middle East, and other regions. In their early life stages, locusts move in hopper bands, which are huge aggregations traveling on the ground. Our main goal is to understand the underlying mechanisms for the emergence and organization of these bands. We construct an agent-based model that tracks individual locusts and a continuum model that tracks the evolution of locust density. Both these models are motivated by experimental observations …

Kinetic Monte Carlo Methods For Computing First Capture Time Distributions In Models Of Diffusive Absorption, Daniel Schmidt

HMC Senior Theses

In this paper, we consider the capture dynamics of a particle undergoing a random walk above a sheet of absorbing traps. In particular, we seek to characterize the distribution in time from when the particle is released to when it is absorbed. This problem is motivated by the study of lymphocytes in the human blood stream; for a particle near the surface of a lymphocyte, how long will it take for the particle to be captured? We model this problem as a diffusive process with a mixture of reflecting and absorbing boundary conditions. The model is analyzed from two approaches. …

Pattern Recognition In Stock Data, Kathryn Dover

HMC Senior Theses

Finding patterns in high dimensional data can be difficult because it cannot be easily visualized. There are many different machine learning methods to fit data in order to predict and classify future data but there is typically a large expense on having the machine learn the fit for a certain part of a dataset. We propose a geometric way of defining different patterns in data that is invariant under size and rotation. Using a Gaussian Process, we find that pattern within stock datasets and make predictions from it.

Incorporating The Centers For Disease Control And Prevention Into Vaccine Pricing Models, Dina Sinclair

HMC Senior Theses

The American vaccine pricing market has many actors, making it a complex system to model. Because of this, previous papers have chosen to model only vaccine manufacturers while leaving out the government. However, the government is also an important actor in the market, since it buys over half of vaccines produced. In this work, we aim to introduce the government into vaccine pricing models to better recommend pricing strategies to the Centers for Disease Control and Prevention.

Product Development Resilience Through Set-Based Design, Stephen H. Rapp

Wayne State University Dissertations

Often during a system Product Development program external factors or requirements change, forcing system design change. This uncertainty adversely affects program outcome, adding to development time and cost, production cost, and compromise to system performance. We present a development approach that minimizes the impacts, by considering the possibility of changes in the external factors and the implications of mid-course design changes. The approach considers the set of alternative designs and the burdens of a mid-course change from one design to another in determining the relative value of a specific design. The approach considers and plans parallel development of alternative designs …

Eigenvalue Dependence Of Numerical Oscillations In Parabolic Partial Differential Equations, R. Corban Harwood

Faculty Publications - Department of Mathematics

This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations can create infeasible results. Since oscillation-free behavior is not ensured by stability conditions, a more precise condition would be useful for accurate solutions. Using Von Neumann and spectral analyses, we find and explore oscillation-free conditions for several finite difference schemes. Further relationships between oscillatory behavior and eigenvalues is supported with numerical evidence and proof. Also, evidence suggests that the oscillation-free stability condition for a consistent linearization may be sufficient to provide oscillation-free stability …

Steady And Stable: Numerical Investigations Of Nonlinear Partial Differential Equations, R. Corban Harwood

Faculty Publications - Department of Mathematics

Excerpt: "Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation."

A Review Of Random Matrix Theory With An Application To Biological Data, Jesse Aaron Marks

Masters Theses

"Random matrix theory (RMT) is an area of study that has applications in a wide variety of scientific disciplines. The foundation of RMT is based on the analysis of the eigenvalue behavior of matrices. The eigenvalues of a random matrix (a matrix with stochastic entries) will behave differently than the eigenvalues from a matrix with non-random properties. Studying this bifurcation of the eigenvalue behavior provides the means to which system-specific signals can be distinguished from randomness. In particular, RMT provides an algorithmic approach to objectively remove noise from matrices with embedded signals.

Major advances in data acquisition capabilities have changed …

On Some Impulse Control Problems With Constraint, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified.

Forcing Optimality And Brandt's Principle, Domenico Napoletani, Marco Panza, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the …

Flow Conditions In The Intracranial Aneurysm Lumen Are Associated With Inflammation And Degenerative Changes Of The Aneurysm Wall, J. Cebral, E. Ollikainen, Bong Jae Chung, F. Mut, V. Sippola, B. R. Jahromi, R. Tulamo, J. Hernesniemi, M. Niemelä, A. Robertson, J. Frösen

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Saccular intracranial aneurysm is a common disease that may cause devastating intracranial hemorrhage. Hemodynamics, wall remodeling, and wall inflammation have been associated with saccular intracranial aneurysm rupture.Weinvestigated how saccular intracranial aneurysm hemodynamics is associated with wall remodeling and inflammation of the saccular intracranial aneurysm wall. MATERIALS AND METHODS: Tissue samples resected during a saccular intracranial aneurysm operation (11 unruptured, 9 ruptured) were studied with histology and immunohistochemistry. Patient-specific computational models of hemodynamics were created from preoperative CT angiographies. RESULTS: More stable and less complex flows were associated with thick, hyperplastic saccular intracranial aneurysm walls, while slower flows …

Numerical Solutions Of The Radiosity Equation By The Galerkin Method For The Spherical Pyramid (Mars Project), Qiuyang Deng

Mathematics Theses

The Radiosity of a surface is the rate at which energy leaves that surface. It includes the energy emitted by a surface as well as the energy reflected. In this thesis, a spherical shaped interior space was designed on a spacecraft, which one day might land on Mars. The Radiosity model was used to determine the brightness inside the space. A global Galerkin method is used to solve the Radiosity Equation for several spherical shapes. This research is based on the study of the Radiosity Equation for occluded surfaces using the Collocation Method by Atkinson and Chein. The previous research …

Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …

Adrc Based Control Of Nonlinear Dynamical System With Multiple Sources Of Disturbance And Multiple Inputs, Chan Mi Park

College of Graduate Studies: Theses & Dissertations

In this thesis, we study the stability of Active Disturbance Rejection Control (ADRC) applied to controlling the Lorenz system. The Lorenz system is a nonlinear dynamical system that we attempt to control. In fact, the system is used to model convection flow such as that found in thermosyphons, electric circuits, and lasers. We are stabilizing the Lorenz system along with a few disturbances. Thus, to stabilize this chaotic system, a robust controller is required. The ADRC system is known as as effective method to stabilize a dynamical system. With the help of the Extended State Observer (ESO), the system can …

Dynamics Of Gene Networks In Cancer Research, Paul Scott

College of Graduate Studies: Theses & Dissertations

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …

A Markov Decision Process Approach To Adaptive Contact Strategies, Artur Grygorian

College of Graduate Studies: Theses & Dissertations

In the field of survey methodology, optimizing contact strategies helps organizations increase response rates using their allocated budget. Markov Decision Processes (MDP) are widely used to model decision-making strategies in situations where the outcomes have a random component. In this research, we use MDPs and adaptive sampling techniques to construct a strategy that, based on target audience characteristics, suggests the best contact policy. The data we use comes from the First Destination Survey conducted by the Office of Career Services at Georgia Southern University. The constructed model is quite flexible and can be used by other organizations to optimize their …

Applications Of Flow Network Models In Finance, Angel J. Woods

College of Graduate Studies: Theses & Dissertations

In this thesis we explore the applications of flow networks in practical problems in finance. After introducing basic definitions and background information, we first survey some known applications of flow networks in theoretical mathematics. We also briefly comment on their potential applications in the setting of financial flow networks. We then construct networks from practical financial flows and present the construction, reasoning, and known applications. Lastly, we show a design of financial flow networks that takes time into consideration and discuss its applications.