Applied Mathematics Commons^™

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between …

Nonlinear Coupled Effects In Nanomaterials, Sia Bhowmick

Theses and Dissertations (Comprehensive)

Materials at the nanoscale have different chemical, structural, and optoelectrical properties compared to their bulk counterparts. As a result, such materials, called nanomaterials, exhibit observable differences in certain physical phenomena. One such resulting phenomenon called the piezoelectric effect has played a crucial role in miniature self-powering electronic devices called nanogenerators which are fabricated by using nanostructures, such as nanowires, nanorods, and nanofilms. These devices are capable of harvesting electrical energy by inducing mechanical strain on the individual nanostructures. Electrical energy created in this manner does not have environmental limitations. In this thesis, important coupled effects, such as the nonlinear piezoelectric …

Models For High Dimensional Spatially Correlated Risks And Application To Thunderstorm Loss Data In Texas, Tobias Merk

Masters Theses

"Insurance claims caused by natural disasters exhibit spatial dependence with the strength of dependence being based on factors such as physical distance and population density, to name a few. Accounting for spatial dependence is therefore of crucial importance when modeling these types of claims. In this work, we present an approach to assess spatially dependent insurance risks using a combination of linear regression and factor copula models. Specifically, in loss modeling, observed dependence patterns are highly nonlinear, thus copula-based models seem appropriate since they can handle both linear and nonlinear dependence. The factor copula approach for estimating the spatial dependence …

An Investigation Of The Influence Of The 2007-2009 Recession On The Day Of The Week Effect For The S&P 500 And Its Sectors, Marcel Alwin Trick

Masters Theses

"Several studies have shown that the mean returns and the volatility structure of stock markets change seasonally or by day of the week. For instance, some authors found out that Monday returns are lower compared to Friday returns or that volatility on Wednesdays are lower compared to the rest of the week. Other researchers showed that these effects have changed after certain periods of economic stress. This led to the question, whether the day of the week effects in returns and volatility are in the US stock market and if patterns have changed from pre-recession through the 2007-2009 recession into …

Operational Research: Multi-Period Stowage Policies Within A Multi-Zone Storage Framework., Joseph Loeffler

All Graduate Theses, Dissertations, and Other Capstone Projects

This paper will be extending the single period stowage decision model presented by [Yuan, 2017] into a multi-period stowage decision model. The stowage decision determines how incoming items are distributed and stored across multiple storage zones. The amount of items that can be picked in any given storage zone is finite within a single time period. With this constraint, this research attempts to optimize how items are stored across many zones to meet uncertain demand requirements. A simulation study will be performed to compare the stowage policies given by [Yuan, 2017] to see how well they generalize to multi-period model. …

Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona

Honors Undergraduate Theses

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of …

Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

Theses and Dissertations--Mathematics

In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H¹-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, …

Spherulitic Growth And Thermodynamic Equilibrium In Multicomponent Elastic Films Under Solvent-Vapor Annealing, Ding Zhao

Theses and Dissertations--Mathematics

In this dissertation, we will study solvent-vapor induced spherulitic growth in multicomponent thin films modeled as prestressed elastic solids. The interface between the crystalline phase and the amorphous phase will be treated as an evolving thermodynamic system and no diffusion of any component will be considered.

The dissertation is divided into three parts. In Part I we will determine necessary conditions of thermodynamic equilibrium between the two solid phases, the inter- face, and the vapor. In Part II we will derive the thermodynamic driving force for spherulitic growth in multicomponent elastic thin films. In Part III we will investigate the …

A Representation Theorem For Material Tensors Of Textured Thin Sheets With Weak Planar Anisotropy, Yucong Sang

Theses and Dissertations--Mathematics

Herein we consider material tensors that pertain to thin sheets or thin films, which we model as two-dimensional objects. We assume that the thin sheet in question carries a crystallographic texture characterized by an orientation distribution function defined on the rotation group SO(3), which is almost transversely-isotropic about the sheet normal so that mechanical and physical properties of the thin sheet have weak planar-anisotropy. We present a procedure by which a special orthonormal basis can be determined in each tensor subspace invariant under the action of the orthogonal group O(2). We call members of such special bases irreducible basis tensors …

Concavity In Fractional Calculus, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

No abstract provided.

When Numerical Analysis Crosses Paths With Catalan And Generalized Motzkin Numbers, Paul W. Eloe, Catherine Kublik

Mathematics Faculty Publications

We study a linear doubly indexed sequence that contains the Catalan numbers and relates to a class of generalized Motzkin numbers. We obtain a closed form formula, a generating function and a nonlinear recursion relation for this sequence. We show that a finite difference scheme with compact stencil applied to a nonlinear differential operator acting on the Euclidean distance function is exact, and exploit this exactness to produce the nonlinear recursion relation. In particular, the nonlinear recurrence relation is obtained by using standard error analysis techniques from numerical analysis. This work shows a connection between numerical analysis and number theory, …

Exploration Of Counter Examples Of Balanced Sets, Jake Allen Weber

Honors Program Theses

Mathematicians are often intrigued with patterns, many times finding themselves looking for pieces of structure within a data set. This research project is no different in that we have explored our vast data set for substructure.

Our goal is to identify the following: how many data points are necessary to guarantee our set has a balanced set/substructure? Naturally rephrasing the previous question, we also ask ourselves what is the largest set that does not have a balanced subset/substructure? This alternate phrasing set us down our current path. We focused on the largest sets with no balanced substructure and what they …

Money Matters: An Analysis Of Campaign Finance In United States House Of Representatives Elections, 2010-2016, Destiny Leitz

Honors Program Theses

Money in politics is the single largest threat to the democratic system in the United States. It influences everything in politics, from the candidates to the issues debated. Every American knows that running for office requires large amounts of funding, and being elected requires even more. People worry that only the wealthiest voices are being heard; of course, candidates who depend on money from wealthy donors for campaign strength would never support unfavorable policies for their donors. Clearly, money in politics threatens the core democratic principles upon which America was founded. However, few people discuss whether the money really makes …

The Vendor In A Retail Setting: A Survey, Jesse Laporte

All Graduate Theses, Dissertations, and Other Capstone Projects

We consider the problem of managing nonperishable inventory as a vendor in a grocer setting. To manage inventory effectively, we must meet the demand of our customers as closely as we can. Too much inventory results in holding costs and ties up a large amount of capital and too little inventory results in lost sales or substitution. It is typical in a retail setting for the vendor to have access to past ordering data, but this data is only representative of the demand when we have sufficient inventory. Otherwise, the demand exceeds the inventory on hand and we lose, in …

Random Walks On Simple Two-Dimensional Manifolds, Tom Eichlersmith

Departmental Honors Projects

A C++ implementation of random walks is constructed with examples for the plane, sphere, and torus included. This package is available publicly, and can be expanded to different situations on the included surfaces as well as other surfaces. The random walks are studied by measuring how long they take to reach a pre-defined escape region on the surface. These escape regions and their interaction with the surface are what affect the behavior of the random walks the most.

A Primer On Noise-Induced Transitions In Applied Dynamical Systems, Eric Forgoston, Richard O. Moore

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic …

Models For Decision-Making, Steven Cosares

Open Educational Resources

No abstract provided.

Derivation Of The Hellinger-Reissner Variational Form Of The Linear Elasticity Equations, And A Finite Element Discretization, Bram Fouts

REU Final Reports

In this paper we are going to derive the linear elasticity equations in the Strong Form to the Hellinger Reissner Form. We find a suitable solution to solve our stress tensor. Then we will use finite element discretization from. We will run tests on a unit cube and multiple other shapes, which are described at the end. We view the different magnitudes of the displacement vector of each shape.

Fluid-Dynamic Models Of Geophysical Waves, Alan Compelli

Doctoral

Geophysical waves are waves that are found naturally in the Earth's atmosphere and oceans. Internal waves, that is waves that act as an interface between uids of dierent density, are examples of geophysical waves. A uid system with a at bottom, at surface and internal wave is initially considered. The system has a depth-dependent current which mimics a typical ocean set-up and, as it is based on the surface of the rotating Earth, incorporates Coriolis forces. Using well established uid dynamic techniques, the total energy is calculated and used to determine the dynamics of the system using a procedure called …