Physical Sciences and Mathematics Commons^™

Thermal Effects On Domain Orientation Of Tetragonal Piezoelectrics Studied By In Situ X-Ray Diffraction, Wonyoung Chang, Alexander H. King, Keith J. Bowman

Alexander H. King

Thermal effects on domain orientation in tetragonal lead zirconate titanate (PZT) and lead titanate (PT) have been investigated by using in situ x-ray diffraction with an area detector. In the case of a soft PZT, it is found that the texture parameter called multiples of a random distribution (MRD) initially increases with temperature up to approximately 100 °C and then falls to unity at temperatures approaching the Curie temperature, whereas the MRD of hard PZT and PT initially undergoes a smaller increase or no change. The relationship between the mechanical strain energy and domain wall mobility with temperature is discussed.

Modeling The Potential Impact Of Rectal Microbicides To Reduce Hiv Transmission In Bathhouses, Romulus Breban, Ian Mcgowan, Chad M. Topaz, Elissa Schwartz, Peter Anton, Sally Blower

Chad M. Topaz

We evaluate the potential impact of rectal microbicides for reducing HIV transmission in bathhouses. A new mathematical model describing HIV transmission dynamics among men who have sex with men (MSM) in bathhouses is constructed and analyzed. The model incorporates key features affecting transmission, including sexual role behavior (insertive and receptive anal intercourse acts), biological transmissibility of HIV, frequency and efficacy of condom usage, and, most pertinently, frequency and efficacy of rectal microbicide usage. To evaluate the potential impact of rectal microbicide usage, we quantify the effect of rectal microbicides (ranging in efficacy from 10% to 90%) on reducing the number …

A Nonlocal Continuum Model For Biological Aggregations, Chad M. Topaz, Andrea L. Bertozzi, Mark E. Lewis

Chad M. Topaz

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact support and steep edges that correspond to localized biological aggregations, or clumps. These steady state clumps are approached through a dynamic coarsening process. In the limit of large population size, the clumps approach a constant density swarm with abrupt edges. We use energy arguments to understand the nonlinear selection of clump solutions, and to predict the internal density in …

The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller

Theses, Dissertations and Capstones

The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …

Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia

Faculty Publications

This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical …

Algebraic Characterizations Of Graph Imbeddability In Surfaces And Pseudosurfaces, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a finite connected graph G and specifications for a closed, connected pseudosurface, we characterize when G can be imbedded in a closed, connected pseudosurface with the given specifications. The specifications for the pseudosurface are: the number of face-connected components, the number of pinches, the number of crosscaps and handles, and the dimension of the first Z2-homology group. The characterizations are formulated in terms of the existence of a dual graph G ∗ on the same set of edges as G which satisfies algebraic conditions inspired by homology groups and their intersection products.

Bias Matroids With Unique Graphical Representations, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a 3-connected biased graph Ω with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of Ω is uniquely represented by Ω.

Electrical Properties Of Unintentionally Doped Semi-Insulating And Conducting 6h-Sic, William C. Mitchel, W. D. Mitchell, Z. Q. Fang, S. R. Smith, Helen Smith, Igor Khlebnikov, Y. I. Khlebnikov, C. Basceri, C. Balkas

Mathematics and Statistics Faculty Publications

Temperature dependent Hall effect (TDH), low temperature photoluminescence (LTPL), secondary ion mass spectrometry (SIMS), optical admittance spectroscopy (OAS), and thermally stimulated current (TSC) measurements have been made on 6H-SiC grown by the physical vapor transport technique without intentional doping. n- and p-type as well semi-insulating samples were studied to explore the compensation mechanism in semi-insulating high purity SiC. Nitrogen and boron were found from TDH and SIMS measurements to be the dominant impurities that must be compensated to produce semi-insulating properties. The electrical activation energy of the semi-insulating sample determined from the dependence of the resistivity …

On Adaptive Testing In Orthogonal Saturated Designs, Daniel T. Voss, Weizhen Wang

Mathematics and Statistics Faculty Publications

Adaptive, size-a step-down tests are provided for the analysis of orthogonal saturated designs. The tests work effectively under effect sparsity, and include as special cases the individual nonadaptive tests of Berk and Picard (1991) and the simultaneous nonadaptive tests of Voss (1988). The approach is similar to that used by Wang and Voss (2003) to construct adaptive confidence intervals, but testing is simpler because one can use the same denominator for all statistics. Step-down tests also have a clear power advantage over simultaneous confidence intervals and analogous single-step tests, as is demonstrated theoretically and assessed via simulation.

The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang, Huaizhong Zhao

Articles and Preprints

The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2.

In Part 1, we prove general existence and compactness theorems for C^k-cocycles of semilinear see’s and spde’s. Our results cover a large class of semilinear see’s as well as certain semilinear spde’s with Lipschitz and non-Lipschitz terms such as stochastic reaction diffusion equations and the …

Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia

Alejandro Garcia

This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical …

Representation Properties Of Definite Lattices In Function Fields, Jean Edouard Bureau

LSU Doctoral Dissertations

This work is made of two different parts. The first contains results concerning isospectral quadratic forms, and the second is about regular quadratic forms. Two quadratic forms are said to be isospectral if they have the same representation numbers. In this work, we consider binary and ternary definite integral quadratic form defined over the polynomial ring F[t], where F is a finite field of odd characteristic. We prove that the class of such a form is determined by its representation numbers. Equivalently, we prove that there is no nonequivalent definite F[t]-lattices of rank 2 or 3 having the same theta …

Filippov's Operator And Discontinuous Differential Equations, Khalid Abdulaziz Alshammari

LSU Doctoral Dissertations

The thesis is mainly concerned about properties of the so-called Filippov operator that is associated with a differential inclusion x'(t) ε F(x(t)) a.e. t ε [0,T], where F : Rⁿ → Rⁿ is given set-valued map. The operator F produces a new set-valued map F[F], which in effect regularizes F so that F[F] has nicer properties. After presenting its definition, we show that F[F] is always upper-semicontinuous as a map from Rⁿ to the metric space of compact subsets of Rⁿ endowed with the Hausdorff metric. Our main approach is to study the …

Limit Theorems For Weighted Stochastic Systems Of Interacting Particles, Jie Wu

LSU Doctoral Dissertations

The goal of this dissertation is to (a) establish the weak convergence of empirical measures formed by a system of stochastic differential equations, and (b) prove a comparison result and compactness of support property for the limit measure. The stochastic system of size n has coefficients that depend on the empirical measure determined by the system. The weights for the empirical measure are determined by a further n-system of stochastic equations. There is a random choice among N types of weights. The existence and uniqueness of solutions of the interacting system, weak convergence of the empirical measures, and the identification …

Topics In Quantum Topology, Khaled Moham Qazaqzeh

LSU Doctoral Dissertations

In chapter 1, which represents joint work with Gilmer, we define an index two subcategory of a 3-dimensional cobordism category. The objects of the category are surfaces equipped with Lagrangian subspaces of their real first homology. This generalizes the result of [9] where surfaces are equipped with Lagrangian subspaces of their rational first homology. To define such subcategory, we give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over R. In chapter 2, we find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus …

Parallel Algorithms For Multicriteria Shortest Path Problems, David L. Sonnier

Journal of the Arkansas Academy of Science

This paper presents two strategies for solving multicriteria shortest path problems with more than two criteria. Given an undirected graph within vertices, medges, and a set of K weights associated with each edge, we define a path as a sequence of edges from vertex s to vertex t. We want to find the Pareto-optimal set of paths from s to t. The solutions proposed herein are based on cluster computing using the Message-Passing Interface (MPI) extensions to the C programming language. We solve problems with 3 and 4 criteria, using up to 8 processors in parallel and using solutions based …

Multivariate Expansion Associated With Sheffer-Type Polynomials And Operators, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

With the aid of multivariate Sheffer-type polynomials and differential operators, this paper provides two kinds of general expansion formulas, called respectively the first expansion formula and the second expansion formula, that yield a constructive solution to the problem of the expansion of A(ˆt)f([g(t)) (a composition of any given formal power series) and the expansion of the multivariate entire functions in terms of multivariate Sheffer-type polynomials, which may be considered an application of the first expansion formula and the Sheffer-type operators. The results are applicable to combinatorics and special function theory.

Sequences Of Numbers Involved In Unsolved Problems, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Here it is a long list of sequences, functions, unsolved problems, conjectures, theorems, relationships, operations, etc. Some of them are inter-connected. 1) Consecutive Sequence: 1,12,123,1234,12345,123456,1234567,12345678,123456789,12345678910, 1234567891011,123456789101112,12345678910111213,... How many primes are there among these numbers? In a general form, the Consecutive Sequence is considered in an arbitrary numeration base B.

References:

Student Conference, University of Craiova, Department of Mathematics, April 1979, "Some problems in number theory" by Florentin Smarandache.

Arizona State University, Hayden Library, "The Florentin Smarandache papers" special collection, Tempe, AZ 85287-1006, USA.

The Encyclopedia of Integer Sequences", by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, …

An Optimal Brain Can Be Composed Of Conflicting Agents, Adi Livnat, Nicholas Pippenger

All HMC Faculty Publications and Research

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under natural physiological limitations, an optimal decision-making system can involve “selfish” agents that are in conflict with one another, even though the system is designed for a single purpose. It follows that conflict can emerge within a collective even when natural selection acts on the level of the collective only.

The Motion Of A Thin Liquid Film Driven By Surfactant And Gravity, Michael Shearer, Rachel Levy

All HMC Faculty Publications and Research

We investigate wave solutions of a lubrication model for surfactant-driven flow of a thin liquid film down an inclined plane. We model the flow in one space dimension with a system of nonlinear PDEs of mixed hyperbolic-parabolic type in which the effects of capillarity and surface diffusion are neglected. Numerical solutions reveal distinct patterns of waves that are described analytically by combinations of traveling waves, some with jumps in height and surfactant concentration gradient. The various waves and combinations are strikingly different from what is observed in the case of flow on a horizontal plane. Jump conditions admit new shock …

Communicating Applied Mathematics: Four Examples, Daniel E. Finkel, Christopher Kuster, Matthew Lasater, Rachel Levy, Jill P. Reese, Ilse C. F. Ipsen

All HMC Faculty Publications and Research

Communicating Applied Mathematics is a writing- and speaking-intensive graduate course at North Carolina State University. The purpose of this article is to provide a brief description of the course objectives and the assignments. Parts A–D of of this article represent the class projects and illustrate the outcome of the course:

• The Evolution of an Optimization Test Problem: From Motivation to Implementation, by Daniel E. Finkel and Jill P. Reese

• Finding the Volume of a Powder from a Single Surface Height Measurement, by Christopher Kuster

• Finding Oscillations in Resonant Tunneling Diodes, by Matthew Lasater

• …

Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore

All HMC Faculty Publications and Research

In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing …

Classifying Quadratic Number Fields Up To Arf Equivalence, Jeonghun Kim

LSU Doctoral Dissertations

Two number fields K and L are said to be Arf equivalent if there exists a bijection T : ­Ω_K → Ω_­L of places of K and of L such that K_P and L_TP are locally Arf equivalent for every place P ε Ω_K. That is, |K^*_p/K^*2_p| = |L^*_TP/L^*2_TP|, type[( , )_P] = type[( , )_TP], and Arf(r_P ) = Arf(r_TP ) for every place P ε Ω_K, where r_P is the local …

Circuits And Structure In Matroids And Graphs, Brian Daniel Beavers

LSU Doctoral Dissertations

This dissertation consists of several results on matroid and graph structure and is organized into three main parts. The main goal of the first part, Chapters 1-3, is to produce a unique decomposition of 3-connected matroids into more highly connected pieces. In Chapter 1, we review the definitions and main results from the previous work of Hall, Oxley, Semple, and Whittle. In Chapter 2, we introduce operations that allow us to decompose a 3-connected matroid M into a pair of 3-connected pieces by breaking the matroid apart at a 3-separation. We also generalize a result of Akkari and Oxley. In …

Optimal Binary Trees With Height Restrictions On Left And Right Branches, Song Ding

LSU Master's Theses

We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth's famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity Theorem. These enabled Knuth to achieve a time complexity of O(n²), while previous algorithms had been O(n³) (n = size of input). We present the known generalization of Knuth's algorithm to trees with a height restriction. Finally, we consider the previously unexamined case of trees with different restrictions on left and …

Eigenvalue Comparisons For Boundary Value Problems Of The Discrete Beam Equation, Jun Ji, Bo Yang

Faculty Articles

We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Delta(4)yi = lambda a(i+2)y(i+2), - 1= b(j), 1

Raves, Clubs And Ecstasy: The Impact Of Peer Pressure, Baojun Song, Melissa Castillo-Garsow, Karen R. Ríos-Soto, Marcin Mejran, Leilani Henso, Carlos Castillo-Chavez

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Ecstasy has gained popularity among young adults who frequent raves and nightclubs. The Drug Enforcement Administration reported a 500 percent increase in the use of ecstasy between 1993 and 1998. The number of ecstasy users kept growing until 2002, years after a national public education initiative against ecstasy use was launched. In this study, a system of differential equations is used to model the peer-driven dynamics of ecstasy use. It is found that backward bifurcations describe situations when sufficient peer pressure can cause an epidemic of ecstasy use. Furthermore, factors that have the greatest influence on ecstasy use as predicted …

The Curl Of A Vector Field: Beyond The Formula, Kimberly Jordan Burch, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical formulas. We investigate when and why a vector field yields an in-spot spin, also known as curl, and develop intuition to predict the sign of the curl of a vector field without calculating it. As an application of the curl, Stokes' theorem and its physical …

Index Future Pricing Under Imperfect Market And Stochastic Volatility, Wei-Hsien Li

LSU Master's Theses

Financial markets in emerging countries are volatile and imperfect, so pricing model under traditional perfect-market frameset may not give reliable price of financial derivatives. The most famous pricing model for stock index future is the cost of carry model. The mis-pricing of cost of carry model inspires lots of following researches. Even transaction costs, dividends, stochastic interest rate, stochastic volatility, market imperfection, and other factors are considered, we still do not obtain a model price consistently better than cost of carry model. But these researches offer important insights, for example, the market needs time to mature and the more complex …

Using Elimination To Describe Maxwell Curves, Lucas P. Beverlin

LSU Master's Theses

Cartesian ovals are curves in the plane that have been studied for hundreds of years. A Cartesian oval is the set of points whose distances from two fixed points called foci satisfy the property that a linear combination of these distances is a fixed constant. These ovals are a special case of what we call Maxwell curves. A Maxwell curve is the set of points with the property that a specific weighted sum of the distances to n foci is constant. We shall describe these curves geometrically. We will then examine Maxwell curves with two foci and a special case …