Applied Mathematics Commons^™

Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer

Senior Independent Study Theses

No abstract provided.

A Posteriori Estimates Using Auxiliary Subspace Techniques, Harri Hakula, Michael Neilan, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd (d ≥ 2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determine the computational complexity of the auxiliary approximation problem. With a carefully chosen auxiliary subspace, we prove that the error is bounded above by the error estimate up to oscillation terms. In addition, we show …

Damage Evolution In Pressurized Domain: A Gradient Based Variational Approach, Navid Mozaffari

LSU Master's Theses

Construction of appropriate models through mathematical analysis for materials in order to find their main properties and ingredients and enhance the numerical simulations to predict their behavior under specific conditions is in interest even in mathematics departments rather than material science and engineering branches. Among these models, gradient damage models have reached to the specific stage because of their ability to bring the effects of micro cracks propagation into conventional continuum mechanics formulation and approximate brittle fracture as one of the most phenomena in the area of material behavior simulation. This thesis includes the application and extension of a previously …

Developing Auxiliary Resource Materials To Support The Engageny Geometry Curriculum, Joanne Griffin

LSU Master's Theses

With the advent of current education reform, and the introduction of the Common Core State Standards for Mathematics, the present offerings of the geometry curriculum have become dated. One contribution to remedy this situation is a project by the state of New York called EngageNY. EngageNY is a common core aligned mathematics curriculum across all grades. The EngageNY Geometry Curriculum Module 1 is the basis from which this thesis was developed. It is the purpose of this thesis to present a supplement to the EngageNY Geometry Module 1 Curriculum and to describe why it is advantageous to have such a …

Reformulations For Control Systems And Optimization Problems With Impulses, Jacob Blanton

LSU Doctoral Dissertations

This dissertation studies two different techniques for analyzing control systems whose dynamics include impulses, or more specifically, are measure-driven. In such systems, the state trajectories will have discontinuities corresponding to the atoms of the Borel measure driving the dynamics, and these discontinuities require further definition in order for the control system to be treated with the broad range of results available to non-impulsive systems. Both techniques considered involve a reparameterization of the system variables including state, time, and controls. The first method is that of the graph completion, which provides an explicit reparameterization of the time and state variables. The …

Robust Preconditioners For The High-Contrast Elliptic Partial Differential Equations, Zuhal Unlu

LSU Doctoral Dissertations

In this thesis, we discuss a robust preconditioner (the AGKS preconditioner) for solving linear systems arising from approximations of partial differential equations (PDEs) with high-contrast coefficients. The problems considered here include the standard second and higher order elliptic PDEs such as high-contrast diffusion equation, Stokes' equation and biharmonic-plate equation. The goal of this study is the development of robust and parallelizable preconditioners that can easily be integrated to treat large configurations. The construction of the preconditioner consists of two phases. The first one is an algebraic phase which partitions the degrees of freedom into high and low permeability regions which …

Selected Problems On Matroid Minors, Jesse Taylor

LSU Doctoral Dissertations

This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds's tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte's characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being …

Ito Formula And Girsanov Theorem On A New Ito Integral, Yun Peng

LSU Doctoral Dissertations

The celebrated Ito theory of stochastic integration deals with stochastic integrals of adapted stochastic processes. The Ito formula and Girsanov theorem in this theory are fundamental results which are used in many applied fields, in particular, the finance and the stock markets, e.g. the Black-Scholes model. In chapter 1 we will briefly review the Ito theory. In recent years, there have been several extension of the Ito integral to stochastic integrals of non-adapted stochastic processes. In this dissertation we will study an extension initiated by Ayed and Kuo in 2008. In Chapter 2 we review this new stochastic integral and …

Exponentially Convergent Generalized Finite Element Method For Multi-Scale Problems, Xu Huang

LSU Doctoral Dissertations

The overall approach I take in the thesis falls into the category of multiscale finite element methods(MsFEM). I work to identify a new class of local approximation spaces with good approximation properties. This is carried out for the equilibrium problem of linear elasticity. The choice of local approximation spaces is motivated by the kolmogorov n-width. Part of my thesis work develops an estimate to show that it is possible to achieve a local approximation error of ô with respect to the energy norm using at most ln^d+1 &frac1ô local basis functions. The global approximation error ôis controlled by the …

Combinatorial Minimal Free Resolutions Of Ideals With Monomial And Binomial Generators, Trevor Mcguire

LSU Doctoral Dissertations

In recent years, the combinatorial properties of monomials ideals and binomial ideals have been widely studied. In particular, combinatorial interpretations of minimal free resolutions have been given in both cases. In this present work, we will generalize existing techniques to obtain two new results. If Lambda is an integer lattice in the n-dimensional integers satisfying some mild conditions, S is the polynomial ring with n variables and R is the group algebra of S[Lambda], then the first result is resolutions of Lambda-invariant submodules of the Laurent polynomial ring in n variables as R-modules. A consequence will be the ability to …

Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt

University Faculty Publications and Creative Works

Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.

Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt

University Faculty Publications and Creative Works

Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.

Lattice-Boltzmann Simulations Of The Thermally Driven 2d Square Cavity At High Rayleigh Numbers, Dario Contrino, Pierre Lallemand, Pietro Asinari, Li-Shi Luo

Mathematics & Statistics Faculty Publications

The thermal lattice Boltzmann equation (TLBE) with multiple-relaxation-times (MRT) collision model is used to simulate the steady thermal convective flows in the two-dimensional square cavity with differentially heated vertical walls at high Rayleigh numbers. The MRT-TLBE consists of two sets of distribution functions, i.e., a D2Q9 model for the mass-momentum equations and a D2Q5 model for the temperature equation. The dimensionless flow parameters are the following: the Prandtl number Pr = 0.71 and the Rayleigh number Ra = 10⁶, 10⁷, and 10⁸. The D2Q9 + D2Q5 MRT-TLBE is shown to be second-order accurate and …

Thermolysis And Kinetics Of Scrap Tyre And Bagasse For Energy Utilization, Petro Ndalila

Tanzania Journal of Engineering and Technology (TJET)

The increase of energy demand has brought concern to find alternative fuel that will at least sustain the requirement. Bagasse and scrap tyre are waste generated in our industrial activities, which can be used in energy production to subsidize the demand. This paper, aim to study the decomposition behaviour and kinetics of biomass (bagasse) and scrap tyre as preliminary stage of fuel sample analysis to be considered for energy production in gasification/combustion or pyrolysis facilities. The behaviour demonstrated with thermogravimetric analyzer (TGA), shows that all samples have high volatile amount release, 84.21% for bagasse and 85.08% for scrap tyre, which …

Optimising The Performance Of Roundabouts In Dar Es Salaam City, David Mfinanga

Tanzania Journal of Engineering and Technology (TJET)

Intersections are one of the major bottlenecks that aggravate congestion in road networks; effective control of which is an important strategy in improving traffic flow. While developing countries have found it hard to adopt sophisticated means of intersection control, they have also not optimised the performance of roundabouts. This paper reviews the performance of roundabouts, which have become increasingly popular in recent years, as simple and low cost forms of intersection control. The performance of three major roundabouts in Dar es Salaam has been analysed and results show that roundabouts can accommodate high traffic volumes without causing excessive delays. The …

Analysis Of Power Efficiency Of A Direct-Driven Locally Fabricated Permanent Magnet Ac Generator For Small-Scale Wind Power Applications In Tanzania, Mussa Iddi Mgwatu Dr.

Tanzania Journal of Engineering and Technology (TJET)

The use of direct-driven permanent magnet alternating current (AC) generators offers the opportunity to reduced costs and increased system efficiency. This type of generator could be the best alternative for rural population whom are not connected to the national grid. To improve the design and efficiency of locally fabricated generators, it is imperative to characterize both their mechanical and electrical parameters. This paper presents the analysis of power efficiency of the synchronous permanent AC generator locally fabricated in Tanzania. In this case, load resistance and rotational speed are characterized using designed experiment. The output current and voltage of the generator …

A Study On The Integration Of A Novel Absorption Chiller Into A Microscale Combined Cooling, Heating, And Power (Micro-Cchp) System, Scott J. Richard

LSU New Orleans Theses and Dissertations

This study explores the application of micro-CCHP systems that utilize a 30 kW gas microturbine and an absorption chiller. Engineering Equation Solver (EES) is used to model a novel single-effect and double-effect water-lithium bromide absorption chiller that integrates the heat recovery unit and cooling tower of a conventional CCHP system into the chiller’s design, reducing the cost and footprint of the system. The results of the EES model are used to perform heat and material balances for the micro-CCHP systems employing the novel integrated chillers, and energy budgets for these systems are developed. While the thermal performance of existing CCHP …

Using Delay-Differential Equations For Modeling Calcium Cycling In Cardiac Myocytes, Ryan Thompson

Theses

The cycling of calcium at the intracellular level of cardiac cells plays a key role in the excitation-contraction process. The interplay between ionic currents, buffering agents, and calcium release from the sarcoplasmic reticulum (SR) is a complex system that has been shown experimentally to exhibit complex dynamics including period-2 states (alternans) and higher-order rhythms. Many of the calcium cycling activities involve the sensing, binding, or diffusion of calcium between intracellular compartments; these are physical processes that take time and typically are modeled by “relaxation” equations where the steady-state value and time course of a particular variable are specified through an …

Stability And Entanglement In An Optomechanical System, Matthew Schumacher

Theses

Optomechanical systems are currently of great interest as they lie at the boundary between quantum and classical mechanics, promising fundamental insights as well as new technologies. The practical operation of an optomechanical system requires that it satisfy the criteria of mechanical stability. Further, for quantum applications, it is important to characterize the degree of nonclassical correlation present between the mechanical and optical subsystems. In this study, we analyze the stability and entanglement in an optomechanical system where couplings linear as well as quadratic in the mechanical displacement are present simultaneously. Such systems can be realized experimentally. Our analysis of the …

Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Extension Of A High-Order Petrov-Galerkin Implementation Applied To Non-Radiating And Radar Cross Section Geometries, William L. Shoemake

Masters Theses and Doctoral Dissertations

Capabilities of a high-order Petrov-Galerkin solver are expanded to include N-port systems. Tait-Bryan angles are employed to launch electro-magnetic waves in arbitrary directions allowing off axis ports to be driven. The transverse-electric (TE) formulation is added allowing waveguide geometries to be driven directly. A grid convergence study is performed on a coax-driven waveguide system. Physical data are matched to a hybrid-T junction (magic-T) electromagnetic waveguide structure to verify the TE driving formulation along with the Tait-Bryan angles and modified post-processing routines. A simple sphere case is used to exercise the radar cross section (RCS) routines and to examine the benefits …

A Population Model For Walleye In Nebraska Irrigation Reservoirs, Robert A. Kill

School of Natural Resources: Dissertations, Theses, and Student Research

Understanding how and why fish population size changes between years is a central theme in fisheries ecology. Fishery agencies have limited time and financial resources, thus there is a need for a quantitative way to direct the limited time and financial resources so agencies can manage fisheries more efficiently. I developed a tool for fishery managers that synthesizes common population indices and evaluated the relative importance of those indices given varying uncertainty in age-0 walleye Sander vitreus survival. Under most circumstances, I determined that resources are best utilized in reducing age-0 survival uncertainty when understanding walleye population growth. I applied …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

No abstract provided.

Elementary Differential Equations, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough.

An …

Introduction To Real Analysis, William F. Trench

Textbooks Collection

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …

Computing Curvature And Curvature Normals On Smooth Logically Cartesian Surface Meshes, John Thomas Hutchins

Boise State University Theses and Dissertations

This thesis describes a new approach to computing mean curvature and mean curvature normals on smooth logically Cartesian surface meshes. We begin by deriving a finite-volume formula for one-dimensional curves embedded in two- or three- dimensional space. We show the exact results on curves for specific cases as well as second-order convergence in numerical experiments. We extend this finite-volume formula to surfaces embedded in three-dimensional space. Exact results are again derived for special cases and second-order convergence is shown numerically for more general cases. We show that our formula for computing curvature is an improvement over using the “cotan” formula …

Comparison Of Mesh And Meshless Methods For Partial Differential Equations Of Galerkin Form, Wallace F. Atterberry

UNLV Theses, Dissertations, Professional Papers, and Capstones

There are two purposes of this research project. The first purpose is to compare two types of Galerkin methods: The finite element mesh method and moving least sqaures meshless Galerkin (EFG) method. The second purpose of this project is to determine if a hybrid between the mesh and meshless method is beneficial.

This manuscript will be divided into three main parts. The first part is chapter one which develops the finite element method. The second part (Chapter two) will be developing the meshless method. The last part will provide a method for combining the mesh and meshless methods for a …

A Hybrid Agent-Based And Differential Equations Model For Simulating Antibiotic Resistance In A Hospital Ward, Lester Caudill, Barry Lawson

Department of Math & Statistics Faculty Publications

Serious infections due to antibiotic-resistant bacteria are pervasive, and of particular concern within hospital units due to frequent interaction among health-care workers and patients. Such nosocomial infections are difficult to eliminate because of inconsistent disinfection procedures and frequent interactions among infected persons, and because ill-chosen antibiotic treatment strategies can lead to a growth of resistant bacterial strains. Clinical studies to address these concerns have several issues, but chief among them are the effects on the patients involved. Realistic simulation models offer an attractive alternative. This paper presents a hybrid simulation model of antibiotic resistant infections in a hospital ward, combining …

Viscosity Dependence Of Faraday Wave Formation Thresholds, Lisa Michelle Slaughter

Physics

This experiment uses an electromagnetic shaker to produce standing wave patterns on the surface of a vertically oscillating sample of silicon liquid. These surface waves, known as Faraday waves, form shapes such as squares, lines, and hexagons. They are known to be dependent upon the frequency and amplitude of the forcing as well as on the viscosity and depth of the liquid in the dish. At a depth of 4mm and for various silicon liquids having kinematic viscosities of 10, 20, and 38 cSt, we determined the acceleration at which patterns form for frequencies between 10 and 60 Hz. For …

Several New Families Of Jarratt’S Method For Solving Systems Of Nonlinear Equations, V. Kanwar, Sanjeev Kumar, Ramandeep Behl

Applications and Applied Mathematics: An International Journal (AAM)

In this study, we suggest and analyze a new and wide general class of Jarratt’s method for solving systems of nonlinear equations. These methods have fourth-order convergence and do not require the evaluation of any second or higher-order Fréchet derivatives. In terms of computational cost, all these methods require evaluations of one function and two first-order Fréchet derivatives. The performance of proposed methods is compared with their closest competitors in a series of numerical experiments. It is worth mentioning that all the methods considered here are found to be effective and comparable to the robust methods available in the literature.