Applied Mathematics Commons^™

A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho

Theses and Dissertations--Mathematics

Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases.

In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△_Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a …

A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran

Mathematics Faculty Publications

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the …

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul

Mathematics Faculty Publications

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation.

Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.

Hamiltonian Approach To The Modeling Of Internal Geophysical Waves With Vorticity, Alan Compelli

Articles

We examine a simplified model of internal geophysical waves in a rotational 2-dimensional water-wave system, under the influence of Coriolis forces and with gravitationally induced waves. The system consists of a lower medium, bound underneath by an impermeable flat bed, and an upper lid. The 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of its conjugate variables and perform a variable transformation to show that it has canonical Hamiltonian structure. We then linearize the system, …

Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems, Vladimir Gerdjikov, Rossen Ivanov, Gaetano Vilasi

Articles

We are analyzing several types of dynamical systems which are both integrable and important for physical applications. The first type are the so-called peakon systems that appear in the singular solutions of the Camassa-Holm equation describing special types of water waves. The second type are Toda chain systems, that describe molecule interactions. Their complexifications model soliton interactions in the adiabatic approximation. We analyze the algebraic aspects of the Toda chains and describe their real Hamiltonian forms.

Building A Predictive Model For Baseball Games, Jordan Robertson Tait

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper, we will discuss a method of building a predictive model for Major League Baseball Games. We detail the reasoning for pursuing the proposed predictive model in terms of social popularity and the complexity of analyzing individual variables. We apply a coarse-grain outlook inspired by Simon Dedeos' work on Human Social Systems, in particular the open source website Wikipedia [2] by attempting to quantify the influence of winning and losing streaks instead of analyzing individual performance variables. We will discuss initial findings of data collected from the LA Dodgers and Colorado Rockies and apply further statistical analysis to …

Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli

Articles

We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.

Multi-Peak Solutions To Two Types Of Free Boundary Problems, Yi Li, Shuangjie Peng

Mathematics and Statistics Faculty Publications

We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the “core” of the solution has multiple connected components, whose boundary called free boundary of the problems consists approximately of spheres which shrink to distinct single points as the parameter tends to zero.

Winter Movements Of Louisiana Pine Snakes (Pituophis Ruthveni) In Texas And Louisiana, Josh B. Pierce, D. Craig Rudolph, Shirley J. Burgdorf, Richard R. Schaefer, Richard N. Conner, John G. Himes, C. Mike Duran, Laurence M. Hardy, Robert R. Fleet

Faculty Publications

Despite concerns that the Louisiana Pine Snake (Pituophis ruthveni) has been extirpated from large portions of its historic range, only a limited number of studies on their movement patterns have been published. Winter movement patterns are of particular interest since it has been hypothesized that impacts of management practices would be reduced during the winter. Using radiotelemetry, we determined winter movement patterns of Louisiana Pine Snakes (11 males, 8 females) in 5 study areas (2 in Louisiana and 3 in Texas). Movements during winter (November–February) were greatly curtailed compared to the remainder of the year; however, snakes occasionally undertook substantial …

Constructive Aspects Of Kochen's Theorem On P-Adic Closures, Evan Michael Eakins

LSU Doctoral Dissertations

In this work we begin with a brief survey of set theory and arithmetic to provide background for a logical procedure to `cleanse' the Axiom of Choice from a proof of a theorem of Kochen's. We accomplish this in the following chapters. We then discuss certain theorems involving definable Skolem functions. These theorems are used in Chapter 5 to give a construction of a p-adic closure of a p-valued field. Certain further considerations and open questions are addressed in the _x000C_final chapter.

Problem Solving Strategies And Metacognitive Skills For Gifted Students In Middle School, Lorena Aguelo Java

LSU Master's Theses

This study is conducted to investigate if the designed four-step method strategy (GEAR strategy adapted from Polya, 1973) in solving math problems has improved students’ performance scores and enhanced the metacognitive skills of gifted students. The respondents of this study include middle school gifted students who took math eight course in the school year 2013-2014 at Westdale Middle School in East Baton Rouge Parish School System. There are four classes of math eight gifted students who participated in the study. The classes were chosen randomly for experimental and controlled group and were equalized on the basis of the pre-test results …

A Direct Solver With O(N) Complexity For Variable Coefficient Elliptic Pdes Discretized Via A High-Order Composite Spectral Collocation Method, A. Gillman, P. G. Martinsson

Dartmouth Scholarship

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The resulting system of linear equations is solved using a direct (as opposed to iterative) solver that has optimal $O(N)$ complexity for all stages of the computation when applied to problems with nonoscillatory solutions such as the Laplace and the Stokes equations. Numerical examples demonstrate that the scheme is capable of computing solutions with a relative accuracy of $10^{-10}$ or better for challenging problems such as highly oscillatory …

Neutrosophic Principle Of Interconvertibility Matter-Energy Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The research aims to reveal and prove the thesis of the neutral and convertibility relationship between constituent constructive elements of the universe: matter, energy and information. The approach perspective is a computationally-communicative neutrosophic one. We configure a coherent and cohesive ideation line. Matter, energy and information are fundamental elements of the world. Among them, there is an inextricable multiple, elastic and evolutionary connection. The elements are defined by the connections between them. Our hypothesis is that the relationship between matter, energy and information is a neutral one. This relationship is not required by the evidence. At this level, it does …

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 …

Material Tensors And Pseudotensors Of Weakly-Textured Polycrystals With Orientation Measure Defined On The Orthogonal Group, Wenwen Du

Theses and Dissertations--Mathematics

Material properties of polycrystalline aggregates should manifest the influence of crystallographic texture as defined by the orientation distribution function (ODF). A representation theorem on material tensors of weakly-textured polycrystals was established by Man and Huang (2012), by which a given material tensor can be expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a number of undetermined material parameters. Man and Huang's theorem is based on the classical assumption in texture analysis that ODFs are defined on the rotation group SO(3), which strictly speaking makes …

Two-Source Energy Balance Model To Calculate E, T, And Et: Comparison Of Priestley-Taylor And Penman-Monteith Formulations And Two Time Scaling Methods, Paul D. Colaizzi, Nurit Agam, Judy A. Tolk, Steven R. Evett, Terry A. Howell, Prasanna H. Gowda, Susan A. O'Shaughnessy, William P. Kustas, Martha C. Anderson

United States Department of Agriculture-Agricultural Research Service / University of Nebraska-Lincoln: Faculty Publications

The two-source energy balance (TSEB) model calculates the energy balance of the soil-canopy-atmosphere continuum, where transpiration is initially determined by the Priestley-Taylor equation. The TSEB was revised recently using the Penman-Monteith equation to replace the Priestley-Taylor formulation, thus better accounting for the impact of large and varying vapor pressure deficits (VPD) typical of advective, semiarid climates. This study is a comparison of the Priestley- Taylor and Penman-Monteith versions of the TSEB (termed TSEB-PT and TSEB-PM, respectively). Evaporation (E), transpiration (T), and evapotranspiration (ET) calculated by the TSEB-PT and TSEB-PM versions were compared to measurements obtained with microlysimeters, sap flow gauges, …

A Pollination Network Of Cornus Florida, James H. Lee

Theses and Dissertations

From the agent-based, correlated random walk model presented, we observe the effects of varying the parameter values of maximum insect turning area, ��_max, density of trees, ω, maximum pollen carryover, ��_max, and probability of fertilization, P_��, on the distribution of pollen within a population of Cornus florida (flowering dogwood). We see that varying ��_max and ��_max changes the dispersal distance of pollen, which greatly affects many measures of connectivity. The clustering coefficient of fathers is maximized when ��_max is between 60° and 90°. Varying ω does not have a major …

A Block Precondtioner For A Mixed Finite Element Method For Biot;S Equations, Maranda Lee Bean

Open Access Theses & Dissertations

In this Thesis, we explore the solution methods for the linear system resulting from a mixed finite element method applied to the Biot's consolidation model. This model describes the coupled interactions between a porous solid and the fluid contained within it. Specifically, we use a method developed by Yi [Numer. Methods for PDEs, 29(5), pp. 1749-1777] that expands Biot's system to include fluid pressure, solid displacement, fluid flux and total stress as primary unknowns.

As the resulting linear system is a large, sparse, saddle point system, we attempt to solve this system via a Schur complement preconditioned iterative method. Using …

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.

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 …