Physical Sciences and Mathematics Commons^™

Materiały Odstresowujące, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Oxidative Carbonylation Of 2-Propyn-1-Ol And 2-Methyl-3-Butyn-2-Ol In An Oscillatory Mode, Sergey N. Gorodsky

Sergey N. Gorodsky

No abstract provided.

Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman

Mikhail Khenner

The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer, which results in the complicated dependence of light reflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillary effect is due to the local thickness-dependent, steady- state temperature profile in the liquid, which is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Linear stability analysis of the model equations set for Ag/Co bilayer predicts the dewetting length scales in the qualitative agreement with experiment.

Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz

Chad M. Topaz

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem’s block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer …

A Local Radial Basis Function Method For The Numerical Solution Of Partial Differential Equations, Maggie Elizabeth Chenoweth

Theses, Dissertations and Capstones

Most traditional numerical methods for approximating the solutions of problems in science, engineering, and mathematics require the data to be arranged in a structured pattern and to be contained in a simply shaped region, such as a rectangle or circle. In many important applications, this severe restriction on structure cannot be met, and traditional numerical methods cannot be applied. In the 1970s, radial basis function (RBF) methods were developed to overcome the structure requirements of existing numerical methods. RBF methods are applicable with scattered data locations. As a result, the shape of the domain may be determined by the application …

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman

Mathematics Faculty Publications

We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.

A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

Mathematics Faculty Publications

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.

Granular Computing For Assessment Of Mild Traumatic Brain Injury, Melaku Ayenew Bogale

Open Access Theses & Dissertations

Mild traumatic brain injury (mTBI) is one of the most common neurological disorders. It is a serious public health problem in the United States. Although, penetrating (open) brain injuries that result in extended period of loss of consciousness (LOC) usually gets attention and well taken care of by the emergency departments, mild traumatic brain injury with no visible sign of damage, may be undetected or misdiagnosed. The clinical assessments and evaluations are mostly based on subjective cognitive and behavioral tests. Many people after suffering mTBI complain about decreased balance, coordination and stability even though the clinical evaluations show no sign …

Analytical And Numerical Solution To The Partial Differential Equation Arising In Financial Modeling, Pavel Bezdek

Open Access Theses & Dissertations

In this work we will present a self-contained introduction to the option pricing problem. We will introduce some basic ideas from the probability theory and stochastic differential equations. Later we will move to the partial differential equations since the option pricing problem arising in financial mathematics when asset is driven by a stochastic volatility process and assumed presence of transaction cost leads to solving non-linear partial dif- ferential equation. We will also present the complete process from deriving the desired partial differential equation to the proof of existence of a solution and also the numerical simulations. Using techniques form stochastic …

Large Eddy Simulation Of Dispersed Multiphase Flow, Yejun Gong

Dissertations, Master's Theses and Master's Reports - Open

This thesis covers two main topics. The first is the comparison between the Reynoldsaveraged Navier-Stokes (RANS) simulation and the Large Eddy Simulation (LES) of high injection pressure diesel sprays under non-evaporating or evaporating conditions. The second topic is the comparison of the fuel behavior in the spray process between the hydrotreated vegetable oil (HVO) and the conventional EN 590, diesel #2 and n-heptane fuels.

To validate the RANS and LES spray simulations, comparisons were made with experimental data. The LES turbulence model, the initial drop size distribution (IDSD), the Levich jet breakup model and the CAB drop breakup model are …

R0 Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, J. Jacobsen, M. A. Lewis

Department of Mathematics: Faculty Publications

Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem im- pacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R₀ for advection-diffusion-reaction equations and on related measures. We apply the measures to popula- tion persistence in rivers under various flow regimes. This …

Penalized Spline Estimation In The Partially Linear Model, Ashley D. Holland

Faculty Dissertations

Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when the dimension of the regressors is large. In this project, we employ penalized B-splines in the context of the partially linear model to estimate the nonparametric component, when both thenumber of knots and the penalty factor vary with the sample size. We obtain mean-square convergence rates and establish asymptotic distributional approximations, with valid standard errors, for the resulting multivariate estimators of both the parametric and nonparametric components in this model. Our results extend and complement the recent theoretical work in the literature …

Dissertation - Preemptive Rerouting Of Airline Passengers Under Uncertain Delays, Lindsey Mccarty

Faculty Dissertations

An airline's operational disruptions can lead to flight delays that in turn impact passengers, not only through the delay itself but also through possible missed connections. Much research has been done on crew recovery (rescheduling crews after a flight delay or cancellation), but little research has been done on passenger reaccommodation. Our goal is to design ways that passenger reaccommodation can be improved so that passengers can spend less time delayed and miss fewer connections.

Since the length of a delay is often not known in advance, we consider preemptive rerouting of airline passengers before the length of the delay …

Hypercube Diagrams For Knots, Links, And Knotted Tori, Ben Mccarty

LSU Doctoral Dissertations

For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. Examples of knots for which the cube number detects chirality are presented. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number. Finally, there is a generalization of cube …

Graham's Variety And Perverse Sheaves On The Nilpotent Cone, Amber Russell

LSU Doctoral Dissertations

In recent work, Graham has defined a variety which maps to the nilpotent cone, and which shares many properties with the Springer resolution. However, Graham's map is not an isomorphism over the principal orbit, and for type A in particular, its fibers have a nice relationship with the fundamental groups of the nilpotent orbits. The goal of this dissertation is to determine which simple perverse sheaves appear when the Decomposition Theorem for perverse sheaves is applied in Graham's setting for type A, and to begin to answer this question in the other types as well. In Chapter 1, we give …

Some Tracking Problems For Aerospace Models With Input Constraints, Aleksandra Gruszka

LSU Doctoral Dissertations

We study tracking controller design problems for key models of planar vertical takeoff and landing (PVTOL) aircraft and unmanned air vehicles (UAVs). The novelty of our PVTOL work is the global boundedness of our controllers in the decoupled coordinates, the positive uniform lower bound on the thrust controller, the applicability of our work to cases where the velocity measurements may not be available, the uniform global asymptotic stability and uniform local exponential stability of our closed loop tracking dynamics, the generality of our class of trackable reference trajectories, and the input-to-state stability of the controller performance under actuator errors of …

Paley-Wiener Theorem For Line Bundles Over Compact Symmetric Spaces, Vivian Mankau Ho

LSU Doctoral Dissertations

We generalize a Paley-Wiener theorem to homogeneous line bundles $L_\chi$ on a compact symmetric space U/K with $\chi$ a nontrivial character of K. The Fourier coefficients of a $\chi$-bi-coinvariant function f on U are defined by integration of f against the elementary spherical functions of type $\chi$ on U, depending on a spectral parameter $\mu$, which in turn parametrizes the $\chi$-spherical representations $\pi$ of U. The Paley-Wiener theorem characterizes f with sufficiently small support in terms of holomorphic extendability and exponential growth of their $\chi$-spherical Fourier transforms. We generalize Opdam's estimate for the hypergeometric functions in a bigger domain with …

Welfare Versus Stability In "Stabilizing An Unstable Economy": A Minskyan Growth Model, Stergios Mentesidis

Senior Projects Spring 2012

The paper focuses on Minsky's financial fragility hypothesis incorporated in a growth model and investigates whether an inherently unstable economy can be stabilized by a big and proactive government. Using dynamical systems theory and expanding a supply-driven growth model developed by Lin, Day and Tse (1992), the paper explores how different government spending programs and financing paths can affect the growth, as well as the stability of a capitalist economy. The results and implications of the new frameworks are analyzed, using analytical and numerical methods of bifurcation, to examine the dependence of optimal government intervention on the economic environment. The …

Chaos In Dynamics: The Non-Linear Waterwheel, Abraham Romerohernandez

Theses Digitization Project

In this study basic principles of Chaos in Dynamics will be presented in the context of Lorenz Equations. In particular, we will see a demonstration of chaotic behavior in the Waterwheel Experiment and show how the dynamics of that experiment are a version of the Lorenz Equations.

Development Of New Mathematical Methods For Post-Pareto Optimality, Victor Manuel Carrillo

Open Access Theses & Dissertations

Many real-world applications of multi-objective optimization involve a large number of objectives. A multi-objective optimization task involving multiple conflicting objectives ideally demands finding a multi-dimensional Pareto-optimal front. Although the classical methods have dealt with finding one preferred solution with the help of a decision-maker, evolutionary multi-objective optimization (EMO) methods have been attempted to find a representative set of solutions in the Pareto-optimal front. Multiple objective evolutionary algorithms (MOEAs), which are biologically-inspired optimization methods, have become popular approaches to solve problems with multiple objective functions. With the use of MOEAs, multiple objective optimization becomes a two-part problem. First, the multiple objective …

Natural Product Xn On Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new product on matrices called the natural product. ...

Thus by introducing natural product we can find the product of column matrices and product of two rectangular matrices of same order. Further this product is more natural which is just identical with addition replaced by multiplication on these matrices. Another fact about natural product is this enables the product of any two super matrices of same order and with same type of partition. We see on supermatrices products cannot be defined easily which prevents from having any nice algebraic structure on the collection …

Neutrosophic Super Matrices And Quasi Super Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study neutrosophic super matrices. The concept of neutrosophy or indeterminacy happens to be one the powerful tools used in applications like FCMs and NCMs where the expert seeks for a neutral solution. Thus this concept has lots of applications in fuzzy neutrosophic models like NRE, NAM etc. These concepts will also find applications in image processing where the expert seeks for a neutral solution. Here we introduce neutrosophic super matrices and show that the sum or product of two neutrosophic matrices is not in general a neutrosophic super matrix. Another interesting feature of this book is …

Ledzewicz Applies Math To Health Sciences, Aldemaro Romero Jr.

Publications and Research

No abstract provided.

Two-Subspace Projection Method For Coherent Overdetermined Systems, Deanna Needell, Rachel Ward

CMC Faculty Publications and Research

We present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image processing. The Kaczmarz method is one of the most popular solvers for overdetermined systems of linear equations due to its speed and simplicity. Here we introduce and analyze an extension of the Kaczmarz method which iteratively projects the estimate onto a solution space given from two randomly selected rows. We show that this projection algorithm provides exponential convergence to the solution in expectation. The convergence rate significantly improves upon …

Subgradient Formulas For Optimal Control Problems With Constant Dynamics, Lingyan Huang

LSU Doctoral Dissertations

In this thesis our fi_x000C_rst concern is the study of the minimal time function corresponding to control problems with constant convex dynamics and closed target sets. Unlike previous work in this area, we do not make any nonempty interior or calmness assumptions and the minimal time functions is generally non-Lipschitzian. We show that the Proximal and Fréchet subgradients of the minimal time function are computed in terms of normal vectors to level sets. And we also computed the subgradients of the minimal time function in terms of the F-projection. Secondly, we consider the value function for Bolza Problem in optimal …

Mathematical Models For Interest Rate Dynamics, Xiaoxue Shan

LSU Master's Theses

We present a study of mathematical models of interest rate products. After an introduction to the mathematical framework, we study several basic one-factor models, and then explore multifactor models. We also discuss the Heath-Jarrow- Morton model and the LIBOR Market model. We conclude with a discussion of some modified models that involve stochastic volatility.

A Numerical Investigation Of Apéry-Like Recursions And Related Picard-Fuchs Equations, Maiia J. Bakhova

LSU Doctoral Dissertations

In this work we investigate a generalization of a recursion which was used by Apery in his proof of irrationality of the zeta function values at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them.

Stability Analysis Of Fitzhugh-Nagumo With Smooth Periodic Forcing, Tyler Massaro, Benjamin F. Esham

Faculty Publications and Other Works -- Mathematics

Alan Lloyd Hodgkin and Andrew Huxley received the 1963 Nobel Prize in Physiology for their work describing the propagation of action potentials in the squid giant axon. Major analysis of their system of differential equations was performed by Richard FitzHugh, and later by Jin-Ichi Nagumo who created a tunnel diode circuit based upon FitzHugh’s work. The resulting differential model, known as the FitzHugh-Nagumo (FH-N) oscillator, represents a simplification of the Hodgkin-Huxley (H-H) model, but still replicates the original neuronal dynamics (Izhikevich, 2010). We begin by providing a thorough grounding in the physiology behind the equations, then continue by introducing some …

Consensus-Type Stochastic Approximation Algorithms, Yu Sun

Wayne State University Dissertations

This work is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a nite state space. The consensus control is achieved by designing stochastic approximation algorithms. In the setup, the regime-switching process (the Markov chain) contains a rate parameter

"Ε> 0 in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a step-size Μ that denes how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under …