Applied Mathematics Commons^™

Shock-Associated Noise Generation In Curved Coanda Turbulent Wall Jets, Caroline P. Lubert, Richard J. Shafer

Department of Mathematics and Statistics - Faculty Scholarship

Curved three-dimensional turbulent Coanda wall jets are present in a multitude of natural and engineering applications. The mechanism by which they form a shock-cell structure is poorly understood, as is the accompanying shock-associated noise (SAN) generation. This paper discusses these phenomena from both a modeling and experimental perspective. The Method of Characteristics is used to rewrite the governing hyperbolic partial differential equations as ordinary differential equations, which are then solved numerically using the Euler predictor-corrector method. The effects of complicating factors -- such as radial expansion and streamline curvature -- on the prediction of shock-cell location are then discussed. This …

Cooper’S Hawk Nest Site Characteristics In The Pineywoods Region, Richard R. Schaefer, D. Craig Rudolph, Josh B. Pierce, Jesse F. Fagan

Faculty Publications

Early accounts describe the Cooper’s Hawk (Accipiter cooperi) as a species in decline in much of North America during the early twentieth century (Bent 1937), particularly when in close proximity to humans (Eaton 1914). This decreasing population trend continued to be recognized later in the century in both Texas (Oberholser 1974) and Louisiana (Lowery 1974). Shooting and trapping during the first half of the 1900s, and pesticide use (especially DDT) after World War II are suggested as primary causes of the decline (Henny and Wight 1972, Bednarz et al. 1990). The Migratory Bird Treaty Act of 1972 and the ban …

Twisted Frobenius-Schur Indicators For Hopf Algebras, Maria Vega

LSU Doctoral Dissertations

The classical Frobenius--Schur indicators for finite groups are character sums defined for any representation and any integer $m\ge 2$. In the familiar case $m=2$, the Frobenius--Schur indicator partitions the irreducible representations over the complex numbers into real, complex, and quaternionic representations. In recent years, several generalizations of these invariants have been introduced. Bump and Ginzburg in 2004, building on earlier work of Mackey from 1958, have defined versions of these indicators which are twisted by an automorphism of the group. In another direction, Linchenko and Montgomery in 2000 defined Frobenius--Schur indicators for finite dimensional semisimple Hopf algebras. In this dissertation, …

Improving Math Instruction In Schools That Serve The Poor, John, L. Jr. Sims

LSU Master's Theses

Public alarm concerning how well U.S. schools are performing in mathematics compared to other developed nations is increasing. Reports of inadequate teaching, poor curriculum design, and low performance on standardized test have been fueled by the media. These issues in American mathematics classrooms are far compounded in schools that serve the poorest in America. When comparing mathematical proficiency rates of U.S. schools with other countries, schools with less than 25% free and reduced lunch score competitively with counterparts in other countries. In contrast, schools with rates of free and reduced lunch higher than 50% score dismally in comparison. Conditions such …

Paley-Wiener Theorems With Respect To The Spectral Parameter, Susanna Dann

LSU Doctoral Dissertations

One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then harmonic analysis on M is closely related to the representations of G and the direct integral decomposition of L^2(M) into irreducible representations of G. R^n can be realized as the quotient R^n=E(n)/SO(n), where E(n) is the orientation preserving Euclidean motion group. The pair (E(n), SO(n)) is a Gelfand pair. Hence this realization of R^n comes with its own natural …

Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko

Mathematics & Statistics Faculty Publications

No abstract provided.

Analytical And Experimental Investigations Of Ships Impact Interaction With One-Sided Barrier, Ihab M. Grace

Wayne State University Dissertations

This study deals with impact interaction of ships with one-sided ice barrier during roll dynamics. An analytical model of ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, brings to the attention the fact that the impact dynamics may have qualitatively different response characteristics to different …

Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Stability, Charles B. Harris, Richard D. Noren

Mathematics & Statistics Faculty Publications

We study stability of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation u'(t) + ∫0 β (t - s)Au(s) ds = 0, t ≥ 0, u(0) = u0, which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real Hilbert space, and β (t) is locally integrable, nonnegative, nonincreasing, convex, and -β'(t) is convex. We establish stability of the method under these hypotheses on β(t). Thus, …

Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng

Department of Mathematics: Faculty Publications

Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

Specification Of Structural Viewer And Analytical Tool (Jecp/Svat), Xingzhong Li

Nebraska Center for Materials and Nanoscience: Faculty Publications

Java Electron Crystallography Package (JECP) is a collection of programs for crystallography and electron diffraction analysis. The package is designed and written by Dr. X.Z. Li. The software can be used as a research tool as well as a teaching aid. The need of a structural viewer/an analytical tool, using the same input data format as the JECP and proJECT software, becomes obvious with the growth of the JECP and proJECT programs and users. There exist many programs for structural design and/or display in various levels developed by individual, research group or software company. Some of them are expensive software …

A Dynamic System Model Of Biogeography-Based Optimization, Daniel J. Simon

Electrical and Computer Engineering Faculty Publications

We derive a dynamic system model for biogeography-based optimization (BBO) that is asymptotically exact as the population size approaches infinity. The states of the dynamic system are equal to the proportion of each individual in the population; therefore, the dimension of the dynamic system is equal to the search space cardinality of the optimization problem. The dynamic system model allows us to derive the proportion of each individual in the population for a given optimization problem using theory rather than simulation. The results of the dynamic system model are more precise than simulation, especially for individuals that are very unlikely …

A Time Series Approach To Electric Load Modelling, Matthias Benjamin Noller

Masters Theses

"With resources becoming more and more scarse [sic] as well as increasing competition caused by the liberalisation of the energy markets electric load modelling becomes ever more important for proper resource allocation.

This work tries to bridge the gap between long-term modelling done mainly via econometric approaches and short-term modelling in which time series models are more commonplace by focussing [sic] on pure time series modelling [sic] and exploring its limits in the process. Due to various seasonalities present in the data the approach chosen starts with a subdivision of the time axis in different time frames: A model for …

Solving The Partial Differential Equation Of Vibrations With Interval Parameters Using The Interval Finite Difference Method, Brenda G. Medina

Open Access Theses & Dissertations

Accuracy and efficiency are among the main factors that drive today's innovative disciplines. As technology rapidly advances, efficiency takes on new meanings but what about accuracy? How accurate is accurate? Human error, uncertainties in measurement, and rounding errors are just some causes of inaccuracy. Interval Computations is an area that allows for such issues to be taken into account; for each measurement attained (for example), an interval can be built by considering the error associated with the measurement, and such an interval can be utilized in the mathematical computations of interest.

We consider the partial differential equation (PDE) of vibrations …

Dispersive Wave Equations For Solids With Microstructure, A. Berezovski, Juri Engelbrecht, Mihhail Berezovski

Publications

The dispersive wave motion in solids with microstructure is considered in the one-dimensional setting in order to understand better the mechanism of dispersion. It is shown that the variety of dispersive wave propagation models derived by homogenization, continualisation, and generalization of continuum mechanics can be unified in the framework of dual internal variables theory.

A Generalized Nonlinear Model For The Evolution Of Low Frequency Freak Waves, Jonathan Blackledge

Articles

This paper presents a generalized model for simulating wave fields associated with the sea surface. This includes the case when `freak waves' may occur through an effect compounded in the nonlinear (cubic) Schrodinger equation. After providing brief introductions to linear sea wave models, `freak waves' and the linear and nonlinear Schrodinger equations, we present a unified model that provides for a piecewise continuous transition from a linear to a nonlinear state. This is based on introducing a fractional time derivative to develop a fractional nonlinear partial differential equation with a stochastic source function. In order to explore the characteristics of …

Cryptography Using Steganography: New Algorithms And Applications, Jonathan Blackledge

Articles

Developing methods for ensuring the secure exchange of information is one of the oldest occupations in history. With the revolution in Information Technology, the need for securing information and the variety of methods that have been developed to do it has expanded rapidly. Much of the technology that forms the basis for many of the techniques used today was originally conceived for use in military communications and has since found a place in a wide range of industrial and commercial sectors. This has led to the development of certain industry standards that are compounded in specific data processing algorithms together …

Modeling, Analysis, And Simulation Of Discrete-Continuum Models Of Step-Flow Epitaxy: Bunching Instabilities And Continuum Limits, Nicholas O. Kirby

University of Kentucky Doctoral Dissertations

Vicinal surfaces consist of terraces separated by atomic steps. In the step-flow regime, deposited atoms (adatoms) diffuse on terraces, eventually reaching steps where they attach to the crystal, thereby causing the steps to move. There are two main objectives of this work. First, we analyze rigorously the differences in qualitative behavior between vicinal surfaces consisting of infinitely many steps and nanowires whose top surface consists of a small number of steps bounded by a reflecting wall. Second, we derive the continuum model that describes the macroscopic behavior of vicinal surfaces from detailed microscopic models of step dynamics.

We use the …

Riordan Arrays Associated With Laurent Series And Generalized Sheffer-Type Groups, Tian-Xiao He

Scholarship

A relationship between a pair of Laurent series and Riordan arrays is formulated. In addition, a type of generalized Sheffer groups is defined using Riordan arrays with respect to power series with non-zero coefficients. The isomorphism between a generalized Sheffer group and the group of the Riordan arrays associated with Laurent series is established. Furthermore, Appell, associated, Bell, and hitting-time subgroups of the groups are defined and discussed. A relationship between the generalized Sheffer groups with respect to different power series is presented. The equivalence of the defined Riordan array pairs and generalized Stirling number pairs is given. A type …

Currency Trading Using The Fractal Market Hypothesis, Jonathan Blackledge, Kieran Murphy

Articles

We report on a research and development programme in financial modelling and economic security undertaken in the Information and Communications Security Research Group (ICSRG, 2011) which has led to the launch of a new company - Currency Traders Ireland Limited - funded by Enterprise Ireland. Currency Traders Ireland Limited (CTI, 2011) has a fifty year exclusive license to develop a new set of indicators for analysing currency exchange rates (Forex trading). We consider the background to the approach taken and present examples of the results obtained to date.

Some Classes Of Graphs That Are Nearly Cycle-Free, Lisa Warshauer

LSU Doctoral Dissertations

A graph is almost series-parallel if there is some edge that one can add to the graph and then contract out to leave a series-parallel graph, that is, a graph with no K₄-minor. In this dissertation, we find the full list of excluded minors for the class of graphs that are almost series-parallel. We also obtain the corresponding result for the class of graphs such that uncontracting an edge and then deleting the uncontracted edge produces a series-parallel graph.

A notable feature of a 3-connected almost series-parallel graph is that it has two vertices whose removal leaves a …