Physical Sciences and Mathematics Commons^™

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

My Trig Book, Bruce Kessler

Mathematics Faculty Publications

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Academy sections of the course. The text has also been used in two online course offerings.

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

A Finite Volume Method For Solving Parabolic Equations On Logically Cartesian Curved Surface Meshes, Donna Calhoun, Christiane Helzel

Donna Calhoun

We present a second-order, finite-volume scheme for the constant-coefficient diffusion equation on curved, parametric surfaces described via smooth or piecewise smooth mappings on logically Cartesian meshes. Our method does not require analytic metric terms, shows second-order accuracy, can be easily coupled to existing finite-volume solvers for logically Cartesian meshes and handles general mixed boundary conditions. We present numerical results demonstrating the accuracy of the scheme, and then use the scheme to solve advection-reaction-diffusion equations modeling biological pattern formation on surfaces.

Soliton Perturbation Theory For A Higher-Order Hirota Equation, Tim Marchant

Tim Marchant

Solitary wave evolution for a higher order Hirota equation is examined. For the higher order Hirota equation resonance between the solitary waves and linear radiation causes radiation loss. Soliton perturbation theory is used to determine the details of the evolving wave and its tail. An analytical expression for the solitary wave tail is derived and compared to numerical solutions. An excellent comparison between numerical and theoretical solutions is obtained for both right- and left-moving waves. Also, a two-parameter family of higher order asymptotic embedded solitons is identified.

Modulation Analysis Of Boundary Induced Motion Of Optical Solitary Waves In A Nematic Liquid Crystal, Tim Marchant

Tim Marchant

We consider the motion of a solitary wave, a nematicon, in a finite cell filled with a nematic liquid crystal. A modulation theory is developed to describe the boundary-induced bouncing of a nematicon in a one-dimensional cell and it is found to give predictions in very good agreement with numerical solutions. The boundary-induced motion is then considered numerically for a two-dimensional cell and a simple extension of the modulation theory from one to two space dimensions is then made, with good agreement being found with numerical solutions for the nematicon trajectory. The role of nematicon shape and relative position to …

A Sensitivity Matrix Methodology For Inverse Problem Formulation, Alex Calpaldi

Alex Capaldi

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the …

A Perturbation Drbem Model For Weakly Nonlinear Wave Run-Ups Around Islands, Tim Marchant

Tim Marchant

In this paper, the dual reciprocity boundary element method (DRBEM) based on the perturbation method is presented for calculating run-ups of weakly nonlinear long waves scattered by islands. Under the assumption that the incident waves are harmonic, the time-dependent nonlinear Boussinesq equations are transformed into three time-independent linear equations by using the perturbation method, where, besides nonlinearity ε, the dispersion μ2 is also included in the perturbed expansion. The first-order solution η0 is found by using the linear long-wave equations. Then η0 is used in two second-order governing equations related to the dispersion and nonlinearity, respectively. Since no any omission …

Characterization Of Compactly Supported Renable Splines With Integer Matrix, Tian-Xiao He, Yujing Guana

Tian-Xiao He

Let M be an integer matrix with absolute values of all its eigenvalues being greater than 1. We give a characterization of compactly supported M-refinable splines f and the conditions that the shifts of f form a Riesz basis.

Bootstrap And Second Order Tests Of Risk Difference, Chris Lloyd

Chris J. Lloyd

Standard approximate tests of the difference of two probabilities have type 1 error that can differ significantly from nominal, even for quite large sample sizes. There are two modern methods of reducing type 1 error. One is to use so-called higher order asymptotics (Reid, 2003) to provide an explicit adjustment to the likelihood ratio statistic. The second is to replace the nuisance parameter in an exact calculation with a null estimate (Young and Lee, 2005), which is a kind of bootstrap. The purpose of this paper is to explain and evaluate these two methods, for testing whether a difference in …

Syllabus Of Mathematics For Economists (Master's Course), Reza Moosavi Mohseni Dr.

Reza Moosavi Mohseni

No abstract provided.

When To Spray: A Time-Scale Calculus Approach To Controlling The Impact Of West Nile Virus, Diana Thomas, Marion Weedermann, Lora Billings, Joan Hoffacker, Robert A. Washington-Allen

Lora Billings

The Development Of Humans – A Study Including Languages, Cultures, Religions And Genetics, Dr. Erik Dahlquist, Dr. Allan Dahlquist

Dr. Erik Dahlquist

The book covers the development of culture, religion, language and genetics of the human population since prehistory. Four main cultures have spread around the globe: 1) Monosyllabic language people with ancestor cult 2) Austroasiatic people with sun worshipping and megalit graves. Counting with 20 as the base 3) Uralic speaking people with kings from the sky, and strong city states. Moon and mother godess. Don´t differentiate between male and female, he and she. 4) Inflectual language speaking people with sky gods and cattles. Indoeuropeans. Often endings differentiating he and she. Shows how original cultures are refelected in todays society.

Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun

Xiao-Jun Yang

It is proposed that local fractional calculas introduced by Kolwankar and Gangal is extended by the concept of Jumarie’s fractional calculus and local fractional definite integral is redefined. The properties and the theorems of local fractional calculus are discussed in this paper.

My Trig Book, Bruce Kessler

Bruce Kessler

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Academy sections of the course. The text has also been used in two online course offerings. Revised 7/19/11.

Free readers are available for all of the files that accompany the book. Mathematica Player is available at http://www.wolfram.com/products/player/. QuickTime Player is available at http://www.apple.com/quicktime/.

Genome-Wide Scan Reveals Association Of Psoriasis With Il-23 And Nf-B Pathways, Rajan P. Nair, Kristina C. Duffin, Cynthia Helms, Jun Ding, Philip E. Stuart, David Goldgar, Johann E. Gudjonsson, Yun Li, Trilokraj Tejasvi, Bing-Jiag Feng, Andreas Ruether, Stefan Schreiber, Michael Weichenthal, Dafna Gladman, Proton Rahman, Steven J. Schrodi, Sampath Prahalad, Stephen L. Guthery, Judith Fischer, Wilson Liao, Pui-Yan Kwok, Alan Menter, G Mark Lathrop, Carol A. Wise, Ann B. Begovich, John J. Voorhees, James T. Elder, Gerald G. Krueger, Anne M. Bowcock, Goncalo R. Abecasis

Steven J Schrodi

Psoriasis is a common immune-mediated disorder that affects the skin, nails and joints. To identify psoriasis susceptibility loci, we genotyped 438,670 SNPs in 1,409 psoriasis cases and 1,436 controls of European ancestry. We followed up 21 promising SNPs in 5,048 psoriasis cases and 5,041 controls. Our results provide strong support for the association of at least seven genetic loci and psoriasis (each with combined P < 5 10-8). Loci with confirmed association include HLA-C, three genes involved in IL-23 signaling (IL23A, IL23R, IL12B), two genes that act downstream of TNF- and regulate NF-B signaling (TNIP1, TNFAIP3) and two genes involved in the modulation of Th2 immune responses (IL4, IL13). Although the proteins encoded in these loci are known to interact biologically, we found no evidence for epistasis between associated SNPs. Our results expand the catalog of genetic loci implicated in psoriasis susceptibility and suggest priority targets for study in other auto-immune disorders.

A Fine Mapping Theorem To Refine Results From Association Genetics Studies, Steven J. Schrodi

Steven J Schrodi

No abstract provided.

Greedy Signal Recovery Review, Deanna Needell, Joel A. Tropp, Roman Vershynin

CMC Faculty Publications and Research

The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees.

Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This …

Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling

Mathematical Sciences Technical Reports (MSTR)

Developing methods for the nondestructive testing of materials is an important area of research for industry. Situations often arise in which the integrity of an object is questioned, but testing it is very difficult. For example, a support bar may be embedded in a larger structure so that testing the bar’s integrity directly would require the impractical task of breaking down the larger structure. Instead, the ends of the bar might be accessible without dismantling the enclosing structure. The goal of nondestructive testing is to use methods that require taking measurements at the ends of the bar alone to give …

Determining The Shape Of A Resistor Grid, Esther Chiew, Vincent Selhorst-Jones

Mathematical Sciences Technical Reports (MSTR)

Impedance imaging has received a lot of attention in the past two decades, as a means for non-destructively imaging the interior of a conductive object. One injects a known electrical current pattern into an object at the exterior boundary, then measures the induced potential (voltage) on some portion of the boundary. The goal is to recover information about the interior conductivity of the object, which (we hope) influences the voltages we measure. Of course one can also use multiple input currents and measured voltages. A variation on this problem is that of "boundary identification," in which some portion of the …

Robust Stability And Optimality Conditions For Parametric Infinite And Semi-Infinite Programs, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper primarily concerns the study of parametric problems of infinite and semi-infinite programming, where functional constraints are given by systems of infinitely many linear inequalities indexed by an arbitrary set T, where decision variables run over Banach (infinite programming) or finite-dimensional (semi-infinite case) spaces, and where objectives are generally described by nonsmooth and nonconvex cost functions. The parameter space of admissible perturbations in such problems is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set T is finite, this space is intrinsically infinite-dimensional (nonreflexive and nonseparable) of the l(infinity)-type. By using …

Transient Analysis Of Heat And Mass Transfer By Natural Convection In Power-Law Fluid Past A Vertical Plate Immersed In A Porous Medium (Numerical Study), Nasser S. Elgazery

Applications and Applied Mathematics: An International Journal (AAM)

This paper attempted a numerical examination of the problem of unsteady free convection with heat and mass transfer from an isothermal vertical flat plate to a non-Newtonian fluid saturated porous medium. The flow in the porous medium was described via the Darcy-Brinkman-Forchheimer model. The simultaneous development of the problem of boundary layers was obtained numerically by finite difference method. Boundary layer and Boussinesq approximations had been incorporated. Numerical calculations were carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles were shown graphically and the physical quantities of the problem were given in tables. It …

Chebyshev Collocation Method For The Effect Of Variable Thermal Conductivity On Micropolar Fluid Flow Over Vertical Cylinder With Variable Surface Temperature, Nasser S. Elgazery, Nader Y. Abd Elazem

Applications and Applied Mathematics: An International Journal (AAM)

An analysis is performed to study the role of a variable thermal conductivity on unsteady free convection in a micro-polar fluid past a semi-infinite vertical cylinder with variable surface temperature in the presence of magnetic filed and radiation. The surface temperature is measured to vary as a power of the axial coordinate measured from the leading edge of the cylinder. The governing non-linear partial differential equations are transformed into a linear algebraic system utilizing Chebyshev collocation method in spatial and Crank-Nicolson method in time. Numerical results for the velocity, angular velocity and temperature profiles as well as for the local …

On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

The a-ary 3-point and 5-point interpolatery subdivision schemes for curve design are introduced for arbitrary odd integer a greater than or equal to 3. These new schemes further extend the family of the classical 4- and 6-point interpolatory schemes.

Soliton Perturbation Theory For The Modified Kawahara Equation, Anjan Biswas

Applications and Applied Mathematics: An International Journal (AAM)

The modified Kawahara equation is studied along with its perturbation terms. The adiabatic dynamics of the soliton amplitude and the velocity of the soliton are obtained by the aid of soliton perturbation theory.

On Existence And Uniqueness Theorem Concerning Time–Dependent Heat Transfer Model, Naji A. Qatanani, Qasem M. Heeh

Applications and Applied Mathematics: An International Journal (AAM)

In this article we consider a physical model describing time-dependent heat transfer by conduction and radiation. This model contains two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-grey surfaces. The aim of this work is to present a reliable framework to prove the existence and the uniqueness of a weak solution for this problem. The existence of the solution can be proved by solving an auxiliary problem by the Galerkin-based approximation method and Moser-type arguments which implies the existence of solution to the original problem. The uniqueness of the solution will …

On The Mixed Sum Of Doubly Infinite And Finite Independent Random Variables, Mridula Garg

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the present paper is to study the distribution of the mixed sum of two random variables. Here we establish a theorem which gives the probability density function (pdf) of sum of doubly infinite and finite independent random variables. The distribution of the infinite and finite independent random variables is given in the form of corollary. As an application of these results we have obtained a distribution of sum of bilateral exponential variate with triangular, Rayleigh with uniform and Weibull with triangular variate. Some graphs of these distributions have also been given.

Establishment Of A Chebyshev-Dependent Inhomogeneous Second Order Differential Equation For The Applied Physics-Related Boubaker-Turki Polynomials, Micahel Dada, O. Bamidele Awojoyogbe, Maximilian Hasler, Karem B. Ben Mahmoud, Amine Bannour

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes Chebyshev-dependent inhomogeneous second order differential equation for the m-Boubaker polynomials (or Boubaker-Turki polynomials). This differential equation is also presented as a guide to applied physics studies. A concrete example is given through an attempt to solve the Bloch NMR flow equation inside blood vessels.

The Möbius Geometry Of Hypersurfaces, Michael Bolt

University Faculty Publications and Creative Works

No abstract provided.

Homotopy Perturbation Method And Padé Approximants For Solving Flierl-Petviashivili Equation, Syed T. Mohynd-Din, Muhammad A. Noor

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable combination of homotopy perturbation method and Padé approximants to investigate the Flierl-Petviashivili (FP) equation. The approach introduces a new transformation necessary for the conversion of the Flierl-Petviashivili equation to a first order initial value problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed homotopy perturbation method is applied to the reformulated first order initial value problem which leads the solution in terms of transformed variable. The desired series solution is obtained by making use of the inverse transformation. The suggested algorithm may …