Applied Mathematics Commons^™

Exact Solutions For Wind-Driven Coastal Upwelling And Downwelling Over Sloping Bathymetry, Dana Lynn Duke, Paul Derek Sinz

Mathematics

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping bathymetries. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial stratification and no initial alongshore flow. An alongshore pressure gradient is …

Inverse Heat Conduction Problem In A Semi-Infinite Circular Plate And Its Thermal Deflection By Quasi-Static Approach, K. C. Deshmukh, S. C. Warbhe, G. D. Kedar, V. S. Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

This paper concerns the inverse heat conduction problem in a semi-infinite thin circular plate subjected to an arbitrary known temperature under unsteady condition and the behavior of thermal deflection has been discussed on the outer curved surface with the help of mathematical modeling. The solutions are obtained in an analytical form by using the integral transform technique.

Approximations Of Sturm-Liouville Eigenvalues Using Sinc-Galerkin And Differential Transform Methods, Marwan Taiseer Alquran, Kamel Al-Khaled

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a comparative study of Sinc-Galerkin method and differential transform method to solve Sturm-Liouville eigenvalue problem. As an application, a comparison between the two methods for various celebrated Sturm-Liouville problems are analyzed for their eigenvalues and solutions. The study outlines the significant features of the two methods. The results show that these methods are very efficient, and can be applied to a large class of problems. The comparison of the methods shows that although the numerical results of these methods are the same, differential transform method is much easier, and more efficient than the Sinc-Galerkin method.

Soliton And Periodic Solutions For (3+1)-Dimensional Nonlinear Evolution Equations By Exp-Function Method, A. Borhanifar, M. M. Kabir

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, (3+1)-dimensional Jimbo-Miwa and (3+1)-dimensional potential-YTSF equations are considered and the Exp-Function method is employed to compute the exact solutions. The solutions obtained by this method are compared with the exact solutions obtained through other methods. These equations play a very important role in mathematical physics and engineering sciences. It is shown that the Exp-Function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics

Effects Of Radiation And Variable Viscosity On Mhd Free Convective Flow And Mass Transfer Over A Stretching Sheet With Chemical Reaction, M. A. Seddeek, A. A. Almushigeh

Applications and Applied Mathematics: An International Journal (AAM)

A similarity solution is proposed for the analysis of steady free convection heat and mass transfer over a stretching sheet. The effect of radiation, chemical reaction and variable viscosity on hydromagnetic heat and mass transfer in the presence of magnetic field are investigated. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solved numerically by means of the fourth-order Runge– Kutta method with shooting technique. A comparison with exact solution is performed and the results are found to be in excellent. Numerical results for the velocity, temperature and concentration as well as …

Temperature Profiles In A Disc Brake, K. Venkateswara Reddy, D. Rama Murthy

Applications and Applied Mathematics: An International Journal (AAM)

The Science of heat transfer allows us to determine the time rate of energy transfer caused by non equilibrium of temperatures. The importance of heat transfer in proper design of Automobiles has long been recognized. In this paper we determined the transient temperature distributions in a disc brake during a single brake application using Finite difference numerical technique. Hyperbolic heat conduction which includes the effect of the finite heat propagation is gaining importance. It is necessary to consider hyperbolic heat conduction in problems involving short time intervals and for very high heat fluxes. Here we considered both parabolic and hyperbolic …

Geometry, Greed, Games, And 'Roids, James Oxley

Dalrymple Lecture Series

A three-legged stool doesn’t wobble. But four-legged stools often teeter because the tips of their legs don’t lie in the same plane.

This phenomenon of dependent sets, first theorized 75 years ago, is the focus of the 16th Dalrymple Lecture in Mathematics, set for 5:30 p.m. Friday (May 21) at the University of Mississippi. James Oxley, who holds an alumni professorship at Louisiana State University, is to deliver the address, which is free and open to the public in the Student Union Ballroom.

“There is some beautiful and intriguing mathematics that arises from some natural problems in geometry and network …

Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper

Mathematical Sciences Technical Reports (MSTR)

We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in …

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …

An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung

Masters Theses & Specialist Projects

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(n) time where n is the number of crossings …

Sparse Representation For Detection Of Transients Using A Multi-Resolution Representation Of The Auto-Correlation Of Wavelets, Caroline Sieger

All Theses

This thesis seeks to detect damped sinusoidal transients, specifically capacitor switching transients, buried in noise and to answer the following questions: 1.) Can the transient s(t;q) be sparsely represented from s&delta(t) = s(t;q) + &epsilon(t) using sparsity methods, where &epsilon(t) is white Gaussian noise? 2.) Does computing the local auto-correlation of the signal around the transient improve detection? 3.) How does the auto-correlation shell representation compare to the wavelet representation? 4.) Which basis is ''best''? 5.) Which method and representation is best? This thesis explores detection schemes based on classical methods and newer sparsity methods. Classical methods considered include reconstruction …

A Numerical Study Of Subgrid Artificial Viscosity Methods For The Navier-Stokes Equations, Keith Galvin

All Theses

This paper studies two artificial viscosity methods for approximating solutions to the Navier&ndashStokes Equations. Both methods that are introduced add stabilization, then remove it only on a coarse mesh. Both methods can be considered as conforming, mixed methods for 1) velocity and its gradient, and 2) velocity and vorticity. Herein we rigorously study the schemes both analytically and computationally, showing that both methods are unconditionally stable and optimally convergent. Numerical experiments show both methods provide improved results over the unstabilized Navier&ndashStokes Equations.

On Directionally Dependent Subdifferentials, Ivan Ginchev, Boris S. Mordukhovich

Mathematics Research Reports

In this paper directionally contextual concepts of variational analysis, based on dual-space constructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulness, necessary and also sufficient optimality conditions in terms of directioual subdifferentials are established, and it is shown that they can be effective in the situations where known optimality conditions in terms of nondirectional subdifferentials fail.

Analyzing Fractals, Kara Mesznik

Renée Crown University Honors Thesis Projects - All

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is self- similar, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the Contraction Mapping Theorem and shifted using linear and affine transformations.

Fractals live in something called a metric space. A metric space, denoted (X, d), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals …

Compressive Sensing, Yue Mao

All Theses

Compressive sensing is a novel paradigm for acquiring signals and has a wide range of applications. The basic assumption is that one can recover a sparse or compressible signal from far fewer measurements than traditional methods. The difficulty lies in the construction of efficient recovery algorithms. In this thesis, we review two main approaches for solving the sparse recovery problem in compressive sensing: l1-minimization methods and greedy methods. Our contribution is that we look at compressive sensing from a different point of view by connecting it with sparse interpolation. We introduce a new algorithm for compressive sensing called generalized eigenvalues …

Neutrosophic Physics: More Problems, More Solutions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

When considering the laws of theoretical physics, one of the physicists says that these laws – the actual expressions of the laws of mathematics and logics being applied to physical phenomena – should be limited according to the physical meaning we attribute to the phenomena. In other word, there is an opinion that a theoretical physicist should put some limitations onto mathematics, in order to “reduce” it to the observed reality. No doubt, we can do it. However, if following this way, we would arrive at only mathematical models of already known physical phenomena. Of course, this might be useful …

The Steiner Linear Ordering Problem: Application To Resource-Constrained Scheduling Problems, Mariah Magagnotti

All Theses

When examined through polyhedral study, the resource-constrained scheduling problems have always dealt with processes which have the same priority. With the Steiner Linear Ordering problem, we can address systems where the elements involved have different levels of priority, either high or low. This allows us greater flexibility in modeling different resource-constrained scheduling problems. In this paper, we address both the linear ordering problem and its application to scheduling problems, and provide a polyhedral study of the associated polytopes.

Increased Accuracy And Efficiency In Finite Element Computations Of The Leray-Deconvolution Model Of Turbulence, Abigail Bowers

All Theses

This thesis develops, analyzes and tests a finite element method for approximating solutions to the Leray–deconvolution regularization of the Navier–Stokes equations. The scheme combines three ideas in order to create an accurate and effective algorithm: the use of an incompressible filter, a linearization that decouples the velocity–pressure system from the filtering and deconvolution operations, and a stabilization that works well with the linearization. A rigorous and complete numerical analysis of the scheme is given, and numerical experiments are presented that show clear advantages of the scheme.

Improved Accuracy For Fluid Flow Problems Via Enhanced Physics, Michael Case

All Dissertations

This thesis is an investigation of numerical methods for approximating solutions to fluid flow problems, specifically the Navier-Stokes equations (NSE) and magnetohydrodynamic equations (MHD), with an overriding theme of enforcing more physical behavior in discrete solutions. It is well documented that numerical methods with more physical accuracy exhibit better long-time behavior than comparable methods that enforce less physics in their solutions. This work develops, analyzes and tests finite element methods that better enforce mass conservation in discrete velocity solutions to the NSE and MHD, helicity conservation for NSE, cross-helicity conservation in MHD, and magnetic field incompressibility in MHD.

The Postsecret Phenomenon: A Contemporary Application Of Existential Psychotherapy, Dan Martin

Senior Honors Projects

In November 2004, as a whimsical break from his monotonous job, Frank Warren decided he would start a small art project in his community. This idea, which he entitled “PostSecret,” involved leaving blank post cards in various public locations that simply asked to “Share a Secret” and listed a few guidelines. Frank’s goal was to “create this non-judgmental, safe place where people could feel comfortable sharing parts of their lives that they've never told a soul.” What he expected to be a small result became a weekly blog, five published books, a traveling art gallery, and a lecture series given …