Physical Sciences and Mathematics Commons^™

Heat-Balance Integral To Fractional (Half-Time) Heat Diffusion Sub-Model, Jordan Hristov

Jordan Hristov

The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic pro file with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the …

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 …

Solutions Of Tenth And Ninth-Order Boundary Value Problems By Modified Variational Iteration Method, Syed Tauseef Mohyud-Din, Ahmet Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the modified variational iteration method (MVIM) for solving the ninth and tenth-order boundary value problems. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm …

Extended Second Welfare Theorem For Nonconvex Economies With Infinite Commodities And Public Goods, Aychiluhim Habte, Boris S. Mordukhovich

Mathematics Research Reports

This paper is devoted to the study of nonconvex models of welfare economics with public goods and infinite-dimensional commodity spaces. Our main attention is paid to new extensions of the fundamental second welfare theorem to the models under consideration. Based on advanced tools of variational analysis and generalized differentiation, we establish appropriate approximate and exact versions of the extended second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations in both marginal price and decentralized price forms.

Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.

A Resource Based Stage-Structured Fishery Model With Selective Harvesting Of Mature Species, T. K. Kar, Swarnakamal Misra

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have considered a model in which revenue is generated from fishing and the growth of the fish depends upon the plankton which in turn follows a logistic law of growth. Here the fish population has two stages, a juvenile stage and a mature stage and we consider the harvesting of the mature fish species. Stability and permanence of the system are discussed. Maximum sustainable yield, maximum economic yield and optimal sustainable yield are obtained and different tax policies are discussed to achieve the reference points.

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.

Comparison Differential Transformation Technique With Adomian Decomposition Method For Dispersive Long-Wave Equations In (2+1)-Dimensions, M. A. Mohamed

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we will introduce two methods to obtain the numerical solutions for the system of dispersive long-wave equations (DLWE) in (2+1)-dimensions. The first method is the differential transformation method (DTM) and the second method is Adomian decomposition method (ADM). Moreover, we will make comparison between the solutions obtained by the two methods. Consequently, the results of our system tell us the two methods can be alternative ways for solution of the linear and nonlinear higher-order initial value problems.

Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.

Bianchi Type I Bulk Viscous Fluid String Dust Cosmological Model With Magnetic Field In Bimetric Theory Of Gravitation, M. S. Borkar, S. S. Charjan

Applications and Applied Mathematics: An International Journal (AAM)

In the presence of both magnetic field and bulk viscosity, Bianchi Type I bulk viscous fluid string dust cosmological model in Rosen’s bimetric theory of gravitation have been investigated by using the technique of Letelier and Stachel. The nature of the model is discussed in the absence of both magnetic field and bulk viscosity. To get a determinate solution, we have assumed the condition that σ is proportional to θ and ζθ = constant where σ is the shear, θ is the expansion in the model and ζ is the coefficient of bulk viscosity. Further the physical and geometrical significance …

Improved Dust Acoustic Solitary Waves In Two Temperature Dust Fluids, E. K. El-Shewy, H. G. Abdelwahed, M. I. Abo El Maaty, M. A. Elmessary

Applications and Applied Mathematics: An International Journal (AAM)

A theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear dust-acoustic solitary waves (DASWs) in an unmagnetized two types of dust fluids (one cold and the other is hot) in the presence of Bolltzmannian ions and electrons. A KdV equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of hot and cold dust charge …

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

Variational Iteration Method For Solving Two-Parameter Singularly Perturbed Two Point Boundary Value Problem, Marwan Taiseer Alquran, Nurettin Doğan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, He’s Variational iteration method (VIM) is used for the solution of singularly perturbed two-point boundary value problems with two small parameters multiplying the derivatives. Some problems are solved to demonstrate the applicability of the method. This paper suggests a patern for choosing the freely selected initial approximation in the VIM that leads to a very well approximation by only one iteration.

Developing An Improved Shift-And-Invert Arnoldi Method, H. Saberi Najafi, M. Shams Solary

Applications and Applied Mathematics: An International Journal (AAM)

An algorithm has been developed for finding a number of eigenvalues close to a given shift and in interval [ Lb,Ub ] of a large unsymmetric matrix pair. The algorithm is based on the shift-andinvert Arnoldi with a block matrix method. The block matrix method is simple and it uses for obtaining the inverse matrix. This algorithm also accelerates the shift-and-invert Arnoldi Algorithm by selecting a suitable shift. We call this algorithm Block Shift-and-Invert or BSI. Numerical examples are presented and a comparison has been shown with the results obtained by Sptarn Algorithm in Matlab. The results show that the …

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.

Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia

Applications and Applied Mathematics: An International Journal (AAM)

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

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 …

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 …

Optimizing Radiology Peer Review: A Mathematical Model For Selecting Future Cases Based On Prior Errors, Yun Robert Sheu, Elie Feder, Igor Balsim, Victor F. Levin, Andrew G. Bleicher, Barton F. Branstetter Iv

Publications and Research

Introduction: Peer review is an essential process for physicians because it facilitates improved quality of patient care and continuing physician learning and improvement. However, peer review often is not well received by radiologists, who note that it is time intensive, subjective, and lacks demonstrable impact on patient care. Current advances in peer review include the RADPEER system with its standardization of discrepancies and incorporation of the peer review process into the PACS itself. Our purpose was to build on RADPEER and similar systems by using a mathematical model to optimally select the types of cases to be reviewed, for each …

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 …

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

Byron E. Bell

Theoretical Models For Wall Injected Duct Flows, Tony Saad

Doctoral Dissertations

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by …

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.

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 …

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 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.

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 …

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 …

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.