Applied Mathematics Commons^™

Electrical Impedance Imaging Of Corrosion On A Partially Accessible 2-Dimensional Region, Court Hoang, Katherine Osenbach

Mathematical Sciences Technical Reports (MSTR)

In this paper we examine the inverse problem of determining the amount of corrosion on an inaccessible surface of a two-dimensional region. Using numerical methods, we develop an algorithm for approximating corrosion profile using measurements of electrical potential along the accessible portion of the region. We also evaluate the effect of error on the problem, address the issue of ill-posedness, and develop a method of regularization to correct for this error. An examination of solution uniqueness is also presented.

Anti-Cloaking: The Mathematics Of Disguise, Theresa C. Anderson, Brooke E. Phillips

Mathematical Sciences Technical Reports (MSTR)

Recent developments in cloaking, the ability to selectively bend electromagnetic waves so as to render an object invisible, have been abundant. Based on cloaking principles, we will describe several ways to mathematically disguise objects in the context of electrical impedance imaging. Through the use of a change-of-variables scheme we show how one can make an object appear enlarged, translated, or rotated by surrounding it with a suitable "metamaterial," a man-made material that selectively redirects current. Analysis of eigenvectors and eigenvalues, which describe how current flows, follow. We prove that in order to disguise an object, a metamaterial must encompass both …

A Variation Of The Carleman Embedding Method For Second Order Systems., Charles Nunya Dzacka

Electronic Theses and Dissertations

The Carleman Embedding is a method that allows us to embed a finite dimensional system of nonlinear differential equations into a system of infinite dimensional linear differential equations. This technique works well when dealing with first-order nonlinear differential equations. However, for higher order nonlinear ordinary differential equations, it is difficult to use the Carleman Embedding method. This project will examine the Carleman Embedding and a variation of the method which is very convenient in applying to second order systems of nonlinear equations.

Well-Posedness Of Minimal Time Problem With Constant Dynamics In Banach Spaces, Giovanni Colombo, Vladimir V. Goncharov, Boris S. Mordukhovich

Mathematics Research Reports

This paper concerns the study of a general minimal time problem with a convex constant dynamic and a closed target set in Banach spaces. We pay the main attention to deriving efficient conditions for the major well-posedness properties that include the existence and uniqueness of optimal solutions as well as certain regularity of the optimal value function with respect to state variables. Most of the results obtained are new even in finite-dimensional spaces. Our approach is based on advanced tools of variational analysis and generalized differentiation.

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

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser 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 reflectivity, the peak laser beam …

Random Walks With Elastic And Reflective Lower Boundaries, Lucas Clay Devore

Masters Theses & Specialist Projects

No abstract provided.

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

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser 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 reflectivity, the peak laser beam …

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

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser 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 reflectivity, the peak laser beam …

Computational Fluid Dynamics Of Aggregating Red Blood Cells In Postcapillary Venules, Bong Jae Chung, Sangho Kim, Paul C. Johnson, Aleksander S. Popel

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Aggregate formation of red blood cells (RBCs) in a postcapillary venular bifurcation is investigated with three-dimensional computer simulations using the Chimera grid method. Interaction energy between the RBCs is modelled by a depletion interaction theory; RBCs are modelled as rigid oblate ellipsoids. The cell-cell interactions of RBCs are strongly dependent on vessel geometry and shear rates. The experimental data on vessel geometry, pseudoshear rates, and Dextran concentration obtained in our previous in vivo RBC aggregation study in postcapillary venules of the rat spinotrapezius muscle were used to simulate RBC aggregation. The computational results were compared to the experimental results from …

Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang

Mathematics Faculty Publications

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem

uu_xu_xxx 0 < x < 1, t > 0, (*)

It is shown …

A Generalized Newton-Penalty Algorithm For Large Scale Ill-Conditioned Quadratic Problems, Maziar Salahi, Moslem Ganji

Applications and Applied Mathematics: An International Journal (AAM)

Large scale quadratic problems arise in many real world applications. It is quite often that the coefficient matrices in these problems are ill-conditioned. Thus, if the problem data are available even with small error, then solving them using classical algorithms might result to meaningless solutions. In this short paper, we propose an efficient generalized Newton-penalty algorithm for solving these problems. Our computational results show that our new simple algorithm is much faster and better than the approach of Rojas et al. (2000), which requires parameter tuning for different problems.

Higher Order Difference Schemes For Heat Equation, Jianzhong Wang

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we construct the explicit difference schemes for the heat equation with arbitrary high orders. We also show the validity of the new schemes by numerical simulations.

Remarks On The Stability Of Some Size-Structured Population Models V: The Case When The Death Rate Depends On Adults Only And The Growth Rate Depends On Size Only, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We continue our study of size-structured population dynamics models when the population is divided into adults and juveniles, started in El-Doma (To appear). We concentrate our efforts in the special case when the death rate depends on adults only, the growth rate depends on size only and the maximum size for an individual in the population is infinite. Three demographic parameters are identified and are shown to determine conditions for the (in)stability of a nontrivial steady state. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. …

Some Applications Of The (G'/G)-Expansion Method For Solving The Nonlinear Partial Differential Equations In Mathematical Physics, Nasir Taghizade, Ahmad Neirameh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we construct the traveling wave solutions involving parameters of the combined Kdv-MKdv equation, the Shorma-Tasso-Olver equation and (2+1)-dimensional Konopelchenko-Dubrovsky equation, by using a new approach method. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions.

Uniform Stabilization Of N-Dimensional Vibrating Equation Modeling ‘Standard Linear Model’ Of Viscoelasticity, Ganesh C. Gorain

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with the elastic vibrations of flexible structures modeled by the ‘standard linear model’ of viscoelasticity in n-dimensional space. We study the uniform exponential stabilization of such kind of vibrations after incorporating separately very small amount of passive viscous damping and internal material damping of Kelvin-Viogt type in the model. Explicit forms of exponential energy decay rates are obtained by a direct method, for the solution of such boundary value problems without having to introduce any boundary feedback.

Pulsatile Flow Of Blood In A Constricted Artery With Body Acceleration, Devajyoti Biswas, Uday Shankar Chakraborty

Applications and Applied Mathematics: An International Journal (AAM)

Pulsatile flow of blood through a uniform artery in the presence of a mild stenosis has been investigated in this paper. Blood has been represented by a Newtonian fluid. This model has been used to study the influence of body acceleration and a velocity slip at wall, in blood flow through stenosed arteries. By employing a perturbation analysis, analytic expressions for the velocity profile, flow rate, wall shear stress and effective viscosity, are derived. The variations of flow variables with different parameters are shown diagrammatically and discussed. It is noticed that velocity and flow rate increase but effective viscosity decreases, …

Spatial Instability Of Electrically Driven Jets With Finite Conductivity And Under Constant Or Variable Applied Field, Saulo Orizaga, Daniel N. Riahi

Applications and Applied Mathematics: An International Journal (AAM)

We investigate the problem of spatial instability of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton’s method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One of these modes is enhanced by the strength Ω of …

Remarks On The Stability Of Some Size-Structured Population Models Iv: The General Case Of Juveniles And Adults, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models is investigated when the population is divided into adults and juveniles. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El-Doma (2006), Farkas, et al. (2008), and El-Doma (2008 a).

Two-Layered Model Of Blood Flow Through Composite Stenosed Artery, Padma Joshi, Ashutosh Pathak, B. K. Joshi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper a steady, axisymmetric flow, with a constricted tube has been studied. The artery has been represented by a two-layered model consisting of a core layer and a peripheral layer. It has been shown that the resistance to flow and wall shear stress increases as the peripheral layer viscosity increases. The results are compared graphically with those of previous investigators. It has been observed that the existence of peripheral layer is useful in representation of diseased arterial system.

Explicit And Exact Solutions With Multiple Arbitrary Analytic Functions Of Jimbo–Miwa Equation, Sheng Zhang, Ying-Na Sun, Jin-Mei Ba, Ling Dong

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a generalized F-expansion method is used to construct exact solutions of the (3+1)-dimensional Jimbo–Miwa equation. As a result, many new and more general exact solutions are obtained including single and combined non-degenerate Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions, each of which contains six arbitrary analytic functions. It is shown that with the aid of symbolic computation the generalized F-expansion method may provide a straightforward and effective mathematical tool for solving nonlinear partial differential equations.

Optimal Filtering Of An Advertising Production System With Deteriorating Items, Lakhdar Aggoun, Ali Benmerzouga, Lotfi Tadj

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider an integrated stochastic advertising-production system in the case of a duopoly. Two firms spend certain amounts to advertise some product. The expenses processes evolve according to the jumps of two homogeneous, finite-state Markov chains. We assume that the items in stock may be subject to deterioration and the deterioration parameter is assumed to be random.

Similarity Solutions For A Steady Mhd Falkner-Skan Flow And Heat Transfer Over A Wedge Considering The Effects Of Variable Viscosity And Thermal Conductivity, M. A. Seddeek, A. A. Afify, A. M. Al-Hanaya

Applications and Applied Mathematics: An International Journal (AAM)

An analysis is carried out to study the Falkner–Skan flow and heat transfer of an incompressible, electrically conducting fluid over a wedge in the presence of variable viscosity and thermal conductivity effects. The similarity solutions are obtained using scaling group of transformations. Furthermore the similarity equations are solved numerically by employing Kellr-Box method. Numerical results of the local skin friction coefficient and the local Nusselt number as well as the velocity and the temperature profiles are presented for different physical parameters.

Remarks On The Stability Of Some Size-Structured Population Models Vi: The Case When The Death Rate Depends On Juveniles Only And The Growth Rate Depends On Size Only And The Case When Both Rates Depend On Size Only, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We continue our study of size-structured population dynamics models when the population is divided into adults and juveniles, started in El-Doma (to appear 1) and continued in El-Doma (to appear 2). We concentrate our efforts in two special cases, the first is when the death rate depends on juveniles only and the growth rate depends on size only, and, the second is when both the death rate and the growth rate depend on size only. In both special cases we assume that the maximum size for an individual in the population is infinite. We identify three demographic parameters and show …

A Graph Theoretic Summation Of The Cubes Of The First N Integers, Joseph Demaio, Andy Lightcap

Faculty Articles

In this Math Bite we provide a combinatorial proof of the sum of the cubes of the first n integers by counting edges in complete bipartite graphs.

Some New Problems In Changepoint Analysis, Jonathan Woody

All Dissertations

Climatological studies have often neglected changepoint effects when modeling
various physical phenomena. Here, changepoints are plausible whenever a station location moves or its instruments are changed. There is frequently meta-data to
perform sound statistical inferences that account for changepoint
information. This dissertation focuses on two such problems in changepoint analysis.
The first problem we investigate involves assessing trends
in daily snow depth series. Here, we introduce a stochastic storage model. The model allows for seasonal features, which permits the
analysis of daily data. Changepoint times are shown to greatly influence estimated trends in one snow depth series and are accounted …

Decoding Of Multipoint Algebraic Geometry Codes Via Lists, Nathan Drake

All Dissertations

Algebraic geometry codes have been studied greatly since their introduction by Goppa . Early study had focused on algebraic geometry codes CL(D;G) where G was taken to be a multiple of a single point. However, it has been shown that if we allow G to be supported by more points, then the associated code may have better parameters. We call such a code a multipoint code and if G is supported by m points, then we call it an m-point code. In this dissertation, we wish to develop a decoding algorithm for multipoint codes. We show how we can embed …

Electromagnetic Scattering Solutions For Digital Signal Processing, Jonathan Blackledge

Other resources

Electromagnetic scattering theory is fundamental to understanding the interaction between electromagnetic waves and inhomogeneous dielectric materials. The theory unpins the engineering of electromagnetic imaging systems over a broad range of frequencies, from optics to radio and microwave imaging, for example. Developing accurate scattering models is particularly important in the field of image understanding and the interpretation of electromagnetic signals generated by scattering events. To this end there are a number of approaches that can be taken. For relatively simple geometric configurations, approximation methods are used to develop a transformation from the object plane (where scattering events take place) to the …

Random Graphs: From Paul Erdős To The Internet, Michał Karoński

Dalrymple Lecture Series

Paul Erdős, one of the greatest mathematicians of the twentieth century, was a champion of applications of probabilistic methods in many areas of mathematics, such as a graph theory, combinatorics and number theory. He also, almost fifty years ago, jointly with another great Hungarian mathematician Alfred Rényi, laid out foundation of the theory of random graphs: the theory which studies how large and complex systems evolve when randomness of the relations between their elements is incurred. In my talk I will sketch the long journey of this theory from the pioneering Erdős era to modern attempts to model properties of …

Hybrid Proximal Methods For Equilibrium Problems, Boris S. Mordukhovich, Barbara Panicucci, Mauro Passacantando, Massimo Pappalardo

Mathematics Research Reports

This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions.

Population Coding Of Tone Stimuli In Auditory Cortex: Dynamic Rate Vector Analysis, Peter Bartho, Carina Curto, Artur Luczak, Stephan L. Marguet, Kenneth D. Harris

Department of Mathematics: Faculty Publications

Neural representations of even temporally unstructured stimuli can show complex temporal dynamics. In many systems, neuronal population codes show “progressive differentiation,” whereby population responses to different stimuli grow further apart during a stimulus presentation. Here we analyzed the response of auditory cortical populations in rats to extended tones. At onset (up to 300 ms), tone responses involved strong excitation of a large number of neurons; during sustained responses (after 500 ms) overall firing rate decreased, but most cells still showed a statistically significant difference in firing rate. Population vector trajectories evoked by different tone frequencies expanded rapidly along an initially …