Applied Mathematics Commons^™

The Boundary Element Method Applied To The Two Dimensional Stefan Moving Boundary Problem, Donald C. Vosika

Theses and Dissertations

This thesis considers problems for which the boundary is not known before the problem is solved and must be determined as part of the solution. We consider a time dependent problem which results in a moving boundary. We look at the heat conduction/diffusion equation in one and two spatial dimensions. We use Green's Theorem to yield a Volterra boundary integral equation which involves an unknown function on the moving boundary. We use the boundary element method to obtain a solution. Graphical results for the two dimensional problem are presented.

Mapping Efficient Numerical Methods To The Solution Of Multiple Objective Linear Programs, Michael A. Shields

Theses and Dissertations

This investigation was initiated to increase the speed, accuracy and capacity of m-simplex algorithms for solving multiple objective linear programming problems. Specifically, improvements were sought through the application of general numerical techniques. It soon became apparent that the m- simplex algorithm, like the simplex algorithm, is heavily dependent upon the technology of solving related systems of linear equations. The numerical arguments for the application of LU triangular matrix factorization techniques to simplex computations are well known. OF special significance to m-simplex performance is the case of rank-k updates to basis factorizations. A stable and efficient LU approach to the rank-k …

A Network Flow And Goal Programming Approach To Modeling The Impact Of Pre-Accession Training To The Trained Personnel Requirements Process, William J. Beveridge

Theses and Dissertations

HQ ATC was tasked to analyze the impact of pre-accession training to the Trained Personnel Required (TPR) and training production process. Pre- accession training is a policy of providing contracted initial skills training to enlistees prior to entering basic military training. The purpose of this study was to develop a method to model the impact of pre-accession training. A network modeling and goal programming approach was used. Comparisons between the current training policy and a pre-accession training policy were made. Sensitivity was conducted on the impact of a balk rate on the new policy. The balk rate is the percent …

On A Lower Bound For The Redundancy Of Reliable Networks With Noisy Gates, Nicholas Pippenger

All HMC Faculty Publications and Research

A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments.

A Double Chain Of Coupled Circuits In Analogy With Mechanical Lattices, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

A unitary transformation obtained from group theoretical considerations is applied to the problem of finding the resonant frequencies of a system of coupled LC-circuits. This transformation was previously derived to separate the equations of motion for one dimensional mechanical lattices. Computations are performed in matrix notation. The electrical system is an analog of a pair of coupled linear lattices. After the resonant frequencies have been found, comparisons between the electrical and mechanical systems are noted.

Unique Solution To Periodic Boundary Value Problems, Yong Sun

Mathematics and System Engineering Faculty Publications

Existence of unique solution to periodic boundary value problems of differential equations with continuous or discontinuous right-hand side is considered by utilizing the method of lower and upper solutions and the monotone properties of the operator. This is subject to discussion in the present paper.

On Modulated Random Measures, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

In this paper the author introduces the notion of a modulated marked random measure, Zξ on the class of locally compact and σ-compact spaces with countable bases. As special cases, are marked processes modulated by ξ are considered where ξ is a semi-Markov or semi-regenerative process. For either case, the intensities k=limt→∞1tE[Zξ([0,t])] are evaluated in terms of parameters of ξ. Examples and applications to inventories, queueing processes and economics are discussed.

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

On A Unique Tree Representation For P4-Extendible Graphs, B. Jamison, S. Olariu

Computer Science Faculty Publications

Several practical applications in computer science and computational linguistics suggest the study of graphs that are unlikely to have more than a few induced paths of length three. These applications have motivated the notion of a cograph, defined by the very strong restriction that no vertex may belong to an induced path of length three. The class of P₄-extendible graphs that we introduce in this paper relaxes this restriction, and in fact properly contains the class of cographs, while still featuring the remarkable property of admitting a unique tree representation. Just as in the case of cographs, the …

Some Aspects Of The Semi-Perfect Elimination, Stephan Olariu

Computer Science Faculty Publications

Several efficient algorithms have been proposed to construct a perfect elimination ordering of the vertices of a chordal graph. We study the behaviour of two of these algorithms in relation to a new concept, namely the semi-perfect elimination ordering, which provides a natural generalization of chordal graphs.

Nonlinear-Interaction Of A Detonation Vorticity Wave, D. G. Lasseigne, T. L. Jackson, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multidomain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results whenever obtained in this study agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient …

Self-Activation And Inhibition: A Simple Nonlinear Model, J. A. Adam

Mathematics & Statistics Faculty Publications

Self-activation and self-inhibition of cell number density (or growth factor concentration) due to a spatially localized source are studied. Both the time-independent and time-dependent models are examined, and the linear stability of the resulting three steady states of the former is discussed.

Analysis And Finite Element Approximation Of Optimal Control Problems For The Stationary Navier-Stokes Equations With Dirichlet Controls, M. D. Gunzburger, L. S. Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

Optimal control problems for the stationary Navier-Stokes equations are examined from analytical and numerical points of view. The controls considered are of Dirichlet type, that is, control is effected through the velocity field on (or the mass flux through) the boundary; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show that optimal solutions exist and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. The n, finite …

A Mathematical Model For Outgassing And Contamination, W. Fang, M. Shillor, E. Stahel, E. Epstein, C. Ly, J. Mcniel, Edward D. Zaron

Civil and Environmental Engineering Faculty Publications and Presentations

A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass transfer across the source-cavity interface, and a generalization of the Langmuir isotherm for the sorption kinetics on the target. Three approximations are considered where the asymptotic behavior of the model for large time is shown as well as the dependence and sensitivity of the model on some of the parameters. Some numerical examples of the full model are then presented together with a proof of the …

A Duality Approach To Best Uniform Convex Approximation, S. E. Weinstein, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Let C[a, b] be the space of continuous functions on [a, b] endowed with the uniform norm llƒll _∞ = sup{ Iƒ(x)1 :x∈ [a, b]}. Let K be the set of convex functions defined on [a, b]. A function g* ∈ K is said to be a best uniform convex approximation to ƒ ∈ C[a, b] if ∥ƒ - g*∥ _∞ = inf { ∥ƒ - g∥_∞ : g ∈ K}.

Parametric Instability Of Supersonic Shear Layers Induced By Periodic Mach Waves, Fang Q. Hu, Christopher K. W. Tam

Mathematics & Statistics Faculty Publications

It is suggested that parametric instability can be induced in a confined supersonic shear layer by the use of a periodic Mach wave system generated by a wavy wall. The existence of such an instability solution is demonstrated computationally by solving the Floquet system of equations. The solution is constructed by means of a Fourier-Chebyshev expansion. Numerical convergence is assured by using a very large number of Fourier and Chebyshev basis functions. The computed growth rate of the induced flow instability is found to vary linearly with the amplitude of the mach waves when the amplitude is not excessively large. …

Graph Products And Covering Graph Imbeddings, Ghidewon Abay Asmerom

Dissertations

No abstract provided.

Improving Networks Reliability, Jamal H. Nouh

Dissertations

No abstract provided.

An Evolution Operator Solution For A Nonlinear Beam Equation, Carl E. Crockett

Theses and Dissertations

A nonlinear partial differential equation, motivated by the transverse vibration of a beam, is shown to have a unique solution. The existence theory, which is in the setting of semigroups and evolution operators, is a composite and synthesis of theorems of Kato. The formulation of the problem and the verification that the formulation leads to a solution are new. The introductory chapter provides background on the topic generally. Chapter 2 provides detailed formulations for the constant coefficient case. Chapter 3 describes nonautonomous cases. The general theorem is presented here. In Chapter 4, a more general case is considered. Namely, Kelvin …

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.

Berry-Esseen-Type Bounds For Signed Linear Rank Statistics With A Broad Range Of Scores, Munsup Seoh

Mathematics and Statistics Faculty Publications

The Berry-Esseen-type bounds of order N^−1/2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.

Rewriteable Sequencings Of Groups, Jeanne Nielsen

Mathematical Sciences Technical Reports (MSTR)

A finite group is called P_n-sequenceable if its nonidentity elements can be listed x₁ , x₂ , ..., x_k so that the product x _i x _i+i · · · x _i+n-1 can be rewritten in at least one nontrivial way for all i. It is shown that S_n , A_n , D_n are P₃-sequenceable, that every finite simple group is P₄ -sequenceable, and that every finite group is P_s-sequenceable. It is conjectured that every finite group is P₃-sequenceable.

Enumerating The Orientable 2-Cell Imbeddings Of Complete N-Partite Graphs, Bruce P. Mull

Dissertations

This dissertation develops formulas for the number of congruence classes of maps of complete, complete bi-partite, complete tripartite, and complete n-partite graphs; these congruence classes correspond to unlabeled imbeddings. The method employed for the enumeration is an extension of that used by Mull, Rieper, and White in 1988. We let the automorphism group act on the set of rotations and use Burnside's Lemma to count orbits for these rotations. Compatible permutations are introduced to determine those automorphisms actually contributing to the number of orbits.

The complete n-partite formula is shown to generalize those of the other three families of graphs. …

On Distance In Graphs And Digraphs, Songlin Tian

Dissertations

One of the most basic concepts associated with a graph is distance. In this dissertation some new definitions of distance in graphs and digraphs are introduced. One principle goal is to extend certain known results involving the standard distance function on graphs to the field of digraphs with an appropriate concept of distance. Several parameters as well as subgraphs and subdigraphs defined in terms of distance are investigated.

Chapter I gives a brief overview of the history of distance and generalized distance in graphs. By presenting a listing of major results in this area, it provides a background for the …

The Enumeration Of Graph Imbeddings, Robert G. Rieper

Dissertations

Graphs can be drawn on surfaces. Here, graphs may have multiple edges or loops (pseudographs), the surfaces are closed orientable 2-manifolds (sphere, torus, etc.) and their generalizations (pseudosurfaces and generalized pseudosurfaces), and the drawings are 2-cell imbeddings. For quite some time it has been known that a connected graph has $\rm \Pi(degree(\upsilon)-1)$! 2-cell imbeddings on surfaces. More detailed information about these imbeddings has been wanting. In addition, many of the imbeddings counted above 'look the same' when all vertex and edge labels are removed. The resulting unlabeled imbeddings are fewer in number and more difficult to enumerate than their labeled …

The Fokker-Planck And Related Equations In Theoretical Population Dynamics, George Derise

Mathematics & Statistics Theses & Dissertations

The population growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics because population growth is basically a random event. There are a large number of chance factors influencing growth that might not be taken into account by deterministic models. The effect of other species (for example, in the chance meeting of a predator), population fluctuations due to weather changes that would alter food …

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

Grid Generation And Flow Computation About A Martian Entry Vehicle, John Edward Stewart

Mechanical & Aerospace Engineering Theses & Dissertations

A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results have been obtained for this vehicle in 1968. These results show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed here to verify the earlier results and to further describe the flight characteristics of this vehicle.

An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using an algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are …

Numerical Investigation Of A Non-Newtonian Material Through A Sudden Pipe Expansion, V. G. Masanja

Tanzania Journal of Engineering and Technology (TJET)

A numerical method for solving two dimensional elliptic boundary-value problems of fourth order is used for finding stationary solutions of the equations of motion for a laminar flow through a sudden pipe expansion of an incompressible non-Newtonian fluid with a constitutive equation of the Reiner-Rivlin (R-R) type. Results for the Newtonian fluid, which is a special case, are in excellent agreement with those by previous investigators and they demonstrate the reliability, superiority and accuracy of the method. Results for the non-Newtonian cases could be of value for fixing ideas about visco-elastic behaviour although the R-R fluid allows only inelasticity: this …

Bimodules Over Cartan Subalgebras, Richard Mercer

Mathematics and Statistics Faculty Publications

Given a Cartan subalgebra A of a non Neumann algebra M, the techniques of Feldman and Moore are used to analyze the partial isometries v in M such that v* Av is contained in A. Orthonormal bases for M consisting of such partial isometries are discussed, and convergence of the resulting generalized fourier series is shown to take place in the Bures A-topology. The Bures A-topology is shown to be equivalent to the strong topology on the unit ball of M. These ideas are applied to A-bimodules and to give a simplified and intuitive proof of the Spectral Theorem …