Physical Sciences and Mathematics Commons^™

Thermal Ignition Analysis In The Laminar Boundary Layer Behind A Propagating Shock Front, Mushtaq Ahmed Khan

Mathematics & Statistics Theses & Dissertations

Asymptotic analysis in the limit of large activation energy is performed to investigate the ignition of a reactive gas in the laminar boundary layer behind a propagating shock front. The study is based on a one-step, irreversible Arrhenius reaction of a premixed gas; therefore, the ignition phenomenon is thermally induced. The boundary layer consists of a thin, diffusive, reaction region at the point where the temperature is maximum and diffusive-convective non-reacting regions adjacent to the reacting region. Both adiabatic and isothermal boundary conditions are examined. For the adiabatic wall, the reaction zone is near the insulated boundary. The reaction zone …

Nozzle Flow With Vibrational Nonequilibrium, John Gary Landry

Mathematics & Statistics Theses & Dissertations

Flow of nitrogen gas through a converging-diverging nozzle is simulated. The flow is modeled using the Navier-Stokes equations that have been modified for vibrational nonequilibrium. The energy equation is replaced by two equations. One equation accounts for energy effects due to the translational and rotational degrees of freedom, and the other accounts for the affects due to the vibrational degree of freedom. The energy equations are coupled by a relaxation time which measures the time required for the vibrational energy component to equilibrate with the translational and rotational energy components. An improved relaxation time is used in this thesis. The …

Some Sampling Designs And Estimation Problems, Hassan Lakkis

Mathematics & Statistics Theses & Dissertations

In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.

In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods …

Rational Cubic B-Spline Interpolation And Its Applications In Computer Aided Geometric Design, Kotien Wu

Mathematics & Statistics Theses & Dissertations

Because of the flexibility that the weights and the control points provide, NURBS have recently become very popular tools for the design of curves and surfaces. If the weights are positive then the NURB will lie in the convex hull of its control points and will not possess singularities. Thus it is desirable to have positive weights.

In utilizing a NURB a designer may desire that it pass through a set of data points {x_i} This interpolation problem is solved by the assigning of weights to each data point. Up to now little has been known regarding the …

Multigrid Acceleration Of Time-Dependent Solutions Of Navier-Stokes Equations, Sarafa Oladele Ibraheem

Mechanical & Aerospace Engineering Theses & Dissertations

Recent progress in Computational Fluid Dynamics is encouraging scientists to look at fine details of flow physics of problems in which natural unsteady phenomena have hitherto been neglected. The acceleration methods that have proven very successful in steady state computations can be explored for time dependent computations. In this work, an efficient multigrid methods is developed to solve the time-dependent Euler and Navier-Stokes equations. The Beam-Warming ADI method is used as the base algorithm for time stepping calculations. Application of the developed algorithm proved very efficient in selected steady and unsteady test problems. For instance, the inherent unsteadiness present in …

Invariant Manifolds Of A Toy Climate Model, Michael Toner

Mathematics & Statistics Theses & Dissertations

According to astronomical theory, ice ages are caused by variations in the Earth's orbit. However, ice core data shows strong fluctuations in ice volume at a low frequency not significantly present in orbital variations. To understand how this might occur, the dynamics of a two dimensional nonlinear differential equation representing glacier/temperature interaction of an idealized climate was studied. Self sustained oscillation of the autonomous equation was used to model the internal mechanisms that could produce these fluctuations. Periodic parametric modulation of a damped internal oscillation was used to model periodic climate response at double the external modulation period. Both phenomena …

Boundary Value Problems In Rectilinearly Anisotropic Thermoelastic Solids, Gilbert Kerr

Mathematics & Statistics Theses & Dissertations

The boundary value problems which are considered are the type that arise due to the presence of a Griffith crack (or cracks) in an anisotropic thermoelastic solid. The thermoelastic field, in such materials, when the infinitesimal theory is employed, is governed by a set of elliptic partial differential equations. The general solution of these equations is expressed in terms of arbitrary analytic functions whose real parts, in turn, are expressed in terms of Fourier type integrals or Fourier series. Integral transform techniques are then used to determine the stress intensity factors (and other pertinent information) for various crack geometries. In …

Some Solutions To A Lens Model With Applications To Warm-Core Eddies, Juping Liu

OES Theses and Dissertations

A model of lens-shaped anticyclonic eddies based on nonlinear shallow water equations is developed. The model is a three-layer fluid and allows for one asymmetric mode as well as specified environmental flows. The solution scheme is a polynomial expansion of the field variables. When inserted into the hydrographic equations, the expansion yields eight first-order differential equations for the time dependent amplitudes. This system of ordinary differential equations is numerically tractable. As long as the initial values meet the requirement of elliptical structure and the prescribed external force is tolerable for the initial values, the numerical solutions are stable. Numerical solutions …

Bounds On Constraint Weight Parameters Of Hopfield Networks For Stability Of Optimization Problem Solutions, Gursel Serpen

Electrical & Computer Engineering Theses & Dissertations

The purpose of the presented research is to study the convergence characteristics of Hopfield network dynamics. The relation between constraint weight parameter values and the stability of solutions of constraint satisfaction and optimization problems mapped to Hopfield networks is investigated. A theoretical development relating constraint weight parameter values to solution stability is presented. The dependency of solution stability on constraint weight parameter values is shown employing an abstract optimization problem. A theorem defining bounds on the constraint weight parameter magnitudes for solution stability of constraint satisfaction and optimization problems is proved. Simulation analysis on a set of optimization and constraint …

The Solution Of A Singular Integral Equation Arising From A Lifting Surface Theory For Rotating Blades, Mark H. Dunn

Mathematics & Statistics Theses & Dissertations

A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied …

On Shock Capturing For Liquid And Gas Media, Tze Jang Chen

Mathematics & Statistics Theses & Dissertations

The numerical investigation of shock phenomena in gas or liquid media where a specifying relation for internal energy is absent poses special problems. Classically, for gas dynamics the usual procedure is to employ a splitting scheme to remove the source terms from the Euler equations, then up-wind biased shock capturing algorithms are built around the Riemann problem for the system which remains. However, in the case where the Euler equations are formulated in the term of total enthalpy, a technical difficulty associated with equation splitting forces a pressure time derivative to be treated as a source term. This makes it …

Indifference Graphs And The Single Row Routing Problem, Peter J. Looges

Computer Science Theses & Dissertations

This thesis investigates the subclass of interval graphs known as indifference graphs. New optimal algorithms for recognition, center, diameter, maximum matching, Hamiltonian path and domination in indifference graphs are presented. The recognition algorithm produces a linear order with properties which allow the solution of the other problems in linear time. Indifference graphs are further applied to the single row routing problem which results in both sequential,. and parallel routing algorithms.

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

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 …

A Root Finding Algorithm For Parallel Architecture Machines, Stuti Moitra

Computer Science Theses & Dissertations

In this thesis a parallel algorithm for determining the zeros of any given analytic function is described. Parallelism is achieved by modifying the traditional bisection algorithm for architecture machines.

Given any user supplied function f(X), continuous on the interval A_o ≤ x ≤ B₀, and the tolerance of accuracy an algorithm of determining up to ten roots, with error of approximation less than or equal to tolerance, on parallel systems like Distributed Array Processor (OAP) and N-cube is considered.

A variation of the bisection method has been adapted for this purpose. At each level of iteration a …

Boundary Value Problems In Elasticity And Thermoelasticity, Stuart Davidson

Mathematics & Statistics Theses & Dissertations

In this dissertation the author solves a series of mixed boundary value problems arising from crack problems in elasticity and thermoelasticity. Using integral transform techniques and separation of variables appropriately, it is shown that the solutions can be found by solving a corresponding set of triple or dual integral equations in some instances, while in others the solutions of triple or dual series relations are required. These in turn reduce to various singular integral equations which are solved in closed form, in two cases, or by numerical methods. The stress intensity factors at the crack tips, the physical parameters of …

An Extension Of Essentially Non-Oscillatory Shock-Capturing Schemes To Multi-Dimensional Systems Of Conservation Laws, Jay Casper

Mathematics & Statistics Theses & Dissertations

In recent years, a class of numerical schemes for solving hyperbolic partial differential equations has been developed which generalizes the first-order method of Godunov to arbitrary order of accuracy. High-order accuracy is obtained, wherever the solution is smooth, by an essentially non-oscillatory (ENO) piecewise polynomial reconstruction procedure, which yields high-order pointwise information from the cell averages of the solution at a given point in time. When applied to piecewise smooth initial data, this reconstruction enables a flux computation that provides a time update of the solution which is of high-order accuracy, wherever the function is smooth, and avoids a Gibbs …

Best Approximation With Geometric Constraints, Yuesheng Xu

Mathematics & Statistics Theses & Dissertations

This is a study of best approximation with certain geometric constraints. Two major problem areas are considered: best L_p approximation to a function in L_p (0,1) by convex functions, (m, n)-convex functions, (m, n)-convex functions and (m, n)-convex splines, for 1 < p < ∞ , and best uniform approximation to a continuous function by convex functions, quasi-convex functions and piecewise monotone functions.

On Vector Sequence Transforms And Acceleration Techniques, Steven L. Hodge

Mathematics & Statistics Theses & Dissertations

This dissertation is devoted to the acceleration of convergence of vector sequences. This means to produce a replacement sequence from the original sequence with higher rate of convergence.

It is assumed that the sequence is generated from a linear matrix iteration x_i+ i = Gx_i + k where G is an n x n square matrix and x_I+1 , x_i,and k are n x 1 vectors. Acceleration of convergence is obtained when we are able to resolve approximations to low dimension invariant subspaces of G which contain large components of the error. When …

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

On The Thermal Stresses Due To A Uniform Heat Flow Past A Circular Hole With A Radial Edge Crack, George F. Edmonds

Mathematics & Statistics Theses & Dissertations

The problem solved in this dissertation is that of finding the stresses in an isotropic, linear, thermoelastic solid when a uniform heat flow is disturbed by the presence of an insulated circular hole with a radial edge crack. By superimposing a Mellin transform solution of the equations of thermoelasticity on a Michell series solution the author reduces the problem to a pair of singular integral equations which are then solved numerically. The stress intensity factors and crack formation energies, quantities of interest to workers in fracture mechanics, are then calculated.

Estimation In Truncated Exponential Family Of Distributions, Laxman M. Hegde

Mathematics & Statistics Theses & Dissertations

Estimating the parameters of a truncated distribution is a well known problem in statistical inference. The non-existence of the maximum likelihood estimator (m.l.e.) with positive probability in certain truncated distributions is not well known. To mention a few results in the literature:

(i) Deemer and Votaw 1955 show that the maximum likelihood estimator does not exist in a truncated negative exponential distribution on 0,T , T > 0 known, whenever the sample mean x (GREATERTHEQ) T/2.

(ii) Broeder 1955 shows that the maximum likelihood estimator of the scale parameter of a truncated gamma distribution, with the shape parameter being known, becomes …

Minimal Norm Constrained Interpolation, Larry Dean Irvine

Mathematics & Statistics Theses & Dissertations

In computational fluid dynamics and in CAD/CAM a physical boundary, usually known only discreetly (say, from a set of measurements), must often be approximated. An acceptable approximation must, of course, preserve the salient features of the data (convexity, concavity, etc.) In this dissertation we compute a smooth interpolant which is locally convex where the data are locally convex and is locally concave where the data are locally concave.

Such an interpolant is found by posing and solving a minimization problem. The solution is a piecewise cubic polynomial. We actually solve this problem indirectly by using the Peano kernel theorem to …

Algebraic Grid Generation Using Tensor Product B-Splines, Bonita Valerie Saunders

Mathematics & Statistics Theses & Dissertations

In general, finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. This thesis discusses the development of an algorithm which produces such a grid when given the boundary description.

Topological considerations in structuring the grid generation mapping are discussed. In particular, this thesis examines the concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid.

The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the …

Triple Trigonometric Series And Their Application To Mixed Boundary Value Problems, Gordon Melrose

Mathematics & Statistics Theses & Dissertations

In this dissertation the author investigates some triple trigonometric series which occur in the solution of mixed boundary value problems in elasticity and potential theory. By choosing a suitable integral representation for the sequence of unknown constants, the problem is reduced to solving a singular integral equation of the first kind. Twenty four cases in which the integral equation can be solved in closed form are discussed in detail.

In later chapters, the application of triple trigonometric series to problems in physics and engineering is demonstrated and closed form solutions for the physical parameters of interest are obtained.

Block Transform Coding Of Presample Filtered Data, Thomas A. Shull

Electrical & Computer Engineering Theses & Dissertations

This dissertation addresses the application of non-adaptive transform coding for bit rate reduction of presampled filtered data. Transform coding is examined as an alternative to conventional pulse code modulation (PCM) for multi-source, fixed rate data acquisition systems. Typical bandlimiting presample filters introduce redundancy into the sequence of data samples. Linear transformation of successive N-length blocks of the data sequence and subsequent binary coding of the resulting components is shown to lead to reduced average bit rate for the same less distortion as PCM.

Four Butterworth filters, two corresponding to eight bit PCM systems, and two corresponding to ten bit PCM …

A Method Of Modeling Multirate Two-Dimensional Recursive Digital Filters Author, Albert P. Gerheim

Electrical & Computer Engineering Theses & Dissertations

This dissertation presents a method of modeling two dimensional sampled data systems with two sampling rates in each dimension. This methodology is applied to the problem of synthesizing two dimensional velocity filters using one dimensional prototypes and multirate concepts.

The modeling method includes the replacement of scalar z-transforms of signals by vectors of polynomials, and the replacement of scalar z-transforms of impulse responses by matrices of polynomials.

The synthesis of velocity filters is accomplished through the use of coordinate transformations in the z-transform domain which skew the ω₁ -ω₂ axes on the unit bidisc. The filters synthesized using …