Physical Sciences and Mathematics Commons^™

Modeling Of Ground Water Aquifer Remediation By Pulsed Pumping When Contaminant Transport Is Affected By Physical, Non-Equilibrium Sorption And Desorption, Jeffrey L. Caspers

Theses and Dissertations

This research postulates and demonstrates a modification incorporating rate-limited sorption effects in the USGS SUTRA code for cleanup of a hypothetical sandy aquifer by pump-and-treat remediation methods. Contaminant transport is assumed to be affected by advection, dispersion, and rate-limited sorption/desorption. Sorption is assumed to be either equilibrium or rate-limited, with the rate-limitation described by either a first-order law, or by Fickian diffusion of contaminant through a spherical immobile pore region. Solutions are arrived at by split operator methods for the transport and one-dimensional Galerkin solutions for the solute concentration equations. The resulting model is tested against an analytical Laplace transform …

Comparisons Of Several Medians In A Lognormal K-Sample Context Where Some Data May Be Left-Censored, Stavros Costa Pouloukas

Dissertations

No abstract provided.

Surface-Induced Ordering In Asymmetric Block Copolymers, Y. Liu, W. Zhao, X. Zheng, Alexander H. King, A. Sing, M. H. Rafailovich, J. Sokolov, K. H. Dai, E. J. Kramer, S. A. Schwarz, O. Gebizlioglu, S. K. Sinha

Alexander H. King

The surface-induced ordering in thin films of asymmetric deuterated polystyrene (dPS)- poly(viny1pyridine) (PVP) diblock and triblock copolymers of comparable polymerization index and PVP volume fraction - 0.25) was studied using transmission electron microscopy, atomic force microscopy, secondary ion massspectrometry, and neutron reflectivity. The morphology of both di- and triblock copolymer films was found to be cylindrical except for the layer adjacent to the silicon oxide surface, which due to the strong interaction of silica with PVP, was lamellar. The spacing between adjacent cylindrical layers was found to be consistent with mean field theory predictions. In the triblock copolymer films the …

Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we prove the existence of self-similar solutions to the anisotropic curve shortening equation.

Minimum Average Distance (Mad) Partitioning For Grid Graphs, Debra L. Meiers

Honors Capstone Projects and Theses

No abstract provided.

Robot Space Coordinate Representation Of Objects In Euclidean Space, Justin Gallagher

Mathematical Sciences Technical Reports (MSTR)

Robot motion control strategies generally center around trajectory planning schemes which are point-to-point. This paper explores the problem of planning robot trajectories which sweep an area in a two-link robot's work space. A diffeomorphism which transforms the linear coordinates of Euclidean space to the non-linear angular coordinates which represent the displacements of the joint motors is developed. It is used to determine the distortion of an object's area at different locations in the robot's work space and for different robot link length geometries. Study of such distortions may lead to an optimization scheme by which the placement of the object …

Remarks On Automorphisms Of Subfactors, Phan Loi

Mathematics and Statistics Faculty Publications

We establish certain properties of automorphisms on an inclusion of AFD type II₁ factors with finite index and finite depth and discuss their applications to the classification problem of AFD type III subfactors, including a different proof of a result on subfactors with principal graph D_n.

Noise Reduction For Speech Enhancement Using Non-Linear Wavelet Processing, Hassan Dehmani

Theses and Dissertations

The problem of speech enhancement presents many obstacles in the speech processing field. This thesis develops several speech de-noising systems that can be used in the time, fourier, and wavelet domains. We present two thresholding techniques soft and hard. The application of these thresholding techniques to noisy speech data is discussed. The combination of both wavelets and the Fourier domains with noisy phase restoration proves to yield the best results in terms of intelligibility. Informal listening tests were conducted in order to compare the effects and differences between the speech de-noising systems.

Applications Of Binary Sequence Of Order K, Xulun Jiang

Theses

The cumulative distribution of the finite sum of the binary sequence of order k is studied and some of its applications discussed. Certain properties of this sequence are studied and uniformly superior bounds for the cumulative distribution under minimal information on the "success" probabilities are derived.

As an application, an optimal randomized response model to collect sensitive information with dependence in the sample is proposed. This dependence is caused by untruthful response to stigmatizing questions and has been ignored in the past procedures.

The proposed method is useful in collecting reliable information in situations where the response is difficult to …

Multirate Time-Frequency Distributions, John R. O'Hair

Theses and Dissertations

Multirate systems, which find application in the design and analysis of filter banks, are demonstrated to also be useful as a computational paradigm. It is shown that any problem which can be expressed a set of vector-vector, matrix-vector or matrix-matrix operations can be recast using multirate. This means all of numerical linear algebra can be recast using multirate as the underlying computational paradigm. As a non-trivial example, the multirate computational paradigm is applied to the problem of Generalized Discrete Time- Frequency Distributions GDTFD to create a new family of fast algorithms. The first of this new class of distributions is …

Rule-Based Run Control And Evaluation For Simulation, Robert F. Gordon Ph.D., Kow C. Chang, Edward A. Macnair

Faculty Works: MCS (1984-2023)

RC 19494 (84719)

Modeling projects are often faced with a large parameter space that has to be explored in order to produce a set of performance measures representing the behavior of the systems under study. In this paper, we describe a software component that provides the analyst with the functionality to specify a design of experiments and execute a search algorithm over the resulting parameter space. The component invokes the associated simulation runs and compares the results to a goal to determine the solution. This component has been implemented as the run control mechanism in the RESearch Queueing Modeling Environment …

An Investigation Of Simulated Annealing Applied To Structural Optimization Problems, Richard C. Mceachin

Theses and Dissertations

This thesis investigates the feasibility of using Simulated Annealing SA in structural optimization problems. The investigation involves solving benchmark structural optimization problems with an SA algorithm, and comparing its solutions to those found by four other optimizers. Overall, the analysis shows that SA has limited applicability in structural optimization. Two primary factors were found to adversely impact the performance of the SA algorithm in these problems. These factors are high dimensionality, and high levels of constraint. The difficulty involved in solving these problems with a random search increases exponentially with the number of dimensions. The number, and non-linearity, of the …

An Air Mission Planning Algorithm For A Theater Level Combat Model, Brian J. Griggs

Theses and Dissertations

This thesis describes the development of an air mission planning algorithm for the Joint Staffs Future Theater Level Model FTLM. The overall problem scope was to develop an algorithm to handle major factors bearing on the combat mission planning problem while providing hook-ups for the FTLM architecture. Other aspects of the problem included finding the appropriate level of detail, developing a fast solving technique, and attempting to use existing data. The problem was handled by using some ideas from existing aircraft allocation algorithms and by adding some new techniques. The proposed air mission planning algorithm supplies the optimum degree of …

Point And Interval Estimation Of Series System Reliability Using Small Data Sets, Craig J. Willits

Theses and Dissertations

This investigation explored the relative performance of several small-sample point and interval estimators for series system reliability. Among point estimators, the maximum likelihood estimator MLE was compared to the corresponding Bayes estimator. In addition, four interval estimators were compared Easterlings modified maximum likelihood integer estimator, the Lindstrom-Madden estimator, and Bayesian probability interval estimators constructed using approximate beta and Bayes Monte Carlo empirical posterior densities. The relative performance of the point estimators was assessed by comparing their mean square errors. For the four interval estimators, the interval coverage probability and the average interval lower bound were examined. The values of these …

Uniqueness Of Stable And Unstable Positive Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam

All HMC Faculty Publications and Research

Abstract not included in this article.

Existence Of Solutions For Second-Order Evolution Inclusions, Nikolaos S. Papageorgiou

Mathematics and System Engineering Faculty Publications

In this paper we examine second-order nonlinear evolution inclusions and prove two existence theorems; one with a convex-valued orientor field and the other with a nonconvex-valued field. An example of a hyperbolic partial differential inclusion is also presented.

Some Triple Sine Series, G. Kerr, G. Melrose, J. Tweed

Mathematics & Statistics Faculty Publications

Two types of triple sine series are investigated. They are reduced to singular integral equations with kernels involving elliptic functions. Closed form solutions are obtained.

Periodic And Homoclinic Orbits In A Toy Climate Model, M. Toner, A. D. Kirwan Jr.

Mathematics & Statistics Faculty Publications

A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet. We apply standard perturbative techniques from dynamical systems theory to study small amplitude periodic orbits about a constant equilibrium. The equations are put in cononical form and the local phase space topology is examined. Maximum and minimum periods of oscillation are obtained and related to the radius of the orbit. An adjacent equilibrium is shown to have saddle character and the inflowing and outflowing manifolds of this saddle are studied using numerical integration. The inflowing manifolds show the region of …

Optical Properties Of Human Uterus At 630 Nm, Steen J. Madsen, Bruce J. Tromberg, Yona Tadir, Pius Wyss, Lars O. Svaasand, Richard C. Haskell

All HMC Faculty Publications and Research

The optical properties of normal and fibriotic human uteri were determined using frequency-domain and steady-state techniques .

Frequency-Domain Photon Migration In Turbid Media, Bruce J. Tromberg, Steen J. Madsen, Curtis Chapman, Lars O. Svaasand, Richard C. Haskell

All HMC Faculty Publications and Research

An analytical model is presented for the propagation of diffuse photon density waves in turbid media. The frequency- and wavelength-dependence of photon density waves are measured using Frequency-domain Photon Migration (FDPM). Media optical properties, including absorption, transport, and fluorescence relaxation times are calculated from experimental results.

Chaos And The Stock Market, Brent M. Monte

Theses Digitization Project

No abstract provided.

Determination Of A Potential From Cauchy Data: Uniqueness And Distinguishability, Lester Caudill

Department of Math & Statistics Faculty Publications

The problem of recovering a potential q(y) in the differential equation:

−∆u + q(y)u = 0 (x,y) &∈ (0, 1) × (0,1)
u(0, y) = u(1, y) = u(x, 0) = 0
u(x, 1) = f(x), u_y(x, 1) = g(x)

is investigated. The method of separation of variables reduces the recovery of q(y) to a non-standard inverse Sturm-Liouville problem. Employing asymptotic techniques and integral operators of Gel'fand-Levitan type, it is shown that, under appropriate conditions on the Cauchy pair (f, g ), q(y) is uniquely determined, in a local sense, up to its mean. We characterize …

Hankel Transforms In Generalized Fock Spaces, John Schmeelk

Mathematics and Applied Mathematics Publications

A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq),where ϕ0∈ℂ and ϕq∈Lp(ℝq), q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of …

A Direct Method For The Inversion Of Physical Systems, Lester Caudill, Herschel Rabitz, Attila Askar

Department of Math & Statistics Faculty Publications

A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. Of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.

Continuity Of Metric Projection, Pólya Algorithm, Strict Best Approximation, And Tubularity Of Convex Sets, Robert Huotari, Wu Li

Mathematics & Statistics Faculty Publications

The notion of tubularity of a convex subset, K, of l∞ (n) was originally introduced to study the convergence of the Pólya algorithm. It is shown in the present paper that this geometric condition provides a characterization of thosed closed convex sets onto which the set-valued metric projection is continuous. In the development of this result, Rice′s strict best approximation is characterized in three new ways, and is shown, assuming tubularity of K, to be a continuous selection. The class of sets on which the Pólya algorithm is known to converge is enlarged to include …

Gauss-Type Quadratures For Weakly Singular Integrals And Their Application To Fredholm Integral Equations Of The Second Kind, Hideaki Kaneko, Yuesheng Xu

Mathematics & Statistics Faculty Publications

In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.

A Fast Numerical Solution Of Scattering By A Cylinder: Spectral Method For The Boundary Integral Equations, Fang Q. Hu

Mathematics & Statistics Faculty Publications

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converge slowly for high frequency waves. In this paper, a fast numerical solution is presented for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of …

Symbol Sense And Its Development In Two Computer Algebra System Environments, Brian A. Keller

Dissertations

The purposes of this study were to: (a) explicate the nature of symbol sense, (b) determine the differential effects of two computer algebra system (CAS) environments on students' development of symbol sense, (c) explore differences in symbol sense among students using a CAS and students not using a CAS, and (d) examine students' achievement in calculus with and without the use of a CAS.

Six sections of first-semester calculus at Western Michigan University during the 1992-93 academic year were used in the study. The investigator taught two CAS sections both semesters (n = 41, 34 Fall and n = 35, …

Reconstruction Of Multiple Cracks From Experimental, Electrostatic Boundary Measurements, Kurt M. Bryan, Valdis Liepa, Michael Vogelius

Mathematical Sciences Technical Reports (MSTR)

We demonstrate the viability of using Electrical Impedance Tomography (EIT) for the reconstruction of multiple macroscopic cracks in a conductive medium.

Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho

Mathematics and Statistics Faculty Publications

Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.