Mathematics Commons^™

The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz

Physics - All Scholarship

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P; Q \Gamma ] = 1, with P and Q \Gamma 2 \Theta 2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations …

Modulated, Frequency-Locked, And Chaotic Cross-Waves, William B. Underhill, Seth Lichter, Andrew J. Bernoff

All HMC Faculty Publications and Research

Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations — a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation. Their interaction, as forcing frequency, f, and forcing amplitude, a, were varied, produced a pattern of Arnold tongues in which two or three frequencies were locked. The overall picture of frequency-locked and -unlocked regions is explained in terms of the Arnold tongues predicted by …

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 …

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 …

An Artificial Neural Approach To The Decomposition Problem, Chandrashekar L. Masti

Electrical & Computer Engineering Theses & Dissertations

The goal of this thesis is to develop an artificial neural approach toward addressing the intractability involved with the decomposition problem. The search for the lattice of substitution property (s. p.) partitions essential to decompositions is cast into the framework of constraint satisfaction. An artificial neural network is developed to provide solutions by performing optimization of a mathematically derived objective function over the problem space. The issue of transitivity is verified to belong to a class of problems beyond the scope of solvability for conventional quadratic-order constraint satisfaction neural networks. A theorem is stated and proved establishing that third-order correlations …

A Nonlinear Eigenvalue Problem In Astrophysical Magnetohydrodynamics: Some Properties Of The Spectrum, John A. Adam

Mathematics & Statistics Faculty Publications

The equations of ideal magnetohydrodynamics (MHD) with an external gravitational potential—a ‘‘magnetoatmosphere’’—are examined in detail as a singular nonlinear eigenvalue problem. Properties of the spectrum are discussed with specific emphasis on two systems relevant to solar magnetohydrodynamics. In the absence of a gravitational potential, the system reduces to that of importance in MHD and plasma physics, albeit in a different geometry. This further reduces to a form isomorphic to that derived in the study of plasma oscillations in a cold plasma, Alfvén wave propagation in an inhomogeneous medium, and MHD waves in a sheet pinch. In cylindrical geometry, the relevant …

Self Consistent Model Of The Glow Discharge, Hao Chen

Electrical & Computer Engineering Theses & Dissertations

The strong spatial variation of the electric field intensity in the vicinity of the cathode of a gas discharge requires the use of microscopic methods to describe the nonequilibrium behavior of the electron dynamics in this region. A one-dimensional Monte Carlo code was developed. It allows one to obtain the distribution of the electron drift velocity and rate coefficients for a given electric field intensity in the cathode fall. The results of this calculation are used to find the density distribution of charged particles in this region and consequently, by means of Poisson's equation, a corrected electric field intensity. In …

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQ_n(x) = z_n^-1 exp[ -H_n(x)]Π dP(x_j), where x = (x₁,..., x_n) ∈ Rⁿ, where H_n is the Hamiltonian, z_n is …

Untitled (Subject: Reverberation), Richard C. Heyser

Unpublished Writings

In this paper, Richard C. Heyser explains how sound reverberates and why he developed a time delay spectrometer (TDS) to measure sound.

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 …

Alternatives In Quantum Theory, Richard C. Heyser

Unpublished Writings

Quantum mechanical descriptions in terms of momentum and position are identified as alternatives under the condition of equal complex-vaulted Lebesgue square integrability. While this does not change any of the formal results obtained in quantum mechanics, it does shed a different interpretive light on the steps that lead up to these results. Instead of being independent, even in concept, momentum and position are identified as being the same thing, merely seen from different views. Neither is required to complement the descriptive capability of the other, since each forms a complete alternative in its own right. Apparent complementarity, as well as …

New Relativistic Paradoxes And Open Questions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Following the Special Theory of Relativity, Florentin Smarandache generalized the Lorentz Contraction Factor to an Oblique-Contraction Factor, which gives the contraction factor of the lengths moving at an oblique angle with respect to the motion direction. He also proved that relativistic moving bodies are distorted, and he computed the Angle-Distortion Equations.

He then showed several paradoxes, inconsistencies, contradictions, and anomalies in the Theory of Relativity.

According to the author, not all physical laws are the same in all inertial reference frames, and he gives several counter-examples. He also supports superluminal speeds, and he considers that the …

The Etc And Instantaneous Intensity, Richard C. Heyser

Unpublished Writings

Richard C. Heyser explains how to measure the energy-time response of an acoustic signal by expressing the energy density in a logarithmic form, which he cales the Energy-Time Curve (ETC).

Synchronized Slide-Tapes In The Physics Laboratory, Loren Quan

University of the Pacific Theses and Dissertations

Media play a large part in most of our daily lives. We watch television; we go to the movies; we listen to the radio. For years educators have been adapting media-related technological advancements for the purpose of teaching in the classroom. Here at the Physics Department of the University of the Pacific, we have adapted the medium of synchronized slide-tapes for use in the laboratory component of our calculus-based introductory physics course.

Untitled (Subject: Energy), Richard C. Heyser

Unpublished Writings

Fundamental energy relations are explored as a basis for the measurement of physical systems. By considering finite dimensional observations in linear Hilbert space it is shown that a necessary and sufficient condition for the conservation of energy is the partitioning of any observation of that energy into two components which will be related through the Hilbert transform. The consequence of this relationship is demonstrated for the equilibrium storage of energy, point-wave duality in measurements, significance of complex representations involving circular form, the meaning of minimum phase and all-pass properties, and the introduction of new measurement characterizations such as the energy-time …

The Two Parts Of Energy, Richard C. Heyser

Unpublished Writings

In this paper, Richard C. Heyser explains the theories behind measuring sound by discussing its energy. Using what he calls abstract geometry, Heyser argues that measuring the transfer properties (that is, pressure and velocity) of sound's energy aids in the discovery of its amplitude and phase (or in-phase and quadrature).

Group Of Point Transformations Of Time Dependent Harmonic Oscillators, Jose Ricardo Bernal

University of the Pacific Theses and Dissertations

In general, a physical system has invariant quantities which are very often related to its symmetry and to the invariance of the equation that describe it. A detailed study of the invariance property of the differential equation will be helpful in understanding this relation.

The work is concerned with a preliminary investigation of the Lie-group which leaves invariant the Newtonian and Lagrangian equation of motion for a one-dimensional harmonic oscillator. A brief review of Ehrenfest's adiabatic principle and the later treatments on exact and adiabatic invariants will be presented.

Some Applications Of Lie Transformation Groups To Classical Hamiltonian Dynamics, Donald Robert Peterson

University of the Pacific Theses and Dissertations

Recent work has established that a group theoretical viewpoint of completely integrable dynamical systems with N degrees of freedom yields an algorithm that provides new information concerning the symmetry transformation group structure of this class of dynamical systems. The work presented here rests heavily on the results presented in reference and it is recommended that the reader consult this reference for a more rigorous discussion of the results given in this thesis.

Brief Theory Of Coherent Processor, Richard C. Heyser

Unpublished Writings

The particular coherent data processor which is to be discussed relies heavily upon several basic concepts. These concepts represent a departure from conventional practice and hence the theoretical description must await their presentation in order to gain some continuity. We will accordingly present the underlying assumptions and signal physics prior to description of the processor itself.

Reducing Uncertainty, Richard C. Heyser

Unpublished Writings

Intended for audio engineers, Richard C. Heyser meant for this paper to bring attention to the misapplication of the theoretical concept, the Uncertainty Principle. Heyser argues that this concept has been "freely applied without regard to the errors which may result due to lack of understanding of its derivation."

The Impulse And Doublet, Richard C. Heyser

Unpublished Writings

The basic problem to which this paper is directed is that of characterization of the acoustic field perceived by an observer and due to a loudspeaker situation in a room. Before immediately jumping into an apparent solution and presenting the results of a set of measurements it is essential to present the considerations leading to that measurment...First, there are at least two ways of characterizing the same acoustic signal if we restrict our attention to a well defined set of parameters...Secondly, since both characterizations define the same thing it must be possible to translate information without loss from one domain …

On The Theory Of Head Waves, Patrick Heelan

Research Resources

When a combined longitudinal and transverse disturbance, diverging from a localized source, strikes a plane boundary between two solid elastic media, several systems of head waves and second order boundary waves are generated, each associated with grazing incidence of one or the other of the reflected or refracted waves. Associated with grazing incidence of P ₁ P₂, the refracted P-wave, is the head wave system comprising P₁P₂P₁ (the "refracted wave" of seismic prospectors), and P₁P₂S₁ (a transverse head wave) in the upper medium, and P₁P_{2 …}

A Short Study Of Laplace's Equation, Sidney Teweles Jr.

Bachelors’ Theses

Perhaps if I set forth my original inspiration for this thesis, the reader will be better able to understand the reason for the apparent limitations of treatment. In my study of differential equations, I had the task set before me of presenting a discussion of Laplace's equation to the class. A seemingly easy matter turned out to be quite difficult for the reason that most texts make but brief use of Laplace's equation. Thus in a mathematics book reference will be made to Laplace's equation simply as example of a mathematical process. Some of these processes are the change of …

Some Contributions Of Pure Math To Science, Herbert B.E. Case

Student and Lippitt Prize Essays

An examination of the connection between math and science through discoveries in the subjects of astronomy, mechanics, physics and chemistry.