Physics Commons^™

Fermi Problems: Educated Guesses, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

Physics - All Scholarship

We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.

Prediction Of The Stochastic Behavior Of Nonlinear Systems By Deterministic Models As A Classical Time-Passage Probabilistic Problem, L. M. Ivanov, A. D. Kirwan Jr., O. V. Melnichenko

CCPO Publications

Assuming that the behaviour of a nonlinear stochastic system can be described by a Markovian diffusion approximation and that the evolution equations can be reduced to a system of ordinary differential equations, a method for the calculation of prediction time is developed. In this approach, the prediction time depends upon the accuracy of prediction, the intensity of turbulence, the accuracy of the initial conditions, the physics contained in the mathematical model, the measurement errors, and the number of prediction variables. A numerical application to zonal channel flow illustrates the theory. Some possible generalizations of the theory are also discussed.

Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

We study the advection of a passive scalar by a vortex couple in the small-diffusion (i.e. large Péclet number, Pe) limit. The presence of weak diffusion enhances mixing within the couple and allows the gradual escape of the scalar from the couple into the surrounding flow. An averaging technique is applied to obtain an averaged diffusion equation for the concentration inside the dipole which agrees with earlier results of Rhines & Young for large times. At the outer edge of the dipole, a diffusive boundary layer of width O(Pe^−½) forms; asymptotic matching to the interior …

Electrostatic Positioning Of Droplets In Turbulent Flows (Lstm 375/Te/93), Nihad E. Daidzic, Adrian Melling

Aviation Department Publications

Report LSTM 375/TE/93, Lehrstuhl fuer Stroemungsmechanik Universitaet Erlangen-Nuernberg Cauerstr. 4, 8520 Erlangen Germany.

The Force On A Sphere In A Tightly Focused Laser Beam, Marc Knudson

Honors Theses, 1963-2015

An investigation of the trapping force on a sphere in a tightly focused laser beam is carried out using a geometrical optics approximation. This calculation generalizes earlier work by allowing the spheres to be located off the beam axis. Additionally, a fifth-order, instead of zeroth-order, Gaussian approximation is used, and beam polarization is explicitly taken into account. The results suggest an interesting experiment, involving a driven damped harmonic oscilator system, which could be performed to test the validity of the theory. This experiment will be the focus of a future study.

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 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 …

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.

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).

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).

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 …}

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.