Bulletin of the American Physical Society
2006 73rd Annual Meeting of the Southeastern Section of the APS
Thursday–Saturday, November 9–11, 2006; Williamsburg, Virginia
Session CC: Theory, General |
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Chair: Chris Carone, College of William & Mary Room: Williamsburg Hospitality House Yorktown |
Thursday, November 9, 2006 10:45AM - 10:57AM |
CC.00001: Quantum spins and their approach to the classical limit Larry Engelhardt We have performed Monte Carlo calculations for both quantum and classical Heisenberg spin models in an effort to study how quantum spins approach the ``classical limit''. This talk will include a brief review of these models and their physical consequences, as well as a summary of our most interesting results. In particular, by considering many values of the intrinsic spin quantum number $s$, we have studied how the discrete energy spectra of (quantum) spin rings approach continuous spectra in the limit $s\to\infty$.\footnote{L. Engelhardt and M. Luban, Phys. Rev. B \textbf{73}, 054430 (2006).} Additionally, by calculating the temperature dependence of the magnetic susceptibility for many geometries, we have also determined the temperature range over which classical spin models will accurately approximate quantum systems.\footnote{L. Engelhardt, M. Luban, and C. Schr{\"o}der, Phys. Rev. B \textbf{74}, 054413 (2006).} [Preview Abstract] |
Thursday, November 9, 2006 10:57AM - 11:09AM |
CC.00002: Energetics and thermal transport of a Brownian heat engine in the underdamped regime. Ronald Benjamin, Ryoichi Kawai Energetics and coherence of transport in the presence of non-uniform temperature is still an open problem.We study the same for a Brownian heat engine based on the Buttiker-Landauer ratchet model. Unlike other ratchet models where the role of inertia is not important in the study of stochastic energetics , efficiency of the Buttiker-Landauer ratchet can only be evaluated properly when inertia is taken into account. We study this system via numerical simulations and present our results. [Preview Abstract] |
Thursday, November 9, 2006 11:09AM - 11:21AM |
CC.00003: ABSTRACT WITHDRAWN |
Thursday, November 9, 2006 11:21AM - 11:33AM |
CC.00004: Radial oscillation of a gas bubble in a fluid as a problem in canonical perturbation theory James Stephens The oscillation of a gas bubble is in a fluid is of interest in many areas of physics and technology. Lord Rayleigh treated the pressure developed in the collapse of cavitation bubbles and developed an expression for the collapse period. Minnaert developed a harmonic oscillator approximation to bubble oscillation in his study of the sound produced by running water. Besides recent interest in bubble oscillation in connection to sonoluminescence, an understanding of oscillating bubbles is of important to oceanographers studying the sound spectrum produced by water waves, geophysicists employing air guns as acoustic probes, mechanical engineers concerned with erosion of turbine blades, and military engineers concerned with the acoustic signatures developed by the propeller screws of ships and submarines. For the oceanographer, Minnaert's approximation is useful, for the latter two examples, Lord Rayleigh's analysis is appropriate. For the case of the airgun, a period of twice Rayleigh's period for the ``total collapse'' of the cavitation bubble is often cited as a good approximation for the period of an air bubble ejected from an air gun port, typically at $\sim $2000 psi), however for the geophysical example, numerical integration is employed from the outset to determine the dynamics of the bubble and the emitted acoustic energy. On the one hand, a bubble can be treated as a harmonic oscillator in the small amplitude regime, whereas even in the relatively moderate pressure regime characteristic of air guns the oscillation is strongly nonlinear and amplitude dependent. Is it possible to develop an analytic approximation that affords insight into the behavior of a bubble beyond the harmonic approximation of Minnaert? In this spirit, the free radial oscillation of a gas bubble in a fluid is treated as a problem in canonical perturbation theory. Several orders of the expansion are determined in order to explore the dependence of the oscillation frequency with bubble amplitude. The expansion to second order is inverted to express the time dependence of the oscillation. [Preview Abstract] |
Thursday, November 9, 2006 11:33AM - 11:45AM |
CC.00005: Chaotic Escape of Specularly Reflecting Rays From a Vase-shaped Cavity Jaison Novick, John Delos, Kevin Mitchell We study the escape of rays from a two dimensional, specularly reflecting open cavity having the shape of a vase. At the narrowest point of the neck of the vase there is an unstable periodic orbit which defines a dividing surface between rays that escape and rays that are turned back into the cavity. We imagine a point source on the cavity wall emitting rays in all directions and we record the time to reach a detector forming the mouth of the vase. We find that the rays arrive at the detector in pulses. The escape time, as a function of the initial conditions, displays a weak self-similarity which is understood upon transformation to a suitable phase space. Here, we find that the self-similarity arises from the intersection of the initial conditions with a homoclinic tangle, which is formed by the intersections of stable and unstable manifolds emanating from the unstable periodic orbit. We present a topological theory that partially predicts the self-similarity. We conclude with an example comparing the predictions to numerical calculations. [Preview Abstract] |
Thursday, November 9, 2006 11:45AM - 11:57AM |
CC.00006: The Parker-Sochacki Method of Solving Differential Equations: Applications and Limitations Joseph W. Rudmin The Parker-Sochacki method is a powerful but simple technique of solving systems of differential equations, giving either analytical or numerical results. It has been in use for about 10 years now since its discovery by G. Edgar Parker and James Sochacki of the James Madison University Dept. of Mathematics and Statistics. It is being presented here because it is still not widely known and can benefit the listeners. It is a method of rapidly generating the Maclauren series to high order, non-iteratively. It has been successfully applied to more than a hundred systems of equations, including the classical many-body problem. Its advantages include its speed of calculation, its simplicity, and the fact that it uses only addition, subtraction and multiplication. It is not just a polynomial approximation, because it yields the Maclaurin series, and therefore exhibits the advantages and disadvantages of that series. A few applications will be presented. [Preview Abstract] |
Thursday, November 9, 2006 11:57AM - 12:09PM |
CC.00007: A General Relativistic Model for the Electron. Joseph D. Rudmin Electron fields are described using Parker Sockacki expansions to solve the Einstein equation. Properties of the expansions suggest why the gravitational constant is so small. [Preview Abstract] |
Thursday, November 9, 2006 12:09PM - 12:21PM |
CC.00008: ABSTRACT WITHDRAWN |
Thursday, November 9, 2006 12:21PM - 12:33PM |
CC.00009: ABSTRACT WITHDRAWN |
Thursday, November 9, 2006 12:33PM - 12:45PM |
CC.00010: D-branes in the QCD Vacuum Harry Thacker Recent Monte Carlo evidence for long range sign-coherent membranes of topological charge in the vacuum of pure-glue QCD is considered in the context of string/gauge duality. Witten's holographic brane construction of four-dimensional Yang-Mills theory from type IIA string theory is reviewed. This leads to a picture of the pure-glue QCD vacuum as consisting of multiple discrete vacua separated by domain walls, a picture suggested much earlier by large-N chiral lagrangian arguments. In the holographically equivalent string theory, the topological charge membranes correspond to D6-branes, which play a fundamental role as the carriers of Ramond-Ramond charge type IIA string theory. [Preview Abstract] |
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