Bulletin of the American Physical Society
Joint Fall 2009 Meeting of the Texas Sections of the APS, AAPT, and SPS
Volume 54, Number 13
Thursday–Saturday, October 22–24, 2009; San Marcos, Texas
Session C5: Theoretical Physics |
Hide Abstracts |
Chair: Martin Sablik, Southwest Research Institute Room: LBJ Student Center 3-14.1 |
Friday, October 23, 2009 4:00PM - 4:12PM |
C5.00001: ABSTRACT WITHDRAWN |
Friday, October 23, 2009 4:12PM - 4:24PM |
C5.00002: Vlasov Evoluton of a Gravitational System via a Spectral Method Josh Alvord, Bruce Miller There are open questions concerning the distribution of clusters in the expanding universe. The coupled Vlasov-Poisson equations govern the evolution of density in mu(position-velocity) space. In the comoving frame, the evolution of the $\mu$-space density $f$ for a one-dimensional gravitational system is governed by the Vlasov-Poisson continuity equation where $a$ is the local acceleration: \[ \frac{\partial f}{\partial t}+v\frac{\partial f}{\partial x}+\frac{\partial af}{\partial v}=0\] Here we introduce a spectral method to obtain a coupled set of ordinary differential equations governing the time dependence of the coefficients. For the bounded position space we utilize a Fourier expansion, whereas for the infinite velocity space we utilize a Hermite expansion. The resulting equations are bilinear and govern the coefficients $\psi_{m,n}(t)$, where $m$ represents the Fourier index and $n$ the Hermite index. By truncating the doubly infinite series they can be integrated numerically to model and simulate the system evolution of $f$, in our case using a traditional fourth-order Runge-Kutta method. We will present the important derivations and preliminary results of the numerical integration. [Preview Abstract] |
Friday, October 23, 2009 4:24PM - 4:36PM |
C5.00003: Computing energy spectra for quantum systems using the Feynman-Kac path integral method J.M. Rejcek, N.G. Fazleev We use group theory considerations and properties of a continuous path to define a failure tree numerical procedure for calculating the lowest energy eigenvalues for quantum systems using the Feynman-Kac path integral method. Within this method the solution of the imaginary time Schr\"{o}dinger equation is approximated by random walk simulations on a discrete grid constrained only by symmetry considerations of the Hamiltonian. The required symmetry constraints on random walk simulations are associated with a given irreducible representation and are found by identifying the eigenvalues for the irreducible representations corresponding to the symmetric or antisymmetric eigenfunctions for each group operator. The numerical method is applied to compute the eigenvalues of the ground and excited states of the hydrogen and helium atoms. [Preview Abstract] |
Friday, October 23, 2009 4:36PM - 4:48PM |
C5.00004: Derivation of Boltzmann's Principle Donald H. Kobe, Michele Campisi Using a classical mechanical model of thermodynamics, we derive Boltzmann's Principle for the entropy $S_{B }= k_{B}$\textit{ ln W, }where $k_{B}$ is Boltzmann's constant and $W $is the number of microstates compatible with an energy $E$. The argument is based on the heat theorem which is the combined first and second laws of thermodynamics. It dates back to the work of Helmholtz and Boltzmann, but the argument has remained almost unknown. We first discuss a one-dimensional model. The phase-space volume entropy, microcanonical distribution, and ergodic theorem naturally emerge for one dimension. The argument is then generalized to an arbitrary number of $N $particles. Using the ergodic hypothesis, we show that the entropy is $S = k_{B}$\textit{ ln $\Phi $, }where \textit{$\Phi $} is the phase-space volume enclosed by a hypersurface of energy $E$. For very large systems with \textit{N $>>$1}, the volume entropy $S $approaches the surface entropy \textit{S $\approx $ s = k}$_{B }$\textit{ln($\Omega $dE)}, where \textit{$\Omega =\partial \Phi $/$\partial $E} is the density of states on the hypersurface of energy $E$ and \textit{dE }is an irrelevant constant. For cells in phase space the size of Planck's constant $h$ the density of states \textit{$\Omega \quad \approx $ W, }which proves Boltzmann's Principle. However, the correct entropy for any number of particles is the phase-space volume entropy $S.$ . [Preview Abstract] |
Friday, October 23, 2009 4:48PM - 5:00PM |
C5.00005: The J-Matrix formalism applied to noisy data series: universal properties of noise Luca Perotti, Daniel Bessis, Daniel Vrinceanu We developed a new method in the spectral analysis of noisy time-series. From the Jacobi recursive relation for the denominators of the Pad\'{e} Approximants of the Z-transform of an infinite time-series, we build a J-Operator where each bound state (inside the unit circle) is associated to one damped oscillator while the essential spectrum, which lies on the unit circle, represents noise. Damped signal and noise are thus clearly separated in the complex plane. For a finite time series, the J-operator is replaced by a finite order J-Matrix J$_{N}$. Eigenvalues (poles of the Pad\'{e} Approximant) corresponding to noise are each correlated to one of the zeros of the Pad\'{e} Approximant and can be cleaned, thus exposing constant amplitude signals. Different classes of noise are analyzed, our formalism allowing efficient calculation of hundreds of poles of the Z-transform. Evidence of universal behaviour in the statistical distribution of poles and zeros of the Z-transform was found: poles and zeros tend, when the the time series goes to infinity, to a uniform angular distribution on the unit circle. The roots of unity thus appear to be noise attractors. We show that the Z-transform allows lossless undersampling and that this property can be used to increase signal detection. We give examples to suggest the power of our method, and discuss the relative importance of (uncorrelated) noise and background signals in practical applications. [Preview Abstract] |
Friday, October 23, 2009 5:00PM - 5:12PM |
C5.00006: High Performance Computing with CUDA Bill Maier The use of CUDA programming using inexpensive, off-the-shelf hardware for high performance computing is discussed. An introduction to the technology is given, along with a brief overview of the requirements for creating a CUDA-enabled system. Advantages and disadvantages of using CUDA for creating physical simulations is presented. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700