Bulletin of the American Physical Society
Joint Fall 2012 Meeting of the Texas Sections of the APS, AAPT, and Zone 13 of the SPS
Volume 57, Number 10
Thursday–Saturday, October 25–27, 2012; Lubbock, Texas
Session B5: Computational and Fundamental Physics |
Hide Abstracts |
Chair: Thomas Gibson, Texas Tech University Room: Holiday Inn Towers Windmill |
Friday, October 26, 2012 10:30AM - 10:42AM |
B5.00001: The Gravitational Potential, Gravitational Acceleration, and Vertical Gravity Gradient of a Rising Thermal Mantle Plume: A Numerical Experiment Juan H. Hinojosa Thermal convection in the mantles of the terrestrial planets is an important mode of heat transfer from the planet's interior. Gravitational instabilities originating at hot, thermal boundary layers at depth, either at the core-mantle boundary or at an interface between the upper mantle and lower mantle, are responsible for a type of convection that gives rise to thermal mantle plumes. Since the inferred horizontal dimensions of mantle plumes as a whole are small compared with their vertical dimensions, it is difficult to observe mantle plumes directly. To better understand the mantle plume's gravitational expression at the surface, the gravitational potential, gravitational acceleration, and vertical gravity gradient of a rising mantle plume are calculated in a series of numerical experiments. An axially symmetric mantle plume is modeled using a composite of spheres and/or disks of various depths, radii, thicknesses, and density contrasts. The density contrast used in the numerical experiments is due to the temperature difference between an isothermal plume and the local geotherm for plumes at depths greater than the depth of pressure-release melt, and is due to the melt density contrast elsewhere. The resulting gravitational quantities for the spheres are obtained with straight-forward, analytical expressions, but those for the disks are obtained by numerical integration. The results of the numerical experiments will be presented. [Preview Abstract] |
Friday, October 26, 2012 10:42AM - 10:54AM |
B5.00002: Comparison of Two Numerical Methods for Computing Fractal Dimensions Yui Shiozawa, Bruce Miller, Jean-Louis Rouet From cosmology to economics, the examples of fractals can be found virtually everywhere. However, since few fractals permit the analytical evaluation of generalized fractal dimensions or R\'enyi dimensions, the search for effective numerical methods is inevitable. In this project two promising numerical methods for obtaining generalized fractal dimensions, based on the distribution of distances within a set, are examined. They can be applied, in principle, to any set even if no closed-form expression is available. The biggest advantage of these methods is their ability to generate a spectrum of generalized dimensions almost simultaneously. It should be noted that this feature is essential to the analysis of multifractals. As a test of their effectiveness, here the methods were applied to the generalized Cantor set and the multiplicative binomial process. The generalized dimensions of both sets can be readily derived analytically, thus enabling the accuracy of the numerical methods to be verified. Here we will present a comparison of the analytical results and the predictions of the methods. We will show that, while they are effective, care must be taken in their interpretation. [Preview Abstract] |
Friday, October 26, 2012 10:54AM - 11:06AM |
B5.00003: Dynamics and stability of one-dimensional plasma with periodic boundary Pankaj Kumar, Bruce Miller We extend the method proposed by Miller and Rouet to formulate analytic solutions for the electric potential and field in a one-dimensional plasma satisfying periodic boundary conditions. We have also devised an event-driven algorithm to follow the time evolution of the system and to study its dynamical properties. In a dynamical system, the presence of positive Lyapunov exponents indicates that the system is chaotic. Of particular interest is the value of the largest (maximal) Lyapunov exponent which is usually sufficient to point toward the degree of chaos in the system. Using our new approach for defining the phase-space distance in systems with periodic boundary, we have employed our algorithm to find the largest Lyapunov exponent in the periodic plasma. Results obtained from our algorithm will be discussed with a view to exploring the dependence of chaotic properties of the system on its initial state. [Preview Abstract] |
Friday, October 26, 2012 11:06AM - 11:18AM |
B5.00004: Studies on a trajectory-based approach to relativistic quantum-particle dynamics Bill Poirier, Hung-Ming Tsai In a recent paper [Bill Poirier, arXiv:1208.6260 [quant-ph]], a trajectory-based formalism has been constructed to study the relativistic dynamics of a single spin-zero quantum particle. Being a generally covariant theory, this formalism introduces a new notion of global simultaneity for accelerated quantum particles. In this talk, we present several examples based on this formalism, including the time evolution of a relativistic Gaussian wavepacket. Energy-momentum conservation relations may also be discussed. [Preview Abstract] |
Friday, October 26, 2012 11:18AM - 11:30AM |
B5.00005: Overview of Spontaneous Frequency Chirping in Confined Plasmas Herbert Berk Spontaneous rapid frequency chirping is now a commonly observed phenomenon in plasmas with an energetic particle component. These particles typically induce so called weak instabilities, where they excite background waves that the plasma can support such as shear Alfven waves. The explanation for this phenomenon attributes the frequency chirping to the formation of phase space structures in the form of holes and clumps. Normally a saturated mode, in the presence of background dissipation, would be expected decay after saturation as the background plasma absorbs the energy of the excited wave. However the phase space structures take an alternate route, and move to a regions of phase space that are~lower energy states of the energetic particle distribution. Through the wave-resonant particle interaction, this movement is locked to the frequency observed by the wave. This phenomenon implies that alternate mechanisms for plasma relaxation need to be considered for plasma states new marginal stability. It is also possible that these chirping mechanisms can be used to advantage to externally control states of plasma. [Preview Abstract] |
Friday, October 26, 2012 11:30AM - 11:42AM |
B5.00006: Noether's Theorem and the Work-Energy Theorem for a Particle in an Electromagnetic Field Donald Kobe Noether's theorem is based on two fundamental principles. The first is the extremum of the action and the second is the invariance of the action under infinitesimal continuous transformations. The first gives Hamilton's principle of least action that results in the Euler-Lagrange equation. The second gives the Rund-Trautman identity for the generators of infinitesimal transformations. We apply these to a charged particle in an external electromagnetic field. The Euler-Lagrange equation gives the equation of motion. A solution of the Rund-Trautman identity for the generators is obtained by solving the generalized Killing equations. When the Euler-Lagrange equation and the Rund-Trautman identity are combined we obtain Noether's theorem for a conserved quantity. Using the equation of motion and the generators of infinitesimal transformations for a charged particle in an external electromagnetic field, we obtain the work-energy theorem. Even though this theorem can be obtained directly from the equation of motion, this problem is a good example of using Noether's theorem that is necessary for more complicated situations. [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