Bulletin of the American Physical Society
Joint Fall 2010 Meeting of the Texas Sections of the APS, AAPT, Zone 13 of SPS and the National Society of Hispanic Physicists
Volume 55, Number 11
Thursday–Saturday, October 21–23, 2010; San Antonio, Texas
Session FA4: Computational and General I |
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Chair: Zlatko Koinov, University of Texas at San Antonio Room: University Center III Harris Room, 2nd floor |
Friday, October 22, 2010 3:00PM - 3:12PM |
FA4.00001: Dynamic Modeling and Simulation of a Real World Billiard Alexandre Hartl, Bruce Miller Scientists have investigated gravitational billiards since they exhibit a variety of dynamical phenomena in nonlinear Hamiltonian systems. The system typically consists of a particle undergoing elastic collisions within a boundary, where the particle assumes a ballistic trajectory between collisions. This paper considers the more realistic situation of an inelastic, rotating, gravitational billiard in which there are retarding forces due to air resistance and friction. In this case the motion is not conservative, and the billiard is a sphere of finite size. Here we present a dynamical model that captures the relevant dynamics required for describing the motion of a real world billiard for arbitrary boundaries. An application of the model considers parabolic, wedge and hyperbolic billiards that are driven sinusoidally. Direct comparisons are made between the model's results and experimental data previously collected. Although several studies have investigated the effect of variable elasticity in relation to the gravitational billiard, this study is the first to incorporate rotation and additional forms of energy dissipation. [Preview Abstract] |
Friday, October 22, 2010 3:12PM - 3:24PM |
FA4.00002: Experimental Study of Ocean Mixing Bruce Rodenborn, Guenther Ebert, Harry L. Swinney Ocean circulation patterns, e.g. the Gulf Stream, depend on mixing produced by the tides and wind. These oceanic currents are critical in maintaining the earth's climate. Global ocean and climate computer models parameratize mixing because it happens at such a small scale. The current understanding of ocean mixing requires about 20\% of the kinetic energy in a turbulent flow to be converted into a change in the fluid's gravitational potential energy. However, this value of mixing efficiency has never been confirmed in laboratory experiments. We study mixing in a fluid contained between two counter-rotating cylinders whose density, like the ocean, varies with height. Using sodium polytungstate salt solution, we achieve an initial vertical density variation of up to 200\%, and then spin the cylinders to mix the fluid. Measurements are made for laminar (smooth) to fully turbulent flows. The flow pattern is visualized using Kalliroscope, and the characteristic vertical length scale is determined from spatial fourier transforms of images. The power input is determined by measuring the torque and rotation rate of both cylinders. The fluid's gravitational potential energy is determined by measuring density as a function of height. We find that mixing efficiency is strongly dependent both on the rotation rates of the cylinders and the total initial density variation. [Preview Abstract] |
Friday, October 22, 2010 3:24PM - 3:36PM |
FA4.00003: Analytical Comparisons of Tree Ring Data, Greenland Ice Core Temperatures and Temperature Fluctuations of the Sargasso Sea James Roberts, Jai Dahiya Embedded in various events on Earth are data that allow us to map the temperature of the Earth over many years. In this work we have chosen the temperature fluctuations in the Sargasso Sea, the changing patterns in tree ring growth and temperature fluctuations in Greenland ice core samples for comparison with a goal to understanding the patterns in global warming. Signatures have been identified that predate the Industrial Revolution, which had been blamed for much of global warming, that indicate that Earth temperatures have enjoyed numerous intervals of both global warming and global cooling. The intention of this work is not to stir controversy but to provoke legitimate debate based on scientific data and processes rather than popular opinion or deduction by ``experts'' in climatology. [Preview Abstract] |
Friday, October 22, 2010 3:36PM - 3:48PM |
FA4.00004: A new generalization of supersymmetric quantum mechanics to arbitrary dimensionality or number of distinguishable particles Thomas Markovich We present here a new approach to generalize supersymmetric quantum mechanics to treat multiparticle and multi-dimensional systems. We do this by introducing a {\em vector} superpotential in an orthogonal hyperspace. In the case of $N$ distinguishable particles in three dimensions this results in a vector superpotential with $3N$ orthogonal components. The original scalar Schr\"odinger operator can be factored into vector ``charge'' operators: $\vec Q_{1}$ and $\vec Q_{1}^{\dagger}$. Using these operators, we can write the original (scalar) Hamiltonian as $H_{1} = \vec Q_{1}^{\dagger}\cdot \vec Q_{1} + E_{0}^{(1)}$. The second sector Hamiltonian is a tensor given by $H_{2} = \vec Q_{1}\vec Q_{1}^{\dagger} + E_{0}^{(1)}$ and is isospectral with $H_{1}$. The vector ground state of sector two, $\vec\psi_{0}^{(2)}$, can be used with the charge operator $\vec Q_{1}^{\dagger}$ to obtain the excited state wave functions of the first sector. This can be used with the sector Hamiltonians alternating between scalar and tensor forms accommodating both variational and Monte Carlo methods to obtain approximate solutions to both scalar and tensor sectors. We demonstrate the approach with examples of a pair of separable 1D harmonic oscillators and the example of a non-separable 2D anharmonic oscillator (or equivalently a pair of coupled 1D oscillators). [Preview Abstract] |
Friday, October 22, 2010 3:48PM - 4:00PM |
FA4.00005: Identifying Inertial Modes in a Hide-Titman Flow Mary Catalano, Robert Blum, Daniel Zimmerman, Don Martin, Daniel Lathrop Inertial modes are internal wave patterns present within a bounded, rotating fluid being restored by the Coriolis force. Hide and Titman\footnote{``Detached Shear Layers in a Rotating Fluid.'' Journal of Fluid Mechanics 29, pp39-60 (1967).} found that a cylindrical container filled with homogeneous liquid and having a thin disk mounted coaxially inside of it will display non-axisymmetric fluid flow when the differential rotation between the cylinder and the disk exceeds a critical threshold. Their essential geometry and setup were replicated and the fluid flow produced was analyzed to ascertain its relationship, if any, to the inertial modes of a cylinder annulus expressed in analytical form by Zhang, et al.\footnote{``On Inertial Waves in a Rotating Fluid Sphere.'' Journal of Fluid Mechanics 437, pp103-119 (2000).} Experimental data and analyses to correlate observed fluid flows with theoretical inertial modes will be presented. [Preview Abstract] |
Friday, October 22, 2010 4:00PM - 4:12PM |
FA4.00006: Developing an Undergraduate Program in Energy Systems John Fanchi Texas Christian University (TCU) is developing an undergraduate program in engineering that prepares students to become engineers with an emphasis in energy systems. Courses in the program include an overview of energy in society that is suitable for the general student population; a technical overview of traditional energy (coal, oil and gas), nuclear energy, and renewable energy; and courses that cover more specialized energy topics. Students participating in this program will improve their understanding of energy systems; be introduced to outstanding scientific and engineering problems; learn about the role of energy in a global and societal context; and evaluate contemporary issues associated with energy. The energy systems curriculum will improve student understanding of activities that are a major component of the economy. As engineering students graduate with an energy systems emphasis, they will take their places in society with a much more sophisticated understanding of energy-related issues affecting their community. This talk will present the status of the new program. [Preview Abstract] |
Friday, October 22, 2010 4:12PM - 4:24PM |
FA4.00007: Schr\"{o}dinger Equation from Hamilton-Jacobi Equation Donald H. Kobe The time-dependent Schr\"{o}dinger equation is now considered fundamental and the time-independent Schr\"{o}dinger equation is derived from it for stationary states. Historically, it was the other way around. Schr\"{o}dinger obtained his time- independent equation first and then obtained the time-dependent equation for time-independent potentials. He then postulated it to be valid in general. We use the classical Hamilton-Jacobi equation to obtain both the time-dependent Schr\"{o}dinger equation and the equation of continutiy. We first derive Schr\"{o}dinger's ``Ansatz'' for the action S in terms of the wave function. By this change of variables the Hamilton-Jacobi equation is transformed into a complex equation. The equation of continuity is obtained from the imaginary part. The real part and the remaining imaginary part are combined to give a Schr\"{o}dinger equation with a nonlinear term that is a remanent of the Hamilton-Jacobi equation. When this nonlinear term is dropped the linear time-dependent Schr\"{o}dinger equation is obtained. This approach fills a gap in the development of the time-dependent Schr\"{o}dinger equation. It also shows the intimate connection between classical and quantum mechanics. [Preview Abstract] |
Friday, October 22, 2010 4:24PM - 4:36PM |
FA4.00008: Motor Controls for the NIFFTE Time Projection Chamber Positioning Stand Daniel Pamplin, Nathan Pickle The next generation nuclear power plants will be more efficient and produce smaller amounts of radioactive waste. Design of these new reactors is limited partially by the lack of precise neutron induced fission cross sections at certain incident neutron energies of several isotopes. In order to reduce the uncertainty of the cross sections to less than 1{\%}, a Time Projection Chamber (TPC) was built by the Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) collaboration. These improvements in precision will be possible due to the TPC's ability for a full 3-D reconstruction of the fission fragment tracks. The NIFFTE TPC will be installed at Los Alamos National Lab's LANSCE facility. Thin targets will be mounted in the center of the TPC in a pressurized hydrogen gas chamber so that both hemispheres of the reaction will be covered. This talk considers the control of the stepper motors that drive the positioning table of the TPC, which has all of its readout electronics attached, to be lined up with the beam. ~This includes both the controlling software and its graphical interface to the MIDAS online data acquisition system. [Preview Abstract] |
Friday, October 22, 2010 4:36PM - 4:48PM |
FA4.00009: A Classical Theory of the Anomalous Zeeman Effect James Espinosa, James Woodyard Over a hundred years ago, it was discovered that spectral lines were shifted by magnetic fields. Lorentz was able to explain a small set of phenomena that was ironically called the normal Zeeman effect. It took more than twenty years for Lande to arrive at a vector model of the atom to explain the majority of shiftings called the anomalous Zeeman effect. Within a couple of years, Uhlenbeck and Goudsmit introduced the idea of a spinning electron that would give an underlying explanation of the vector model rules. It is generally taught that without the concept of spin there can be no explanation of all the spectral splittings caused by a magnetic field. We will present a purely classical model developed by Woldemar Voigt to describe the most famous anomalous splitting, the sodium D line. In addition, his theory correctly describes the transition from the weak field state to the strong one, called the Paschen-Back effect. We will show how his theory matches well with our classical picture of the atom. [Preview Abstract] |
Friday, October 22, 2010 4:48PM - 5:00PM |
FA4.00010: Neutron Elastic and Inelastic Scattering Cross Sections on $^{Nat}$Fe and $^{23}$Na Luke Kersting, Collin J. Lueck, S.F. Hicks, B.P. Crider, M.T. McEllistrem, E.E. Peters, J.R. Vanhoy Neutron elastic and inelastic scattering angular distributions from $^{Nat}$Fe and $^{23}$Na at incident neutron energies of 3.57 and 3.81 MeV have been measured at the University of Kentucky 7 MV Van de Graaff laboratory using neutron time-of-flight techniques. The neutron beam was produced using the $^{3}$H(p,n)He$^{3}$reaction. The scattered neutrons were detected at angles between 20\r{ } and 150\r{ } in 10\r{ } intervals with a hexafluorbenzene detector located approximately 3 m from the scattering samples. Neutron scattering differential cross sections were deduced. These cross sections and their uncertainties are important for understanding neutron-induced reactions in fission reactors and are important for fission reactor criticality calculations. [Preview Abstract] |
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