Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session B21: General Theory |
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Sponsoring Units: DCOMP Chair: David Singh, Oak Ridge National Laboratory Room: D161 |
Monday, March 21, 2011 11:15AM - 11:27AM |
B21.00001: Optimization of Elastic Constant Values in Non-cubic Crystals using Computational Image Matching Madeleine Msall, Timothy Head Point excitation in ultrasound or heat pulse experiments excites non-equilibrium phonons that carry energy along the group velocity direction. Phonon images map the sharp boundaries between high and low flux regions, called caustics, which are directly related to folds in the acoustic wave surface. Computational simulations show that caustic positions are extremely sensitive to the values of the elastic constants. We explore methods of determining the elastic constants using image matching techniques. Given the dependence of single image features on a constellation of constants, there are many local minima encountered in the search. This talk will present quantifiable criteria for image matching in this context and discuss potential heuristic or stochastic methods to deal with the problem of local minima. [Preview Abstract] |
Monday, March 21, 2011 11:27AM - 11:39AM |
B21.00002: Entropic sampling without windows Ronald Dickman, Ant\^onio Cunha-Netto We describe an entropic sampling method that permits estimation of the number of configurations over the full range of energies, with dividing the latter into subsets or ``windows.'' Our method involves progressive refinement of an initial approximation for the density of states, using a set of random walks that span the energy range. Applied to the two-dimensional Ising model the method yields the critical temperature to an accuracy of about 0.01\%, and critical exponents to 0.5\% or better. Predictions for system sizes $L=10$ - 160, for the temperature of the specific heat maximum, and the specific heat at the critical temperature, are in very good agreement with exact results. The antiferromagnetic transition is well represented. Excellent results are also obtained for the three-dimensional Ising model (simple cubic lattice) and the lattice gas with nearest-neighbor exclusion. We observe that attempts to restrict the sampling to a subset of the full energy range lead to distortions in the density of states, even if the restriction is imposed in a smooth manner, rather than with a sharp barrier. [Preview Abstract] |
Monday, March 21, 2011 11:39AM - 11:51AM |
B21.00003: Nearly exact calculations of small atomic and molecular systems using explicilty correlated gaussians Sergiy Bubin, Kalman Varga, Ludwik Adamowicz We demonstrate how very precise (virtually exact) solutions of various quantum mechanical problems can be obtained using the variational method with explicitly correlated Gaussian basis functions (ECGFs). As examples we consider several benchmark systems, such as few-electron atoms and molecules, as well as Coulomb systems containing exotic particles. We also discuss the evaluation of relativistic corrections in the framework of ECGFs. [Preview Abstract] |
Monday, March 21, 2011 11:51AM - 12:03PM |
B21.00004: Metallic Phase of Water Ice Predicted at Megabar Pressures Burkhard Militzer, Hugh Wilson We predict water ice to attain two new crystal structures with Pbca and Cmcm symmetry at 7.6 and 15.5 Mbar, respectively [Phys. Rev. Lett. 105 (2010) 195701]. With density functional calculations, we analyze the structural and electronic properties of these phases at zero temperature. The Pbca phase, like the known high-pressure ice phases VII, VIII, X and Pbcm, is insulating and consists of two interpenetrating hydrogen bonded networks, but the Cmcm phase is metallic and consists of corrugated sheets of H and O atoms. The H atoms are squeezed into octahedral positions between next-nearest O atoms while they occupy tetrahedral positions between nearest O atoms in lower-pressure phases. Our predictions may be testable with ramp compression experiments that can reach megabar pressures at lower temperatures than conventional shock wave experiments. The predicted insulator-to-metal transition would lead to an increase in reflectivity that can be measured with spectroscopic techniques. [Preview Abstract] |
Monday, March 21, 2011 12:03PM - 12:15PM |
B21.00005: Supersymmetric Quantum Mechanics in Multiple Dimensions Applied to Variational Monte Carlo - A Proof of Principle Study Thomas Markovich, Kaushik Maji, Eric Bittner, Don Kouri We present a new approach to variational monte carlo using our N-Dimensional generalization of Supersymmetric Quantum Mechanics. 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. 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] |
Monday, March 21, 2011 12:15PM - 12:27PM |
B21.00006: Electromagnetic and gravitational signatures of black hole and neutron star mergers Steven Liebling Astrophysical binary systems composed of some combination of compact objects (black holes(BH) and neutron stars(NS)) are extremely interesting dynamical systems. Such systems are generally extremely good radiators of gravitational waves, and, in at least some cases, they should be excellent electromagnetic sources. As such, they hold great promise for concurrent detection from both recently completed gravitational wave observatories and from conventional telescopes. I describe recent results achieved with a fully relativistic adaptive code for the merger of BH-BH, BH-NS, and NS-NS systems with magnetic fields. [Preview Abstract] |
Monday, March 21, 2011 12:27PM - 12:39PM |
B21.00007: Quantification of Partially Ordered Sets with Application to Special Relativity Newshaw Bahreyni, Kevin H. Knuth A partially ordered set is a set of elements ordered by a binary ordering relation. We have shown that a subset of a partially ordered set can be quantified by projecting elements onto a pair of chains where the elements of each chain are quantified by real numbers. This results in a quantification based on pairs of real numbers (pair). Intervals, defined by pairs of elements, can be quantified similarly. A pair can be decomposed into a sum of a symmetric pair and an antisymmetric pair and mapped to a unique scalar which results in the Minkowskian form. Changing the basis of quantification from one pair of chains to another, under special conditions, leads to the generalized Lorentz transformation for pairs. We apply these results to a causally-ordered set of events by identifying a chain of events with an observer equipped with a clock in an inertial frame. We obtain the Minkowski metric of flat space-time as well as Lorentz transformations, which results in there being a maximum invariant speed. We find that the mathematics of special relativity arises from quantifying causal relationships among events, and requires neither the principle of relativity nor the fact that the speed of light is constant. [Preview Abstract] |
Monday, March 21, 2011 12:39PM - 12:51PM |
B21.00008: Lunar Orbit Anomaly and GM=tc$^3$ Cosmology Louise Riofrio Studies of the Moon at Johnson Space Center have confirmed a large anomaly in lunar orbital distance, with possible applications to Relativity. Our Lunar Laser Ranging Experiment has reported the Moon's semimajor axis increasing at 3.82 $\pm$ .07 cm/yr, anomalously high. If the Moon were gaining angular momentum at this rate, it would have coincided with Earth less than 2 Gyr ago. The Mansfield sediment (Bills, Ray 2000) measures lunar recession at 2.9 $\pm$ 0.6 cm/yr. Additional observations independently measure a recession rate of 2.82 $\pm$ .08 cm/yr. LLRE differs from independent experiments by 10 sigma. A cosmology where speed of light c is related to time t by GM=tc$^3$ has been suggested to predict the redshifts of Type Ia supernovae, and a 4.507034\% proportion of baryonic matter (Riofrio 2004). If c were changing in the amount predicted, lunar orbital distance would appear to increase by an additional 0.935 cm/yr. An anomaly in the lunar orbit may be precisely accounted for, shedding light on puzzles of ``dark energy.'' In Planck units this may be summarised as M=R=t. [Preview Abstract] |
Monday, March 21, 2011 12:51PM - 1:03PM |
B21.00009: On a Broken Formal Symmetry between Kinetic and Gravitational Energy Armin Nikkhah Shirazi Historically, the discovery of symmetries has played an important role in the progress of our fundamental understanding of nature. This paper will demonstrate that there exists in Newtonian theory in a spherical gravitational field a formal symmetry between the kinetic (KE) and gravitational potential energy (GPE) of a test mass. Put differently, there exists a way of expressing GPE such that the form of the mathematical expression remains invariant under an interchange of KE and GPE. When extended to relativity by a suitable assumption, it leads to a framework that bridges the general relativistic and Newtonian conceptions of gravitational energy, even though the symmetry is broken except in the infinitesimal limit. Recognizing this symmetry at infinitesimal scales makes it possible to write a relativistic equation of an individual graviton, the properties of which under under one interpretation may be unexpected. [Preview Abstract] |
Monday, March 21, 2011 1:03PM - 1:15PM |
B21.00010: The Relativistic Quantized Force: Newton's Second Law, Inertial and Gravitational; Generalization of Schwarzschild Metric for Strong and Weak Gravitational Field Azzam AlMosallami In this paper we derived the relativistic Quantized force, where the force given as a function of frequency[1]. Where, in this paper we defined the relativistic momentum as a function of frequency equivalent to the energy held by a body, and time, and then the quantized force is given as the first derivative of the momentum with respect to time. Subsequently we introduce in section one Newton's second law as it is relativistic quantized, and in section two we introduce the relativistic quantized inertial force, and then the relativistic quantized gravitational force, and the quantized gravitational time dilation. At the end we shall generalize the Schwartzschild metric to describe the weak and strong gravitational field. [Preview Abstract] |
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