Bulletin of the American Physical Society
Joint Spring 2013 Meeting of the Texas Sections of the APS and AAPT and Zone 13 of the SPS
Volume 58, Number 3
Thursday–Saturday, April 4–6, 2013; Stephenville, Texas
Session B3: Computational Physics |
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Chair: Bryant Wyatt, Tarleton State University Room: Science Building 112 |
Friday, April 5, 2013 11:00AM - 11:12AM |
B3.00001: Tangential Relations between Distorted Angles vs. Original Angles of a Traveling General Triangle in Special Relativity Florentin Smarandache Let's consider a traveling general triangle $\Delta $\textit{ABC,} with the speed $v$, along its side \textit{BC }on the direction on the $x-$axis; angles $B$ and $C$ are adjacent to the motion direction, while angle $A$ is of course opposite. Let \textit{AM} be the perpendicular from $A$ to the motion direction \textit{BC}. After the contraction of the side \textit{BC} with the Lorentz factor $C(v)=\sqrt {1-\frac{v^{2}}{c^{2}}} $, and consequently the contractions of the oblique-sides \textit{AB} and \textit{AC} with the oblique-contraction factor \[ OC(v,\theta )=\sqrt {C(v)^{2}\cos^{2}\theta +\sin^{2}\theta } , \] where $\theta $ is the angle between respectively each oblique-side and the motion direction, one gets the general triangle $\Delta A'B'C'$ with the following tangential relations between distorted angles vs. original angles of the general triangle: \[ \tan A'=\tan A\cdot C\left( v \right)\cdot \frac{1-\tan A_{1} \tan A_{2} }{1-\tan A_{1} \tan A_{2} C\left( v \right)^{2}}, \] where angles $A_{1} =BAM$and respectively $A_{2} =MAC$; \[ \tan B'=\frac{\tan B}{C\left( v \right)}; \] \[ \tan C'=\frac{\tan C}{C\left( v \right)}. \] [Preview Abstract] |
Friday, April 5, 2013 11:12AM - 11:24AM |
B3.00002: Comparison of Correlation Function for Path Integral Formulation of Ortho-Positronium in Dense Fluids Terrence Reese, Bruce Miller In previous work the Path Integral Monte Carlo (PIMC) technique was used to simulate a quantum particle (qp) in a dense Lennard-Jones 6-12 fluid having the thermodynamic properties of Xenon. Because of the difference in thermal wavelengths between the qp and the fluid molecules the fluid molecules can be treated classically. This combination of using quantum mechanics for the qp and classical mechanics for the fluid molecules is known as a hybrid model. The path integral formulation represents a qp as a closed chain of P classical particles in which the quantum uncertainty in the position of the qp is manifested in the finite width spread of the polymer chain. The PIMC technique allows standard classical Monte Carlo techniques to be used to compute quantum mechanical equilibrium values like the ortho-Positronium pick-off decay rate. The Correlation Function, C(k), is the mean product of the difference of a variable at the times j and j$+$k with the average value divided by the variance. The correlation length, k, at which C (k) becomes zero, indicates the number of passes before values of the independent variable are statistically independent. The Correlation Function versus the correlation length has been plotted for the decay rate covering different polymer segment lengths, temperatures, densities, and fluid molecule numbers. The number of statistically independent configurations has also been computed for each thermodynamic system. [Preview Abstract] |
Friday, April 5, 2013 11:24AM - 11:36AM |
B3.00003: Functional Programming in Scientific Computing Douglas Moore We look at the typical design goals of scientific/mathematical computing and consider ways in which a functional programming style can be used to achieve them. Programming examples for various domain-specific problems, e.g. constructing the root structure of semi-simple lie algebras, are presented in various popular languages such as C/C++ and MATLAB as well as the functional language Haskell for contrast. [Preview Abstract] |
Friday, April 5, 2013 11:36AM - 11:48AM |
B3.00004: Endohedral fullerene as acceptor: A DFT study on charge trans- fer states of Sc3N@C80-porphyrin complex Fatemeh Amerikheirabadi, Luis Basurto, Rajendra Zope, Tunna Baruah C\textbf{60} fullerene and its derivatives are the most popular acceptors which are used in molecular/polymeric complexes used in organic photovoltaics. Endohedral fullerenes are shown to produce long lived charge separated states. The Sc\textbf{3}N@C\textbf{80}, the third most abundant fullerene after C\textbf{60 }and C\textbf{70}, has a larger cage with a radius of 4.1 Ang. We have carried out a DFT study on the electronic structure of ground and charge transfer states of a model Sc\textbf{3}N@C\textbf{80}-Zn tetraphenyl porphyrin cofacial complex. The C\textbf{80 }cage used in our calculations has icosahedral symmetry. We find that the lowest charge transfer state with a hole on the porphyrin and an electron on the Sc\textbf{3}N@C\textbf{80 }is at 2.1 eV above the ground state. The calculations show that dif- ferent orientations of the Sc\textbf{3}N unit to the porphyrin plane do not significantly alter the electronic structure. The electronic structure of the complex and its components along with the exciton binding energies will be presented. [Preview Abstract] |
Friday, April 5, 2013 11:48AM - 12:00PM |
B3.00005: Orthogonal Polynomial Projection Quantization: A New Hill Determinant Formulation Carlos Handy, Daniel Vrinceanu We present a new formulation\footnote{C. R. Handy and D. Vrinceanu, to appear J. Phys A: Math. Theor. (2013). } (OPPQ) of the configuration space Hill determinant (HD) approach,\footnote{K. Banerjee, Proc. R. Soc. Lond. A 368 155 (1979).} and its momentum space counterpart (MRF),\footnote{C. J. Tymczak, G. S. Japaridze, C. R. Handy, and Xiao-Qian Wang, Phys. Rev. Lett. 80, 3674 (1998).} that has non of the instabilities of the former,\footnote{A. Hautot, Phys. Rev. D 33, 437 (1986).} nor the limitations of both. Let $\Psi $(x) $= \quad \Sigma_{n}$ a$_{n}$ P$_{n}$(x) R(x), where the P$_{n}$ `s are the orthogonal polynomials for a given \textit{reference function}, R(x) \textgreater 0 . If the system admits a linear recursive \textit{moment equation} representation, the a$_{n}$`s become a finite sum with respect to the moments $\mu_{p} \quad = \quad \smallint $ x$^{p} \quad \Psi $(x). Constraining a$_{N} \quad =$ 0,\textellipsis ,a$_{N-ms\, }=$ 0 gives impressive results for the discrete state energies, surpassing MRF. Contrary to HD, OPPQ is an L$^{2}$ formulation in which R(x): (i) does not have to be analytic; and (ii) can be adapted to the asymptotic form of $\Psi $. It has been applied to 1D and 2D anharmonic potentials, including pseudo hermitian systems, as well as the difficult two dimensional dipole problem for modeling edge structures in nanomaterials.\footnote{P. Amore and F. M. Fernandez, J. Phys. B 45, 235004 (2012).} [Preview Abstract] |
Friday, April 5, 2013 12:00PM - 12:12PM |
B3.00006: Follow-on Studies of Hydrogenic Quantum Systems Using the Feynman-Kac Path Integral Method J.M. Rejcek, N.G. Fazleev The Feynman-Kac path integral method is applied to the atomic hydrogen quantum system for the purpose of evaluating eigenvalues of the corresponding eigenfunctions of the Hamiltonian of the system. These are computed by random walk simulations on a discrete grid. The study provides the latest simulation analysis and includes rescaling and the use of symmetry that allows eigenvalues of the corresponding higher order eigenstates to be computed. The method provides exact values in the limit of infinitesimal step size and infinite time for the lowest eigenstates. [Preview Abstract] |
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