Bulletin of the American Physical Society
2005 TSAPS/AAPT/SPS Joint Fall Meeting
Thursday–Saturday, October 20–22, 2005; Houston, TX
Session B2: Theory II |
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Room: Waldorf Astoria A 210A |
Friday, October 21, 2005 2:00PM - 2:12PM |
B2.00001: CO {\&} O Emission Lines in Circumstellar Disks Jesus Enriquez, Inga Kamp CO emission lines have been used to observe Circumstellar Disks around type A stars. CO observations have detected a gas-to-dust ratio much lower than the interstellar gas-to-dust ratio. The reason is that CO is a poor tracer of gas (H2). The main motivation is to check the result from CO with other tracers such as C, C+ and O, with future instruments such as SOFIA, Herschel, APEX and ALMA. Models of emission lines were created with the help of a 2D Monte Carlo code from Hogerheijde {\&} van der Tak (2000) to calculate the line emission from the optically thin disk models. Four different models of different Earth masses were used to create the line profiles for CO and O. The integrated flux of the line profiles were calculated to obtain an easy-to-use plot for observers to get the disk masses for a known integrated flux. [Preview Abstract] |
Friday, October 21, 2005 2:12PM - 2:24PM |
B2.00002: On Control of Chaos in the R\"{o}ssler system Julian Antolin Camarena, Roman Grigoriev In order to control chaos, a deep understanding is required on top of good amounts of mathematical and computational~work: First, the system must be numerically integrated to acquire data in order to construct a Poincare map, this is necessary in order~to construct the iterate maps from which the periodic orbits and fixed points (period-1 orbits). Second, the Jacobian is computed at each fixed point. From the Jacobian the eigenverctors and eigenvalues are obtained in order to identify the stable and unstable manifolds. From this point on, one can apply the necessary control algorithms to achieve the desired, predetermined, and controlled~system dynamics. [Preview Abstract] |
Friday, October 21, 2005 2:24PM - 2:36PM |
B2.00003: The Coulomb Force between Two Charged Balls G.E. Hite, T.J. Hyland, W.M. Haymes It is common to demonstration Coulomb's law by using two charged balls. It is often stated that this demonstration verifies with good accuracy that the force varies inversely as the square of the distance between the balls centers, i.e. 1/R$^2$. However, it has been known for over a hundred years that the force between two oppositely charged balls only varies in this manner when the separation between the balls is large compared to their diameters. In fact, the force actually diverges as the separation between the balls vanishes! It will be shown via the use of image charges that the force between oppositely charged balls can be approximated within 5% by a rather simple and intuitive expression. An improved version of the pendulum experiment demonstrates that whereas the data vary by almost an order of magnitude form the inverse square behavior, there is good agreement with the theoretical prediction. [Preview Abstract] |
Friday, October 21, 2005 2:36PM - 2:48PM |
B2.00004: The curved SN1a Hubble plots R.L. Collins Recent Hubble plots, of distance vs. red shift, curve upward at the large distances afforded by using distant SN1a supernovae as ``standard candles.'' Hubble plots are intended to be of present distance vs. red shift, and were expected to be linear absent acceleration. The light left long ago, and observed distance must be extrapolated to present distance. Further, distance measured by “dimness” is optical distance. This can be corrected to geometrical distance, using GR, or by using mass-metric relativity (http://arXiv.org/pdf/physics/0012059.), which assigns to space an index of refraction, $n=(1+GM/rc^{2})^{2}$. This index easily accounts for the deflection of starlight and the Shapiro time delay, tests that have been cited as affirming GR. It changes with time, since all distances ``r'' increase as the big bang expands. On modeling this to two parameters, the Hubble plot is well fitted by choosing total mass $M=6.03 \times 10^{52}$ kg and $T=16.24 \times 10^{9}$ years since the big bang. These agree well with estimates found using other methods. The present index of refraction of space, due to all mass in our big bang, is 2.41. The full paper is available at http://arxiv.org/pdf/physics/0101033. [Preview Abstract] |
Friday, October 21, 2005 2:48PM - 3:00PM |
B2.00005: Symmetry analysis of the quantum oscillator Balraj Menon The symmetry analysis of differential equations had its beginnings at the end of the nineteenth century in the work of the Norwegian mathematician Sophus Lie, and arose in his investigation of solutions of differential equations. The applications resulting from the explicit determination of the symmetries of a differential equation are numerous. They include, the construction of new solutions of a differential equation from known solutions, the construction of special solutions of the differential equation, and in the interplay between symmetries and conservation laws, enshrined in the celebrated theorems of the German mathematician Emmy Noether. This talk primarily focusses on the task of determining the symmetries of a differential equation and the application of the method to the quantum oscillator. Some novel and interesting time-dependent solutions of the quantum oscillator generated by the symmetry analysis are presented and their significance discussed. The mathematical formalism underlying the symmetry analysis is accessible to undergraduates with a knowledge of multivariate calculus and some exposure to differential equations. The symmetry analysis of differential equations is a fruitful area of research for the theoretically inclined undergraduate, encompassing areas such as the analysis of PDEs, computer algebra and computer visualization. [Preview Abstract] |
Friday, October 21, 2005 3:00PM - 3:12PM |
B2.00006: Modeling graphene layers and single-walled carbon nanotubes with regularized $\delta $-function potentials Han Hsu, L.E. Reichl Using \textit{ab initio} methods to study the interaction between strong electromagnetic fields and thin films or crystalline materials would be extremely difficult. A common way is to use simplified models with several fitting parameters to simulate real physical systems. In this paper, we propose a model to simulate the $\pi $ electrons in a graphene layer and single-walled carbon nanotubes. We let the atomic potential of each carbon atom be replaced by a two-dimensional attractive regularized $\delta $ function and construct a honeycomb lattice of regularized $\delta $ function to reproduce the band structure of a graphen layer and nanotubes. We also use this model to calculate the electron wave functions of nanotubes with finite length. The results are in good agreement with first principle calculations. With the accuracy and simplicity provided by this model, it can be a good candidate to study the interaction between the $\pi $ electrons of nanotubes and electromagnetic fields in nonperturbative regime. [Preview Abstract] |
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