Bulletin of the American Physical Society
APS April Meeting 2012
Volume 57, Number 3
Saturday–Tuesday, March 31–April 3 2012; Atlanta, Georgia
Session T14: Computational Methods and Implementation |
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Sponsoring Units: DCOMP Chair: Ronald Mickens, Clark Atlanta University Room: Grand Hall East C |
Monday, April 2, 2012 3:30PM - 3:42PM |
T14.00001: Investigation of an Unforced Duffing Equation having Fractional Power Damping Ronald E. Mickens, Ray Bullock, W. Eugene Collins The Duffing ODE provides a standard model for nonlinear oscillations for a broad range of phenomena in the natural and engineering sciences. The effects of dissipation are generally included by adding a ``friction" force term, $f(v)$, proportional to an integer power of the velocity. Thus, oscillations take place, but with a decreasing amplitude, and which only decrease to zero in an infinite time interval. We examine the case where $f(v)=-av^p$, $a>0$ and $0 < p < 1$, and demonstrate that the amplitude of the oscillations become zero in a finite time [1]. This result may have relevance for the vibrations of carbon nanotubes and sheets of graphene sheets [2]. \\[4pt] [1] R. E. Mickens, Truly Nonlinear Oscillators (World Scientific, London, 2010). \\[0pt] [2] A. Eichler et al., Nature Nanotechnology, Vol. 6 (June 2011), 339--342. [Preview Abstract] |
Monday, April 2, 2012 3:42PM - 3:54PM |
T14.00002: Estimate of the Damping Force Exponential Coefficient for an Oscillating Beam S. Ray Bullock, W. Eugene Collins$^1$, Ronald E. Mickens For many dynamic systems damping/dissipative forces (DDF) are important. These forces are generally modeled in the equations of motion by terms linear in the ``velocity." An example is the standard damped, linear harmonic oscillator. However, for complex systems a broader range of functional forms is required for the associated DDF. If the fact that such systems only oscillate in a finite number of cycles is taken into account, then the leading term of the DDF is proportional to $v^\alpha$, where $\alpha$ lies in the interval $(0,1)$. We present preliminary experimental results, for a vibrating beam, implying that $\alpha\sim 0.9$. To obtain this value we derive a theoretical relationship between the damping time and the ``initial amplitude" of the beam, a relationship which does not depend on knowing {\it a priori} the exact equations of motion. Our findings are relevant for the study and analysis of vibrations in carbon nano-tubes and graphene sheets. [Preview Abstract] |
Monday, April 2, 2012 3:54PM - 4:06PM |
T14.00003: Dispersion corrections in the boron buckyball and nanotubes Rosi Gunasinghe, Cherno Kah, Kregg Quarles, Xiao-Qian Wang We have investigated structural and electronic properties of the B$_{80}$ buckyball and boron nan-otubes by means of dispersion-corrected density-functional calculations. Our analysis reveals the vibrational stability for the icosahedral B$_{80}$ with the inclusion of dispersion corrections, in contrast to the instability to a tetrahedral B$_{80}$ with puckered capping atoms from preceding density-functional theory calculations. Similarly, the dispersion-corrected density-functional calculations yield non-puckered boron nanotube conformations and an associated metallic state for zigzag tubes. Our study indicates that the incorporation of long-range dispersive interactions is particularly important to the structural and electronic properties of boron fullerenes and nanotubes. [Preview Abstract] |
Monday, April 2, 2012 4:06PM - 4:18PM |
T14.00004: Relative stability of boron fullerenes: A dispersion-corrected density-functional study Larry Riche, Rosi Gunasinghe, Xiao-Qian Wang We have studied the stability of various boron fullerene structures via dispersion-corrected desity-functional calculations. Our results reveal that the energy order of fullerenes strongly depends on the exchange-correlation functional employed in the calculation. A systematic study elucidates the importance of incorporating dispersion forces to account for the intricate interplay of two and three centered bonding in boron nano-structures. Futhermore, the inclusion of dispersion correction stabilizes high symmetry conformations that are vibrationaly unstable in the preceding density-functional calculations. We also discuss the use of graphics unit processor accelerated algorithms for the calculations. [Preview Abstract] |
Monday, April 2, 2012 4:18PM - 4:30PM |
T14.00005: Distributed computing with an ATLAS Tier 3 cluster at KSU David Joffe The use of distributed, or ``grid,'' computing provides an excellent opportunity for small physics programs at primarily undergraduate institutions to participate in large scale projects, such as LHC experiments. The ATLAS Tier 3 cluster currently being set up at Kennesaw State University will use the distributed computing environment developed by the ATLAS collaboration to function as part of the ATLAS tiered analysis structure and thus contribute to the overall ATLAS physics program. The cluster will also provide a unique environment for KSU undergraduates to gain first-hand experience and knowledge of leading-edge computational techniques. [Preview Abstract] |
Monday, April 2, 2012 4:30PM - 4:42PM |
T14.00006: Surface plasmon resonance based infrared photo-detectors Yigit Aytac, Unil Perera At present materials can be engineered to control propagation of light in certain directions at certain wavelengths. Such materials are called photonic crystals which contain a periodic arrangement of metals and dielectric materials on a wavelength scale. Surface Plasmon Resonances (SPR) in metallic and dielectric nano-arrays can be used to enhance the response of photo-detectors. There are variety of potential ways to increase the performance of infrared photo-detectors by using electromagnetic enhancement and dependence of the resonance wavelength on the arrays size, shape and the local dielectric environment integration of these apertures. A detailed analysis of the optical properties of the waveguides in two and three dimensions with periodically perforated array structures is presented. Transmission and reflection spectra, resonant modes and field patterns of photonic crystals were calculated and imaged with using FDTD (Finite-difference Time-domain) method by numerical analysis of the non-linear dispersion relation. Additionally, by varying the orientation of holes on the wave-guide, polarization sensitivity was achieved in the model. [Preview Abstract] |
Monday, April 2, 2012 4:42PM - 4:54PM |
T14.00007: Construction of An Approximate Periodic Solution to a Modified Lewis Equation 'Kale Oyedeji There have been many papers published on the construction of approximate periodic solutions of various types of non-linear differential equations. Many techniques have also been developed for obtaining approximate solutions. Among them are the method of Krylov-Bogoliubov-Mitropolsky, the harmonic balance, and the averaging method. We investigate the periodic solution of a modified Lewis equation \"{x}+$x^{3}$=?($1-|x|$)\'{x}, * where ? is a small and positive parameter, because of its strong cubic nonlinearity. Using an extension of the Mickens-Oyedeji method [1] developed by Cveticanin [2], we calculate the exact angular frequency for the equation \"{x}+$x^{3}$=0, ** and using the result of a first-order averaging method to calculate the approximate periodic solution of Eq. (*). Our result is compared with numerical calculations and there is a good agreement between our result and numerical calculations. [Preview Abstract] |
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