Bulletin of the American Physical Society
82nd Annual Meeting of the APS Southeastern Section
Volume 60, Number 18
Wednesday–Saturday, November 18–21, 2015; Mobile, Alabama
Session G2: Statistical and Non-Linear Physics |
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Chair: Ed Green, University of North Georgia Room: Riverview Plaza Hotel Mobile Bay Ballroom I |
Friday, November 20, 2015 11:00AM - 11:12AM |
G2.00001: \textbf{Diffusion kinetics of small islands of Ni on Cu (111) and Cu on Ni (111) using the self-learning kinetic Monte Carlo (II) simulations and rationale for variation based on first-principles calculation} Shree Ram Acharya, Talat S. Rahman We elucidate the diffusion kinetics of two dimensional small islands (upto 8 atoms) of Ni on Cu(111) and Cu on Ni(111) using Self-Learning Kinetic Monte Carlo (SLKMC-II)[1] method which allows occupancy of both fcc and hcp sites on the fcc (111) surface for the identification of local neighborhood of a diffusing atom. In this method, the activation energy barriers for various possible single-atoms, multi-atoms and concerted processes are calculated using semi-empirical embedded-atom method potential on the fly and stores them in a database. The rationale for the variation of activation energy barriers on those systems is presented based on first principle calculations. We present the rate limiting processes for diffusion of islands of various sizes and their energetics: concerted processes on Ni/Cu(111) and various competing single atom or multi-atom and concerted processes on Cu/Ni(111). We also report temperature dependence of the diffusion constants and frequency of occurrence of single-atom, multi-atom and concerted processes for these islands. The size dependence of effective energy barriers derived from the Arrhenius plots is also discussed. [1].S.I.Shah, et al., J.Phys. Condens. Matter 24(2012)354004 [Preview Abstract] |
Friday, November 20, 2015 11:12AM - 11:24AM |
G2.00002: Response of many species systems to perturbation Shadi Esmaeili, Michel Pleimling We study the responses of predator-prey systems to a transient perturbation. We focus our attention on many species systems evolving on a two-dimensional lattice. Of interest are the two transitions: 1) into a new steady state while the perturbation is in effect, and 2) back to the original steady state after the perturbation has been removed. Using Monte Carlo simulations we monitor these transitions via the space-time correlation function and the derived correlation length. The perturbation we consider in this study is realized as a change in the interaction scheme. This perturbation mimics changes in the species' predation preferences as a result of changes in environmental conditions. [Preview Abstract] |
Friday, November 20, 2015 11:24AM - 11:36AM |
G2.00003: Non-equilibrium relaxation in a two-dimensional stochastic lattice Sheng Chen, Uwe C. Täuber We study a stochastic Lotka- Volterra model on a two-dimensional square lattice with periodic boundary conditions. This spatially extended stochastic model for predator-prey competition and coexistence displays complex, correlated spatio-temporal structures and is governed by large fluctuations. The system tends to quickly relax into a quasi-stationary state. If the local prey carrying capacity is finite, there emerges an extinction threshold for the predator population at a critical value of the predation rate. We investigate the non-equilibrium relaxation in the vicinity of this critical point. We obtain a power law dependence between the relaxation time and predation rate (critical slowing down), and numerically determine the associated critical exponents. Following a sudden predation rate change to its critical value, one observes critical aging with a universal scaling exponent. [Preview Abstract] |
Friday, November 20, 2015 11:36AM - 11:48AM |
G2.00004: Quantum Feynman Ratchet Ketan Goyal, Ryoichi Kawai As nanotechnology advances, understanding of the thermodynamic properties of small systems becomes increasingly important. Such systems are found throughout physics, biology, and chemistry manifesting striking properties that are a direct result of their small dimensions where fluctuations become predominant. The standard theory of thermodynamics for macroscopic systems is powerless for such ever fluctuating systems. Furthermore, as small systems are inherently quantum mechanical, influence of quantum effects such as discreteness and quantum entanglement on their thermodynamic properties is of great interest. In particular, the quantum fluctuations due to quantum uncertainty principles may play a significant role. In this talk, we investigate thermodynamic properties of an autonomous quantum heat engine, resembling a quantum version of the Feynman Ratchet, in non-equilibrium condition based on the theory of open quantum systems. The heat engine consists of multiple subsystems individually contacted to different thermal environments. [Preview Abstract] |
Friday, November 20, 2015 11:48AM - 12:00PM |
G2.00005: Mathematical Analysis of a Singular, Nonlinear, Periodically Driven Oscillator Ronald Mickens We investigate the possible solutions of the second-order differential equation \begin{equation} m\overset{\cdot \cdot }{x}+\overset{\cdot }{x}+x^{3}=\sin t, \tag{*} \end{equation}% for the limiting case where $m=0$. Applying the method of harmonic balance [1], we determine both first- and second-order approximations to the periodic solution. We also show, using the qualitative theory of differential equations [2], that this periodic solution is an attractor, i.e., regardless of the initial condition, $x_{0}=x(0),$ the solution eventually becomes arbitrarily close to this periodic solution. This work extends the results of Elias [3]. \bigskip [1] \ Ronald E. Mickens., \textit{Oscillations in Planar Dynamic Systems} (World Scientific, Singapore, 1996); see Chapter 4. [2] \ See ref. [1], Appendix I. [3] \ U. Elias, \textit{Qualitative analysis of a differential equation of Abel}, MAA Monthly (February 2008), pps. 147-149. [Preview Abstract] |
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