Bulletin of the American Physical Society
79th Annual Meeting of the APS Southeastern Section
Volume 57, Number 16
Wednesday–Saturday, November 14–17, 2012; Tallahassee, Florida
Session GB: Statistical and Nonlinear Physics |
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Chair: Mark Jack, Florida A&M University Room: DoubleTree Salon AB |
Friday, November 16, 2012 8:30AM - 8:42AM |
GB.00001: Surface critical behavior at a nonequilibrium phase transition Hyunhang Park, Michel Pleimling We study the local critical phenomena at a dynamic phase transition by means of numerical simulations of the kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer $Q(z)$ and the layer susceptibility $\chi_{Q}(z)$, and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the nonequilibrium system is not identical to that of the equilibrium system in three dimensions. [Preview Abstract] |
Friday, November 16, 2012 8:42AM - 8:54AM |
GB.00002: Non-equilibrium steady states in a two-temperature Ising ring with Kawasaki dynamics Nick Borchers, Michel Pleimling, R.K.P. Zia From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we explore a simple modification of the venerable Ising model in hopes of shedding some light on these issues. While it was shown by Ising that there is no phase transition in the one-dimensional Ising model, a system attached to two heat reservoirs exhibits many of the hallmarks of phase transition. When the system settles into a non-equilibrium steady-state it exhibits numerous interesting phenomena, including an unexpected ``freezing by heating.'' These phenomena will be explored and possible approaches to understanding the behavior will be suggested. [Preview Abstract] |
Friday, November 16, 2012 8:54AM - 9:06AM |
GB.00003: Shape Comparison Between Non-equilibrium Droplets and Equilibrium Crystal Shapes for the 2D Ising Model Howard L. Richards, Austin Shields, Austin Germiller, Jesse Raffield We use the Boost Graph Library to identify droplets in the single-droplet region of metastable decay for the 2D Ising model (using a single-spin flip algorithm), and likewise for equilibrium crystals (using Kawasaki dynamics). As a quantitative way of comparing shapes, we measure the number of broken bonds for the droplets/crystals and also (using the \texttt{igraph} library) the graph-theoretic diameter. Both measurements show that the droplets and crystals have the same shapes on average. This is consistent with earlier research, which used the nucleation rate of droplets to compare their surface free energy with the free energy of equilibrium crystals. The advantage of the present method is that it can be extended to nucleation and growth on irregular lattices. [Preview Abstract] |
Friday, November 16, 2012 9:06AM - 9:18AM |
GB.00004: Random Network Models of Power Grids Per Arne Rikvold, Ibrahim Abou Hamad, Svetlana V. Poroseva Power grids are complex engineering systems of vital importance to modern societies, and it is important to understand how to improve their resilience to various kinds of damage. However, it is often difficult to obtain detailed data on the structures, generating capacities, and power demands for real power systems. In order to be able to test network-analysis algorithms under a variety of conditions, it is therefore useful to develop artificial models that can be tuned to reflect properties of real grids, and that also can be scaled to study effects of the grid size and shape. Here we present a methodology to use Monte Carlo simulations to generate random grids that agree with the degree distribution for the vertices (power plants and consumers) and the length distribution for the transmission lines in the Florida high-voltage power grid. These model grids are used to test the performance of algorithms to partition the grid into semi-independent islands. We find that it is more difficult to partition the model grids than the real Florida grid, suggesting that the real grid contains correlations that are absent in our current generation of models. [Preview Abstract] |
Friday, November 16, 2012 9:18AM - 9:30AM |
GB.00005: Relaxation dynamics of magnetic flux lines subject to correlated disorder Ulrich Dobramysl, Hiba Assi, Michel Pleimling, Uwe C. T\"{a}uber Technological applications of type-II superconductors in magnetic fields require a careful investigation and characterization of the stationary and transient properties of vortex matter. Naturally occurring disorder and artificially introduced crystal defects acting as pinning sites, together with repulsive vortex-vortex interactions lead to rich and complex physics. We study the out-of-equilibrium relaxation of a system of vortex lines, subject to columnar pinning sites, and characterize the transient behavior via two-time quantities. To this end, we model these vortex lines as interacting elastic lines and employ a Langevin molecular dynamics algorithm to simulate the dynamics of the discretized system. In particular, we compare the flux line relaxation in the presence of correlated, columnar pinning sites to previously obtained data on randomly-placed pinning sites. By varying the flux line length, we investigate the differences in the relaxation between point-like vortices and extended vortex lines. [Preview Abstract] |
Friday, November 16, 2012 9:30AM - 9:42AM |
GB.00006: Exact Results on Potts Model in a Generalized External Field Yan Xu, Robert Ellsworth Shrock The $q$-state Potts model is a spin model that has been of longstanding interest as a many-body system in statistical physics. A natural generalization is to consider this model in a generalized external field that favors or disfavors spin values in a subset $I_s=\{1,...,s\}$ of the total set of $q$-state spin values. We obtain a powerful exact formula (Shrock formula) for the partition function of this generalized Potts model on various families of graphs $G$, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. An important property of this formula is that it expresses $Z(G,q,s,v,w)$ in a graph-theoretic manner as a sum of contributions from spanning subgraphs $G'$ of the graph $G$, rather than as a sum over spin configurations. Using this general formula, we derive a number of exact properties of $Z(G,q,s,v,w)$. We also analyze an interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)\equiv Z(G,q,s,-1,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. [Preview Abstract] |
Friday, November 16, 2012 9:42AM - 9:54AM |
GB.00007: Improved method of calculation of mode lifetime in low dimension Yang Gao, Murray Daw While vibrational mode lifetimes is an important property of materials, the method of calculation is surprisingly undeveloped. Recently, Dickel and Daw [1,2] proposed a theory to do the calculation efficiently. It is developed based on the Liouvillan and the recursion method. The mode lifetime can be represented in terms of moments of the power spectrum of Liouvillan. To verify the theory numerically, we applied this method and molecular dynamics to three different models of low dimension. Calculations are done by molecular dynamics(MD) and Monte Carlo(MC), and the result shows that the relation between mode lifetime $\tau$ and moments can be found, \[ \tau = F( \mu_2, \mu_4, \mu_6, ... ) \] and also lifetime can be approximated nicely with some low order moments: \[ \tau = \tau_2 \tilde F(\gamma_4, \gamma_6, ... ), \tau_2 = \sqrt{\frac{1}{\mu_2}} , \gamma_n = \frac{\mu_n}{\mu_2^{\frac{n}{2}}} \] \\[4pt] [1] D.~Dickel \& M.~S. Daw. Improved calculation of mode lifetimes, part i: Theory. {\em Comp. Mat. Sci.}, 47:698, 2009.\\[0pt] [2] D.~Dickel \& M.~S. Daw. Improved calculation of mode lifetimes, part ii: Numerical Result {\em Comp. Mat. Sci.}, 2010. [Preview Abstract] |
Friday, November 16, 2012 9:54AM - 10:06AM |
GB.00008: Neutral species domination on different lattices for the symmetric stochastic cyclic competition of four species Ben Intoy, Sven Dorosz, Michel Pleimling Although the mean-field solution for four species in cyclic competition is generally in good agreement with stochastic results, it fails to describe the extinction and absorbing states that finite size systems inevitably fall into. We study the effects of dimension, lattice type, and swapping rate between particles on the time it takes for the system to go into a static absorbing state, which consists of a neutral species pair. The lattice types discussed include the well mixed environment, one-dimensional line with periodic and closed boundary conditions, the Sierpinski triangle, and the two-dimensional square with periodic and closed boundary conditions. All simulations are run with less than a thousand sites, as in the symmetric case extinction time dramatically increases with lattice size. We find that for some of the studied lattices there are long and short lived configurations. [Preview Abstract] |
Friday, November 16, 2012 10:06AM - 10:18AM |
GB.00009: Preliminary Analysis of the Inverse-x Oscillator 'Kale Oyedeji, Ronald E. Mickens The inverse-x oscillator has the following equation \begin{equation} \ddot{x}+\frac{1}{x}=0. \end{equation} While the motion is singular at $x=0$, nevertheless, all of the solutions are bounded in $x$ and periodic in time. In addition to proving these behaviors, we calculate the exact period and present a (preliminary) analysis of the periodic solutions with respect to the construction of analytic approximations. The procedures used involve phase-space methods and harmonic balance. [Preview Abstract] |
Friday, November 16, 2012 10:18AM - 10:30AM |
GB.00010: Dynamics of Oscillatory Systems Having A Fractional Power Damping Force Ronald E. Mickens In standard mathematical models of dynamic systems the effects of dissipation/damping is represented by a linear term proportional to the velocity, i.e., if $x$ is a relevant coordinate, then this force is $F=-\lambda \dot{x},$ where $\lambda $ is a positive parameter, and the over-dot denotes differentiation in time. For a conservative system, the application of such a force produces motions for which $x$ goes to zero in an infinite time. We demonstrate that the use of a nonlinear dissipation/damping force proportional to $\dot{x}$ raised to a fractional power, i.e., \begin{equation} F=-\lambda \left[ sgn(\dot{x})\right] |\dot{x}|^{a}, \ \ 0 < a < 1, \end{equation} gives rise to dynamics for which the motion ceases in a finite time. Using the example of the Duffing equation and the method of first-order averaging, we illustrate this phenomenon. We also discuss the application of these results to the analysis of vibrations in nano-tubes and graphene sheets. [Preview Abstract] |
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