Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session U33: Dynamics and Systems Far From Equilibrium |
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Sponsoring Units: GSNP Chair: Harvey Gould, Clark University Room: Baltimore Convention Center 336 |
Thursday, March 16, 2006 8:00AM - 8:12AM |
U33.00001: Critical behavior and Griffiths effects in the disordered contact process Thomas Vojta, Mark Dickison We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte-Carlo simulations for times up to $10^9$ and system sizes up to $10^7$ sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of $10^4$ or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder. [Preview Abstract] |
Thursday, March 16, 2006 8:12AM - 8:24AM |
U33.00002: Monte Carlo Studies of Phase Separation in Compressible 2-dim Ising Models S.J. Mitchell, D.P. Landau Using high resolution Monte Carlo simulations, we study time-dependent domain growth in compressible 2-dim ferromagnetic ($s=1/2$) Ising models with continuous spin positions and spin-exchange moves [1]. Spins interact with slightly modified Lennard-Jones potentials, and we consider a model with no lattice mismatch and one with 4\% mismatch. For comparison, we repeat calculations for the rigid Ising model [2]. For all models, large systems ($512^2$) and long times ($10^ 6$~MCS) are examined over multiple runs, and the growth exponent is measured in the asymptotic scaling regime. For the rigid model and the compressible model with no lattice mismatch, the growth exponent is consistent with the theoretically expected value of $1/3$ [1] for Model B type growth. However, we find that non-zero lattice mismatch has a significant and unexpected effect on the growth behavior.\\ \\ Supported by the NSF.\\ \\ $[1]$ D.P. Landau and K. Binder, {\em A Guide to Monte Carlo Simulations in Statistical Physics}, second ed. (Cambridge University Press, New York, 2005).\\ $[2]$ J. Amar, F. Sullivan, and R.D. Mountain, Phys.\ Rev.\ B 37, 196 (1988). [Preview Abstract] |
Thursday, March 16, 2006 8:24AM - 8:36AM |
U33.00003: Rate of Entropy Extraction in Compressible Turbulence. Mahesh Bandi, Walter Goldburg, John Cressman The rate of change of entropy is measured for a system of particles floating on the surface of a fluid maintained in a turbulent steady state. This rate of entropy ${\dot S}$ equals the time integral of the two point temporal velocity divergence correlation function with a negative prefactor. The measurements satisfactorily agree with the sum of Lyapunov exponents (Kolmogorov-Sinai entropy rate) measured from previous simulations, as expected of dynamical systems that are very chaotic (Sinai-Ruelle-Bowen statistics). [Preview Abstract] |
Thursday, March 16, 2006 8:36AM - 8:48AM |
U33.00004: Non-constant nucleation rate in a system in apparent metastable equilibrium Hui Wang, Harvey Gould, Kipton Barros, Aaron Schweiger, Bill Klein The distribution of nucleation times for the two-dimensional Ising model with nearest-neighbor and with long-range interactions is simulated using the Metropolis algorithm. The distribution is exponential at long times as would be expected if the nucleation rate is a constant, but is suppressed at earlier times even after the mean magnetization is apparently in metastable equilibrium. We explain this discrepancy by investigating the relaxation behavior of the clusters whose size is comparable to the nucleating droplet. [Preview Abstract] |
Thursday, March 16, 2006 8:48AM - 9:00AM |
U33.00005: 4:1 Resonance phenomena in the forced Belousov-Zhabotinsky chemical reaction Bradley Marts, Anna Lin The oscillatory Belousov-Zhabotinsky (BZ) reaction has been successfully used to study generic aspects of resonance in spatially extended systems parametrically forced with pulses of light. Experiments have reproduced Arnol'd tongues and pattern forming behavior predicted by reaction diffusion models and amplitude equations. We use the BZ reaction to experimentally demonstrate a transition in the 4:1 resonance regime from patterns of pi/2 fronts to patterns of pi fronts. The transition matches the theoretical predictions. Above a certain driving strength, traveling pi/2 fronts become unstable and a new stable pattern of stationary pi fronts emerges. [Preview Abstract] |
Thursday, March 16, 2006 9:00AM - 9:12AM |
U33.00006: Mode locking in quasiperiodic structures Creighton Thomas, A. Alan Middleton AC driven extended systems, such as charge density waves or arrays of Josephson junctions, exhibit mode locking or giant Shapiro steps. This mode locking is seen experimentally as plateaus in a generalized velocity or current as a function of drive parameter. In conventional mode locking, the frequency of the response is a rational multiple of the frequency of the AC drive. For a model, we use a sandpile automaton model with local nonlinear update rules. When random quenched disorder is present in the automaton, a Devil's staircase with mode locking at all rational numbers has been previously seen. We investigate the use of quasiperiodic structures in place of the disordered structures. We find the novel phenomena of mode locking where the currents are a quasiperiodic multiple of the drive frequency. These quasiperiodic steps turn out to be stable to thermal fluctuations. Application of this model to Josephson junction arrays and structured colloidal systems will be presented. [Preview Abstract] |
Thursday, March 16, 2006 9:12AM - 9:24AM |
U33.00007: Periodic time dependent problems in nonequilibrium quantum statistical mechanics Selman Hershfield The usual Kadanoff-Baym or Keldysh formulation of nonequilibrium quantum statistical mechanics can be reformulated for steady state problems in terms of a nonequilibrium density matrix of the form $\exp (-(H - Y)/k_B T)$, where $H$ is the hamiltonian and $Y$ contains the information about how the system is driven out of equilibrium.$^*$ This approach has now been used to solve exactly solvable models as well as in approximate techniques. Here we show that for a periodic time dependent hamiltonian there is a similar formulation in terms of a nonequilibrium density matrix, where the density matrix acts in one higher dimension than in the original problem. Thus, a time dependent nonequilibrum problem is mapped onto a time independent nonequilibrium problem in one higher dimension. This is true for interacting as well as noninteracting problems. The approach is illustrated by applying it to some exactly solvable time dependent nonequilibrium problems such as tunneling through a resonant level where the level and/or the voltage applied are time dependent.\\ $*$ S. Hershfield, PRL {\bf 70}, 2134 (1993). [Preview Abstract] |
Thursday, March 16, 2006 9:24AM - 9:36AM |
U33.00008: On Rolling Loaded Dice Gary White When an unfair die is tossed, what are the factors that determine the side upon which it lands? Sir Hermann Bondi (see European Journal of Physics 14, pp. 136-140) asked a related theoretical question in 1993 with the intention of determining the theoretical probability of a coin landing on its edge. He notes that the center of mass, the coefficients of restitution and friction, and the radius of gyration all play a role, perhaps. A simple model assumes that the probability of landing on a particular side is proportional to the solid angle subtended from the center of mass, but this model predicts too few base landings for tall cylinders, and too many rolling landings for squatty cylinders. Here we propose a thermodynamic modification of this model which qualitatively improves the match between experiment and theory by introducing an effective ``temperature'' parameter. We apply the model to several different geometrical shapes where the landing odds are not even, including right circular cylinders, rectangular prisms, hemispheres and semi-cylinders. We obtain, perhaps unreasonably, somewhat promising results. [Preview Abstract] |
Thursday, March 16, 2006 9:36AM - 9:48AM |
U33.00009: Broad spectrum period adding chaos in a transistor circuit. Thomas Carroll Period adding chaos, in which a driven system makes transitions such as period 2-chaos-period 3-chaos-period 4, is well known. In most cases, however, the frequency of the chaotic signal is close to the frequencies of the periodic signals. I have done expriments with a simple circuit in which the chaos has a very broad power spectrum, covering 6 orders of magnitude. I have confirmed this broad band feature in numerical simulations of the circuit. These experiments have technological implications, because they show that a narrow band high frequency signal could produce broad band interference in even simple circuits. [Preview Abstract] |
Thursday, March 16, 2006 9:48AM - 10:00AM |
U33.00010: Solving the Problem of Excessive Time Delay in Attractor Reconstruction Louis Pecora, Jon Nichols, Thomas Carroll, Linda Moniz We recently showed that the seemingly separate problems of finding a proper time delay and then finding a proper embedding dimension for attractor reconstruction are really the same problem which can be solved with a mathematical statistic faithful to the Takens reconstruction theorem. This approach also deals well with disparate time scales in data, and optimally choosing time series to use from a multivariate data set. However, the problem of when a time delay is too long for a chaotic time series remains. We introduce a new statistic that resolves this issue. The statistic is based on the mathematical observation that long time delays will result in data points that do not adequately populate the dynamical system's manifold. We present results with models and data that show we can predict when we have used excessively long time delays in attractor reconstruction. [Preview Abstract] |
Thursday, March 16, 2006 10:00AM - 10:12AM |
U33.00011: Stochastic Loewner evolution driven by L\'evy processes Ilia Rushkin, Panagiotis Oikonomou, Leo Kadanoff, Ilya Gruzberg Standard stochastic Loewner evolution (SLE) is driven by a continuous Brownian motion, which then produces a continuous fractal trace. If jumps are added to the driving function, the trace branches. We consider a generalized SLE driven by a superposition of a Brownian motion and a stable L\'evy process. The situation is defined by the usual SLE parameter, $\kappa$, as well as $\alpha$ which defines the shape of the stable L\'evy distribution. The resulting behavior is characterized by two descriptors: $p$, the probability that the trace self- intersects, and $\tilde{p}$, the probability that it will approach arbitrarily close to doing so. These descriptors are shown to change qualitatively and singularly at critical values of $\kappa$ and $\alpha$. These transitions occur as $\kappa$ passes through four (a well-known result) and as $\alpha$ passes through one (a new result). Numerical simulations are then used to explore the associated touching and near-touching events. [Preview Abstract] |
Thursday, March 16, 2006 10:12AM - 10:24AM |
U33.00012: Positional Order and Diffusion Processes in Particle Systems Hiroshi Watanabe, Yukawa Satoshi, Nobuyasu Ito In particle systems, a relation between the positional order parameter $\Psi$ and the mean square displacement $M$ is derived to be $\Psi \sim \exp(-v{K}^2 M/2d)$ with a reciprocal vector $v{K}$ and the dimension of the system $d$. On the basis of the equiation, the behavior of $\Psi$ is found to be $\Psi \sim \exp(-v{K}^2 D t)$ when the system involves normal diffusion with a diffusion constant $D$. While the behavior in two-dimensional solid is predicted to be $M \sim \ln t$, numerical simulations shows a linear diffusion $M \sim t$. This can be explained by a swapping diffusion process which allows particles to diffuse without destroying the positional order. [Preview Abstract] |
Thursday, March 16, 2006 10:24AM - 10:36AM |
U33.00013: Brownian dynamics of colloids in tilted periodic potential Weiqiang Mu, Gang Wang, Gabriel Spalding, John Ketterson We have studied the Brownian movements of micron-sized colloidal spheres in the presence of a periodic potential and the potential associated with gravity (which together form a so-called tilted-washboard potential). The optical potential is generated by the interference of two argon laser beams that are tightly focused through a common objective lens to form an in-plane standing wave in the vicinity of a substrate surface. As the intensity of standing wave is increased, the escape time of a particle trapped in a given potential well to the next lower one increases super-exponentially. More generally we have measured the time dependence of the probability density distribution of a colloidal particle as a function of the amplitude of the standing wave. The experimental data have been compared with a simulation based on the numerical integration of the Smoluchowski equation in the presence of the optical and gravitational potentials. [Preview Abstract] |
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