Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session L9: Focus Session: Systems Far from Equilibrium II |
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Sponsoring Units: GSNP DBP Chair: Michel Pleimling, Virginia Polytechnic Institute and State University Room: 303 |
Tuesday, March 17, 2009 2:30PM - 3:06PM |
L9.00001: A Reacting Particles System arising from the Conserved Kuramoto-Sivashinsky Equation Invited Speaker: We study an interacting particles system arising from a mapping to the Conserved Kuramoto-Sivashinsky equation. Particles represent vanishing regions of diverging curvature, joined by arcs of a universal parabola; nearest particles are attracted to one another at a rate inversely proportional to their distance, and coalesce upon encounter. Although the model is deterministic, a coarse-grained representation yields a diffusion equation with negative coefficient: the build up of instabilities corresponds to the coalescence events. A preliminary analysis of the model correctly predicts the growth of the typical inter- particle gap with time, but fails to reproduce interesting structure of the probability distribution function for the gap observed in simulations, including a non-trivial power-law at small distances, and a faster than gaussian decay at large distances. At yet an higher level of abstraction, trails of coalescing events may too be viewed as ``particles'' that propagate ballistically at a speed proportional to the background density, and that annihilate upon encounter. [Preview Abstract] |
Tuesday, March 17, 2009 3:06PM - 3:18PM |
L9.00002: Noisy Transport in Reaction-Diffusion Systems with Quenched Disorder Andrew Missel, Karin Dahmen Reaction-diffusion (RD) models are useful tools for studying a wide variety of natural phenomena. The effects of quenched disorder in the reaction rates on RD models is not completely understood, especially in parameter regimes where internal noise or stochasticity is also important. In this talk, I will discuss an RD model in which both quenched disorder and stochasticity are important. I will show how ideas from the theory of hopping conduction in doped semiconductors and first passage percolation can be used to make predictions for a number of important transport-related features in the model: the infection time, or time needed for the population to traverse the system; the velocity of the front moving through the system; and the dynamic roughening of the coarse-grained front. I will also present the results of simulations of the model that largely confirm these analytical predictions. [Preview Abstract] |
Tuesday, March 17, 2009 3:18PM - 3:30PM |
L9.00003: Monte Carlo simulation and linear stability analysis of Turing pattern formation in noisy reaction-subdiffusion systems Keng-Hwee Chiam, Jiawei Chiu Subdiffusion is an important physical phenomenon observed in many systems. However, numerical techniques to study it, especially when coupled to noisy reactions, are lacking. In this talk, we develop an efficient Monte Carlo algorithm based on the Gillespie algorithm and the continuous-time random walk to simulate noisy reaction-subdiffusion systems. Using this algorithm, we investigate Turing pattern formation in the Schnakenberg model with subdiffusion. First, we show that, as the system becomes more subdiffusive, the homogeneous state becomes more difficult to destablize and Turing patterns form less easily. Second, we show that, as the number of particles in the system decreases, the magnitude of noise increases and again the Turing patterns form less easily. Third, we show that, as the system becomes more subdiffusive, the ratio between the two diffusive constants must be higher in order to observe Turing patterns. Finally, we also carry out linear stability analysis to validate the results obtained from our algorithm. [Preview Abstract] |
Tuesday, March 17, 2009 3:30PM - 3:42PM |
L9.00004: Continuous Time Random Walks with Internal Dynamics Stephan Eule, Rudolf Friedrich, Frank Jenko We formulate a generalized master equation for a class of Continuous Time Random Walks (CTRWs) in the presence of a presribed deterministic evolution between the successive transitions. This formulation is exemplified by means of a generalized advection-diffusion and a jump-diffusion scheme. Based on the generalized master equation the corresponding fractional evolution equations are presented. [Preview Abstract] |
Tuesday, March 17, 2009 3:42PM - 3:54PM |
L9.00005: Unusual finite-size crossover features in driven lattice gases George L. Daquila, Uwe C. Tauber We study the temporal scaling behavior of the autocorrelation function for the asymmetric exclusion process (ASEP) on a ring in one dimension as function of system size and hopping bias. We have performed extensive Monte Carlo simulations using standard and continuous time algorithms to extract the long-time asymptotic scaling behavior for some very large systems. Even for the totally asymmetric exclusion process (TASEP), the effective exponent for the temporal autocorrelation function displays an extremely slow crossover towards the asymptotic value 2/3, with unusual features. For the ASEP, the crossover time grows with increasing backwards hopping rates. In contrast, we observe standard crossover behavior and much shorter crossover times in two- and three-dimensional lattice gases. [Preview Abstract] |
Tuesday, March 17, 2009 3:54PM - 4:06PM |
L9.00006: Contact process with mobile disorder Ronald Dickman I study scaling properties of the absorbing-state phase transition in the one-dimensional contact process with mobile disorder via numerical simulation and the pair approximation. In this model, the dilution sites are permanently inactive but are free to diffuse, exchanging positions with the other sites, which host a basic contact process. Even though the disorder variables are not quenched, the critical behavior is drastically affected: the critical exponent $\delta$ and the ratio $\beta/nu_\perp$ are found to vary continuously with vacancy concentration and hopping rate. At the critical point, the mean lifetime $\tau$ scales with system size $L$ as $\tau \sim (\ln L)^\zeta $, rather than as a power law; the anomalous scaling of the lifetime is associated with fluctuations in the vacancy density. [Preview Abstract] |
Tuesday, March 17, 2009 4:06PM - 4:18PM |
L9.00007: Fluctuation ratios in reaction-diffusion systems Sven Dorosz, Michel Pleimling We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic time reversibility. Studying a quantity that for an equilibrium system is related to the work done to the system, we observe that under certain conditions oscillations appear on top of an exponential behavior of transient fluctuation ratios. We argue that these oscillations encode properties of the probability currents in state space. [Preview Abstract] |
Tuesday, March 17, 2009 4:18PM - 4:30PM |
L9.00008: Work-fluctuation relations for a Brownian particle in an electromagnetic field J.I. Jim\'enez-Aquino, R.M. Velasco, F.J. Uribe In statistical physics of nano-sized systems out of equilibrium, a variety of theoretical approaches and experimental demonstrations to prove some work-fluctuation have been reported recently in the literature[1,5]. In this work , we discuss how some of those theoretical approaches can be extended to give a proof of some work-fluctuation relations for an electrically charged harmonic oscillator in the presence of an uniform electromagnetic field. The perspectives of our proposal will also be discussed. [1] R. van Zon and E. G. D. Cohen, Phys. Rev. E {\bf 67}, 046102 (2003). [2] C. Bustamante, J. Liphardt, F. Ritort, Phys. Today {\bf 58} (7), 43 (2005). [3] D. J. Evans, D. J. Searles, Adv. Phys. {\bf 51}, 1529 (2002). [4] G. M. Wang {\it et al}., Phys. Rev. Lett. {\bf 89}, 050601 (2002). [5] A. M. Jayannavar, M. Sahoo, Phys, Rev. E {\bf 75}, 032102 (2007). [Preview Abstract] |
Tuesday, March 17, 2009 4:30PM - 4:42PM |
L9.00009: Stochastic current switching behavior in semiconductor superlattices Stephen Teitsworth, Huidong Xu Numerical simulation results are presented for a discrete drift-diffusion model that describes electronic transport in weakly-coupled semiconductor superlattices under voltage bias and also includes shot noise in the tunneling currents. Sequential resonant tunneling between quantum wells is the primary conduction mechanism and noise terms are treated as delta-correlated in space and time. We study the response of this system to abrupt steps in applied voltage in a range for which the current-voltage characteristics exhibit bistability. The system switches from a metastable state to a stable state with a stochastically varying delay time, a process corresponding to relocation of charge density from one (critical) quantum well to an adjacent one. We find that the mean delay time $\tau$ varies as $\ln \tau \propto V - V_{th}^{3/2}$ where $V$ and $V_{th}$ denote, respectively, the system voltage and the voltage at the boundary of the bistability range [1]; $\tau$ also depends exponentially on the cross-sectional area of the superlattice. An effective one-dimensional potential energy is constructed for the charge density in the critical quantum well. We find that noise contributions of the quantum wells far from the critical well have a significant effect on the switching process. [1] O. A. Tretiakov and K. A. Matveev, Phys. Rev. B. \textbf{71}, 165326 (2005). [Preview Abstract] |
Tuesday, March 17, 2009 4:42PM - 4:54PM |
L9.00010: Fluctuation relations in a driven, nonlinear micromechanical torsional oscillator Corey Stambaugh, H.B. Chan Fluctuation relations in a periodically driven micromechanical oscillator are investigated. The system is first studied in a linear regime by applying a weak drive. The ratio of the work variance to the mean work is shown to be independent of the driving frequency, consistent with standard fluctuation relations for a steady state system near thermal equilibrium. When a strong drive is applied to the system the response becomes nonlinear and the system displays bistability. The work variance in this nonlinear system, driven far from equilibrium, is predicted to show a strong frequency dependence not seen in the linear case. For such bistable system the total variance has two contributing components. The first component, involving intrastate fluctuations about one stable attractor, is expected to scale with a power law dependence as the system approaches the bifurcation point where the occupied state disappears. The second component of the work variance for interstate fluctuations is shown to have a strong frequency dependence near the kinetic phase transition where the populations of the two states are comparable. The relationship between the work and variance is compared to previous results, the work variance in the linear regime, and to theory. [Preview Abstract] |
Tuesday, March 17, 2009 4:54PM - 5:06PM |
L9.00011: ABSTRACT WITHDRAWN |
Tuesday, March 17, 2009 5:06PM - 5:18PM |
L9.00012: Work distributions in the T=0 Random Field Ising Model Xavier Illa, Josep Maria Huguet, Eduard Vives The T=0 Random Field Ising Model is a prototype model for the study of collective phenomena in disordered systems. The model can be numerically studied from two different points of view: on the one hand, the exact ground state calculation provides an approach to the equilibrium phase diagram. On the other the use of a local relaxation dynamics based on single spin-flips provides a good framework for the understanding of avalanche dynamics and hysteresis, which is closer to experimental observations. In this sense, the model is a good workbench for the comparison of equilibrium and out-of-equilibrium trajectories. We perform a numerical study of the three-dimensional Random Iield Ising Model at T=0. We compare work distributions along metastable trajectories obtained with the single-spin flip dynamics with the distribution of the internal energy change along equilibrium trajectories. The goal is to investigate the possibility of extending the Crooks fluctuation theorem to zero temperature when, instead of the standard ensemble statistics, one considers the ensemble generated by the quenched disorder. We show that a simple extension of Crooks fails close to the disordered induced equilibrium phase transition due to the fact that work and internal energy distributions are very asymmetric. [Preview Abstract] |
Tuesday, March 17, 2009 5:18PM - 5:30PM |
L9.00013: Far-From-Equilibrium Measurements of Thermodynamic Length Edward Feng, Gavin Crooks Thermodynamic length is a path function that generalizes the notion of length to the surface of thermodynamic states. Here, we show how to measure thermodynamic length in far-from-equilibrium single molecule experiments using the work fluctuation relations. For these microscopic systems, it proves necessary to define the thermodynamic length in terms of the Fisher information. Consequently, the thermodynamic length can be directly related to the magnitude of fluctuations about equilibrium. The work fluctuation relations link the work and the free energy change during an external perturbation on a system. Using these results, we determine how to re-weight the probability of a trajectory to determine the equilibrium averages at an intermediate point of the protocol in which the system is out-of-equilibrium. This allows us to measure the thermodynamic length in single molecule experiments. [Preview Abstract] |
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