Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session B22: Systems Far from Equilibrium |
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Sponsoring Units: GSNP Chair: Beate Schmittman, Virginia Polytechnic Institute and State University Room: Colorado Convention Center 108 |
Monday, March 5, 2007 11:15AM - 11:27AM |
B22.00001: Aging in disordered magnets and local scale-invariance Michel Pleimling, Malte Henkel The aging of the bond-disordered two-dimensional Ising model quenched to below its critical point is studied through the two-time autocorrelator and thermoremanent magnetization (TRM). The corresponding aging exponents are determined. The form of the scaling function of the TRM is well described by the theory of local scale-invariance.\\[0.5cm] M. Henkel and M. Pleimling, Europhys. Lett. {\bf 76}, 561 (2006). [Preview Abstract] |
Monday, March 5, 2007 11:27AM - 11:39AM |
B22.00002: Minimal Modeling of Driven Dissipative Systems Yair Shokef, Dov Levine By simple modeling of dissipative interactions we resolve fundamental questions related to systems far from thermal equilibrium, such as granular materials, foams and colloidal suspensions. We solve the non-Boltzmann energy distribution, demonstrate the violation of time-dependent fluctuation- dissipation relations, show that different measures of effective temperatures generally differ, and address further issues such as ergodicity breaking and detailed balance violation. [Preview Abstract] |
Monday, March 5, 2007 11:39AM - 11:51AM |
B22.00003: Work Distributions far from Equilibrium in Quantum Spin Chaines Sven Dororsz We are investigating the non equilibrium steady state for different quantum spin chaines by an exact numerical calculation. The systems, initially in a canonical state, are driven out of equilibrium by a periodic external force which couples to each site. Motivated by the Jarzynski relation and the fluctuation theorem for quantum systems we analyze in detail the probability distribution P(W). Both finite and infinite temperatures are discussed. General properties independent of the nature of the interaction are identified and we observe two dynamic regimes in the limit of small and large frequencies. The intermediate regime is caracterized by resonance peaks in the distribution. The moments of the distribution can be exploited to discuss the possible definitions of a Jarzynski-operator for quantum systems. [Preview Abstract] |
Monday, March 5, 2007 11:51AM - 12:03PM |
B22.00004: Conjugate Field and Fluctuation-Dissipation Relation for the Dynamic Phase Transition in the Two-dimensional Kinetic Ising Model D.T. Robb, P.A. Rikvold, A. Berger, M.A. Novotny The two-dimensional kinetic Ising model, when exposed to an oscillating magnetic field with zero time-average, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter $Q$ is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we apply a square-wave field with (for the first time) a non-zero period-averaged magnetic field, $H_b$, and study the scaling of the dynamic order parameter with respect to $H_b$. We find evidence that the field scaling exponent, $\delta_{\mathrm{d}}$, at the critical period of the DPT is equal to the exponent for the critical isotherm, $\delta _{\mathrm{e}}$, in the equilibrium Ising model. A finite-size scaling analysis of the dynamic order parameter in the critical region provides further support for this result. We also demonstrate numerically that a fluctuation-dissipation relation (FDR), with an effective temperature $T_{\mathrm{eff}}\left(T, P, H_0\right)$ depending on the period, and possibly the temperature and field amplitude, holds for the dynamic order parameter and its conjugate field. This FDR justifies our use of the scaled variance of $Q$ as a proxy for the nonequilibrium susceptibility, $\partial \langle Q \rangle / \partial H_b$. [Preview Abstract] |
Monday, March 5, 2007 12:03PM - 12:15PM |
B22.00005: A possible classification of nonequilibrium steady states. Royce K.P. Zia, Beate Schmittmann We propose a general classification of nonequilibrium steady states in terms of their stationary probability distribution and the associated probability currents. The stationary probabilities can be represented graph-theoretically as directed Cayley trees; closing a single loop in such a graph leads to a representation of probability currents. This classification allows us to identify all choices of transition rates, based on a master equation, which generate the same nonequilibrium steady state. We explore the implications of this freedom, e.g., for entropy production, and provide a number of examples. [Preview Abstract] |
Monday, March 5, 2007 12:15PM - 12:27PM |
B22.00006: Noise induced chaos in optically driven colloidal rings. Yael Roichman, George Zaslavsky, David G. Grier Given a constant flux of energy, many driven dissipative systems rapidly organize themselves into configurations that support steady state motion. Examples include swarming of bacterial colonies, convection in shaken sandpiles, and synchronization in flowing traffic. How simple objects interacting in simple ways self-organize generally is not understood, mainly because so few of the available experimental systems afford the necessary access to their microscopic degrees of freedom. This talk introduces a new class of model driven dissipative systems typified by three colloidal spheres circulating around a ring-like optical trap known as an optical vortex. By controlling the interplay between hydrodynamic interactions and fixed disorder we are able to drive a transition from a previously predicted periodic steady state to fully developed chaos. In addition, by tracking both microscopic trajectories and macroscopic collective fluctuations the relation between the onset of microscopic weak chaos and the evolution of space-time self-similarity in macroscopic transport properties is revealed. In a broader scope, several optical vortices can be coupled to create a large dissipative system where each building block has internal degrees of freedom. In such systems the little understood dynamics of processes like frustration and jamming, fluctuation-dissipation relations and the propagation of collective motion can be tracked microscopically. [Preview Abstract] |
Monday, March 5, 2007 12:27PM - 12:39PM |
B22.00007: Fluctuation-dissipation relations in driven dissipative systems Guy Bunin, Yair Shokef, Dov Levine Exact theoretical results for the violation of time dependent fluctuation-dissipation relations in driven dissipative systems are presented. The ratio of correlation to delayed response in the stochastic model introduced in [Phys. Rev. Lett. 93, 240601 (2004)] is shown to depend on measurement time. The fluctuation temperature defined by this ratio differs both from the temperature of the environment performing the driving, and from other effective temperatures of the system, such as the average energy (or ``granular temperature''). General explanations are given for the time independence of fluctuation temperature for simple measurements or long measurement times. [Preview Abstract] |
Monday, March 5, 2007 12:39PM - 12:51PM |
B22.00008: Time Correlations on the Ziff-Gulari-Barshad Model with Random Defects C.S. Dias, A. Cadilhe We studied a generalized version of the Ziff, Gulari, and Barshad model (1986), i.e., of the $A + B_2$ reaction, in order to accomodate the presence of a given fraction of inert sites present on the substrate. Specifically, we show their impact on the kinetics of the catalysis, particularly on the time correlation of the reactants distribution on the surface, to monitorize the evolution, in time, of a list of reactants of both species. We also characterize the reactant cluster structure in the presence of impurities by resorting to the Hoshen-Kopelmann algorithm. We have found two diferent regimes of the time correlation, namely, an initial exponential decay at short times, and a second regime given by a streched exponential decay at late times of the number of surviving particles. [Preview Abstract] |
Monday, March 5, 2007 12:51PM - 1:03PM |
B22.00009: Renormalization Group Treatment of the Trapping Reaction Jack Hanson, Scott McIsaac, Benjamin Vollmayr-Lee We consider the trapping reaction $A+B\to A$, with diffusing traps ($A$) and particles ($B$), where the traps additionally undergo either an annihilation ($A+A\to\emptyset$) or coalescence ($A+A\to A$) reaction. This two-species reaction-diffusion system exhibits asymptotic power law decays in both the trap and particle densities, and simple scaling in the trap-trap ($AA$) and particle-trap ($AB$) correlation functions. However, simulations indicate the induced particle-particle correlations scale as $C_{BB}(x,t) = t^{\phi} f(x/t^{1/2})$ with an anomalous dimension $\phi$ [B.P. V-L and R.C. Rhoades]. We perform a one-loop renormalization group calculation of this exponent for $d<2$ --- which involves 59 diagrams --- and demonstrate that the anomalous dimension is universal and is due to a renormalization of the initial particle density. Our results are compared to the simulation data. [Preview Abstract] |
Monday, March 5, 2007 1:03PM - 1:15PM |
B22.00010: Comparing Extremal and Hysteretic Optimization in Spin Glasses Bruno Goncalves, Stefan Boettcher We compare the capabilities of the $HO$\footnote{PRL 89, 150201} and the $EO$\footnote{PRL 86, 5211} heuristic in finding spin glass ground states. Using a one-parameter model recently discussed by Katzgraber and Young \footnote{PRB 67, 134410} that interpolates between the mean-field, infinte-dimensional SK spin glass and the finite-dimensional EA lattice spin glass, we evaluate the heuristics as a function of that parameter. Our results show interesting variations in algorithmic behavior that elucidates their properties. It may also indicate a transition in the physics between high and low-dimensional spin glasses. [Preview Abstract] |
Monday, March 5, 2007 1:15PM - 1:27PM |
B22.00011: Shock-induced crystalline instabilities Ramon Ravelo, Brad Lee Holian, Timothy C. Germann Uniaxial deformations of single crystals such as those produced under planar shock loading can produce structural instabilities which compete with defect nucleation mechanisms. In fcc single crystals under (110) shock loading, the resulting body-centered orthorhombic crystal structure develops a long-wavelength dynamical instability associated with tetragonal shear distortions, which occurs at lower strains (pressures) than those predicted by the vanishing of the elastic constants at finite pressure (stiffness coefficients). \footnote[2]{J. Wang, S. Yip, S.R. Phillpot, D. Wolf, Phys. Rev. Lett. {\bf 71}, 4182 (1993)} The criterion for these instabilities is derived and verified by equilibrium and non-equilibrium molecular dynamics simulations [Preview Abstract] |
Monday, March 5, 2007 1:27PM - 1:39PM |
B22.00012: Hydrodynamic solutions of spatially-varying 1D exclusion processes Greg Lakatos, Tom Chou We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents are exact as long as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions. [Preview Abstract] |
Monday, March 5, 2007 1:39PM - 1:51PM |
B22.00013: Off-Lattice 3D Eden Cluster Growth Model Eric Kuennen The Eden model for 2D clusters is understood to be in a large universality class of models and phenomena which have 1D surfaces with growth dynamics as predicted by the KPZ equation. However, the growth behavior of 3D Eden clusters, and that of the KPZ equation for 2D surfaces, is less well understood and a matter of some controversy. Determining which growth phenomena belong to the KPZ universality class in 3D is an important unsolved problem in statistical physics. Previous studies of the Eden model in 3D have all used an underlying lattice and grew clusters vertically from a flat substrate. Since Eden clusters grown on a lattice exhibit significant anisotropies, and in many natural phenomena growth occurs radially from a seed, in this paper, I propose a 3D Eden model for off-lattice clusters grown radially from a seed. With large-scale computer simulations, I investigate the kinetic roughening of the surface by estimating the surface-width growth exponent, in order to determine whether 3D Eden growth indeed belongs to the KPZ universality class. Noise-reduction techniques are used, and for validation the model is applied to a flat substrate geometry, which makes it possible to estimate the roughness exponent as well. [Preview Abstract] |
Monday, March 5, 2007 1:51PM - 2:03PM |
B22.00014: Nucleation and growth of islands during submonolayer deposition on Ag/Ag(100) Nuno Araujo, Antonio Cadilhe The growth of multilayer thin films is strongly influenced by the formation of the first layer. We introduce a kinetic Monte Carlo model to study the nucleation and growth of the first layer in the regime of high values of the incoming flux. We simulate the deposition of Ag adatoms on the Ag(100) substrate at a temperature of 200 K for values of the incident flux of particles ranging between 0.01 ML/s and 1.00 ML/s. To characterize the nucleation process we studied the dependence of the mean island density during growth and the island size distribution on the incident flux of particles. Varying the flux of incident adatoms allows us to tune the relevance of the different elemental processes taking place during the deposition stage. In the limit of high fluxes, we show that scaling functions do not match and the island size distribution function does not have a maximum value coincidental with the mean island size. [Preview Abstract] |
Monday, March 5, 2007 2:03PM - 2:15PM |
B22.00015: Surface Growth Modeling of Load Balancing in Parallel Discrete Event Simulations (PDES) Poonam Verma, Mark Novotny We study a non-equilibrium surface growth model of load balancing for conservative Parallel Discrete Event Simulations (PDES) [Korniss et al., Science 299, {\bf 677} (2003); Guclu et al., Phys. Rev. E {\bf 73}, 066115 (2006)]. Load balancing improves the performance of the parallel simulations by distributing the work load over all processors evenly. These models for static load balancing are in the Kardar-Parisi-Zhang (KPZ) universality class, with the KPZ process often mixed with a Random Deposition (RD) process [Kolakowska et al., Phys. Rev. E {\bf 73}, 011603 (2006)]. We study how the utilization and the desynchronization behave when the load changes randomly during the simulation. We compare the static and dynamic load balancing results for the models of PDES. The underlying framework proposed in [L. N. Shchur and M. A. Novotny Phys. Rev. E {\bf 70}, 026703 (2004)], is that the Local Simulated time (LST) is associated with the nodes and not with the processing elements. [Preview Abstract] |
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