Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session V24: Focus Session: Non-equilibrium Dynamics of Adsorption Diffusion and Reaction |
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Sponsoring Units: GSNP Chair: Bob Ziff, University of Michigan Room: LACC 411 |
Thursday, March 24, 2005 11:15AM - 11:27AM |
V24.00001: Exact Joint Density-Current Probability Function for the Asymmetric Exclusion Process Martin Depken, Robin Stinchcombe We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems with nonequilibrium phase transitions. We derive the exact form of the joint probability function for the bulk density and current, both for finite systems, and in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques, and by introducing a modified version of the original operator algebra. As in equilibrium systems, the probability-normalization constant for the steady-state probabilities is shown to completely characterize the fluctuations, albeit in a manner very different from that of a standard equilibrium partition function. [Preview Abstract] |
Thursday, March 24, 2005 11:27AM - 11:39AM |
V24.00002: Universal scaling function in discrete time asymmetric exclusion processes Nicholas Chia, Ralf Bundschuh In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz' original publication this universality has been verified for a variety of continuous time systems in the KPZ universality class. We study the Derrida-Lebowitz scaling function for multi-particle versions of the discrete time Asymmetric Exclusion Process. We find that in this discrete time system the Derrida-Lebowitz scaling function not only properly characterizes the large system size limit, but even accurately describes surprisingly small systems. These results have immediate applications in searching biological sequence databases. [Preview Abstract] |
Thursday, March 24, 2005 11:39AM - 11:51AM |
V24.00003: The Trapping Reaction with Mobile and Reacting Traps Benjamin Vollmayr-Lee, Robert Rhoades We study the trapping reaction $A+B\to B$ in the case where both species of particle are mobile, and the traps themselves are annihilating $B+B\to 0$ or coagulating $B+B\to B$. We allow for a mixed trap reaction, with probability $p$ of annihilation and $1-p$ of coagulation, for the general case of unequal diffusion constants and variable trapping rate. We develop a computational technique that enables determination of the full probability distribution of the $A$ particles for a particular realization of the $B$ particles, which provides highly accurate measures for the $A$ particle density and correlations. The $A$ particle density is found to exhibit power law decay in all cases with a nontrivial decay exponent, and the $A$ particle correlations exhibit scaling with an anomolous dimension. Our results are compared with various exact solutions, Schmoluchowski theory, and renormalization group predictions in applicable limits. [Preview Abstract] |
Thursday, March 24, 2005 11:51AM - 12:27PM |
V24.00004: On the Relation Between Diffusion-Limited Coalescence and Annihilation Invited Speaker: The close similarity between the hierarchies of multiple-point correlation functions for the diffusion-limited coalescence and annihilation processes has caused some recent confusion, raising doubts as to whether such hierarchies uniquely determine an infinite particle system. We elucidate the precise relations between the two processes, arriving at the conclusion that the hierarchy of correlation functions does provide a complete representation of a particle system on the line. We also introduce a new hierarchy of probability density functions, for finding particles at specified locations and none in between. This hierarchy is computable for coalescence, through the method of empty intervals, and is naturally suited for questions concerning the ordering of particles on the line. [Preview Abstract] |
Thursday, March 24, 2005 12:27PM - 12:39PM |
V24.00005: Driven classical diffusion with strong correlated disorder Jing-Xian Lin, Leonid Pryadko We analyze one-dimensional motion of an overdamped classical particle in the presence of external disorder potential and an arbitrary driving force $F$. In thermodynamical limit the effective force-dependent mobility $\mu(F)$ is self-averaging, although the required system size may be exponentially large for strong disorder. The transport in the system is linear (mobility is finite) in the limits of very small and very large $F$. For a strong disorder potential with power-law correlations at large distances, $\langle V(x)V(y)\rangle \sim |x-y|^{-n}$, $n>0$, we identify a wide intermediate regime with a power-law dependence of the logarithm of $\mu(F)$ on the driving force. [Preview Abstract] |
Thursday, March 24, 2005 12:39PM - 12:51PM |
V24.00006: Self-organized Criticality and Absorbing States: Lessons from the Ising model Gunnar Pruessner, Ole Peters I will report on an analysis of a suggested path to self-organized criticality. Originally, this path was devised to ``generate criticality'' in systems displaying an absorbing-state phase transition, but closer examination of the mechanism reveals that it can be used for any continuous phase transition. The Ising model as well as the Manna model are used to demonstrate how the finite-size scaling exponents depend on the tuning of driving and dissipation rates with system size. The findings limit the explanatory power of the mechanism to non-universal critical behavior. [Preview Abstract] |
Thursday, March 24, 2005 12:51PM - 1:03PM |
V24.00007: Noise in Disordered Systems: Higher Order Spectra in Avalanche Models Amit Mehta, Karin Dahmen, Michael Weissman, Timothy Wotherspoon We present a novel analytic calculation of the Haar power spectra, and various higher order spectra, of mean field avalanche models. We also compute these spectra from a simulation of the zero-temperature mean field random field Ising Model and infinite range random field Ising model in three dimensions. We extract universal scaling exponents and compare mean field results and simulation results and experimental results for Barkhausen noise in magnets. Applications to other systems with avalanche noise are also discussed. [Preview Abstract] |
Thursday, March 24, 2005 1:03PM - 1:39PM |
V24.00008: Stochastic Sandpiles: Scaling and Universality Invited Speaker: Sandpiles, a class of statistical models of particles diffusing on a lattice, whose dynamics involves a threshold for activity, have attracted great interest in statistical physics. In the simplest case, the model is equivalent to a collection of random walkers with the restriction that an isolated walker is imobile: at least two walkers must occupy the same site to be active. In general, sandpile models exhibit a phase transition between an active stationary state and an absorbing (frozen) one, for which the relevant parameter (analogous to temperature) is the density of walkers, which is conserved by the dynamics. This feature makes it possible to introduce a control mechanism (slow loss of particles, and particle insertion in the absence of activity) that maintains the system at the critical point, in the apparent absence of adjustable parameters yielding self-organized criticality (SOC). In this talk I will describe recent analytical and numerical results on stationary and time-dependent properties, avalanche distributions, the nature of the critical point, and generic slow relaxation in stochastic sandpiles. [Preview Abstract] |
Thursday, March 24, 2005 1:39PM - 1:51PM |
V24.00009: Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder Zhenhua Wu, Eduardo L\'{o}pez, Sergey Buldyrev, Lidia Braunstein, Shlomo Havlin, Eugene Stanley We study the current flow paths between two edges in a random resistor network on a $L\times L$ square lattice. Each resistor has resistance $e^{ax}$, where $x$ is a uniformly-distributed random variable and $a$ controls the broadness of the distribution. We find (a) the scaled variable $u\equiv L/a^\nu$, where $\nu$ is the percolation connectedness exponent, fully determines the distribution of the current path length $\ell$ for all values of $u$. For $u\gg 1$, the behavior corresponds to the weak disorder limit and $\ell$ scales as $\ell\sim L$, while for $u\ll 1$, the behavior corresponds to the strong disorder limit with $\ell\sim L^{d_{\mbox{\scriptsize opt}}}$, where $d_{\mbox{\scriptsize opt}} = 1.22\pm0.01$ is the optimal path exponent. (b) In the weak disorder regime, there is a length scale $\xi\sim a^\nu$, below which strong disorder and critical percolation characterize the current path. [Preview Abstract] |
Thursday, March 24, 2005 1:51PM - 2:03PM |
V24.00010: Rare region effects at a non-equilibrium phase transition Mark Dickison, Thomas Vojta We study the nonequilibrium phase transition in a contact process with extended quenched defects by means of Monte-Carlo simulations. We find that the spatial disorder correlations dramatically increase the effects of the impurities. As a result, the sharp phase transition is completely destroyed by smearing. This is caused by effects similar to but stronger than the usual Griffiths phenomena, viz., rare strongly coupled spatial regions can undergo the phase transition independently from the bulk system. We determine both the stationary density in the vicinity of the smeared transition and its time evolution, and we compare the simulation results to a recent theory based on extremal statistics. [Preview Abstract] |
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V24.00011: Super-scaling of Percolation on Rectangular Domains Hiroshi Watanabe, Yukawa Satoshi, Nobuyasu Ito, Chin-Kun Hu For percolation on a $(RL) \times L$ two-dimensional rectangular domains with width $L$ and aspect ratio $R$, we propose that the existence probability of percolating cluster $E_p(L, \epsilon, R) $ as a function of $L$, $R$, and deviation from the critical point $\epsilon$ can be expressed as $F(\epsilon L^{y_t}R^a)$, where $y_t\equiv 1/\nu$ is the thermal scaling power, $a$ is a new exponent, and $F$ is a scaling function. We use Monte Carlo simulation of bond percolation on square lattices to test our proposal and find that it is well satisfied with $a=0.14(1)$ for $R > 2$. We also propose super-scaling for other critical quantities. [Preview Abstract] |
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V24.00012: First Passage Properties of the Erd\"os-Renyi Random Graph Vishal Sood, Sidney Redner, Dani ben-Avraham We study the first-passage properties of the Erd\"os-Renyi random graph. Using an effective medium approximation we find that the mean-first-passage time between pairs of nodes is insensitive to the fraction $p$ of occupied links. This prediction is tested by numerical simulation. However, the inverse first moment exhibits non-monotonic behavior with $p$ near the percolation transition that can be understood on physical grounds. [Preview Abstract] |
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V24.00013: Interparticle gap distributions on one-dimensional discrete lattices Maria D'Orsogna, Tom Chou We analyze the successive binding of two species of particles on a one-dimensional discrete lattice, where the second variety is deposited only after complete adsorption of the first. We consider the two extreme cases of a perfectly irreversible initial deposition, with non-sliding particles, and that of a fully equilibrated one. For the latter we construct the exact gap distribution from the Tonks gas partition function. This distribution is contrasted with that obtained from the Random Sequential Adsorption (RSA) process. We discuss implications for the kinetics of adsorption of the two species, as well as experimental relevance of our results. [Preview Abstract] |
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