Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session V24: Focus Session: Nonequilibrium 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 DensityCurrent 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 nonGaussian, 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 probabilitynormalization constant for the steadystate 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 KardarParisiZhang 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 DerridaLebowitz scaling function for multiparticle versions of the discrete time Asymmetric Exclusion Process. We find that in this discrete time system the DerridaLebowitz 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 VollmayrLee, 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 $1p$ 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 DiffusionLimited Coalescence and Annihilation Invited Speaker: Daniel benAvraham The close similarity between the hierarchies of multiplepoint correlation functions for the diffusionlimited 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 JingXian Lin, Leonid Pryadko We analyze onedimensional motion of an overdamped classical particle in the presence of external disorder potential and an arbitrary driving force $F$. In thermodynamical limit the effective forcedependent mobility $\mu(F)$ is selfaveraging, 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 powerlaw correlations at large distances, $\langle V(x)V(y)\rangle \sim xy^{n}$, $n>0$, we identify a wide intermediate regime with a powerlaw dependence of the logarithm of $\mu(F)$ on the driving force. [Preview Abstract] 
Thursday, March 24, 2005 12:39PM  12:51PM 
V24.00006: Selforganized Criticality and Absorbing States: Lessons from the Ising model Gunnar Pruessner, Ole Peters I will report on an analysis of a suggested path to selforganized criticality. Originally, this path was devised to ``generate criticality'' in systems displaying an absorbingstate 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 finitesize scaling exponents depend on the tuning of driving and dissipation rates with system size. The findings limit the explanatory power of the mechanism to nonuniversal 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 zerotemperature 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: Ronald Dickman 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 selforganized criticality (SOC). In this talk I will describe recent analytical and numerical results on stationary and timedependent 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 uniformlydistributed 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 nonequilibrium phase transition Mark Dickison, Thomas Vojta We study the nonequilibrium phase transition in a contact process with extended quenched defects by means of MonteCarlo 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] 

V24.00011: Superscaling of Percolation on Rectangular Domains Hiroshi Watanabe, Yukawa Satoshi, Nobuyasu Ito, ChinKun Hu For percolation on a $(RL) \times L$ twodimensional 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 superscaling for other critical quantities. [Preview Abstract] 

V24.00012: First Passage Properties of the Erd\"osRenyi Random Graph Vishal Sood, Sidney Redner, Dani benAvraham We study the firstpassage properties of the Erd\"osRenyi random graph. Using an effective medium approximation we find that the meanfirstpassage 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 nonmonotonic behavior with $p$ near the percolation transition that can be understood on physical grounds. [Preview Abstract] 

V24.00013: Interparticle gap distributions on onedimensional discrete lattices Maria D'Orsogna, Tom Chou We analyze the successive binding of two species of particles on a onedimensional 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 nonsliding 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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