456 research outputs found
Spatial Organization in the Reaction A + B --> inert for Particles with a Drift
We describe the spatial structure of particles in the (one dimensional)
two-species annihilation reaction A + B --> 0, where both species have a
uniform drift in the same direction and like species have a hard core
exclusion. For the case of equal initial concentration, at long times, there
are three relevant length scales: the typical distance between similar
(neighboring) particles, the typical distance between dissimilar (neighboring)
particles, and the typical size of a cluster of one type of particles. These
length scales are found to be generically different than that found for
particles without a drift.Comment: 10 pp of gzipped uuencoded postscrip
Exact solutions for a mean-field Abelian sandpile
We introduce a model for a sandpile, with N sites, critical height N and each
site connected to every other site. It is thus a mean-field model in the
spin-glass sense. We find an exact solution for the steady state probability
distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe
Partially asymmetric exclusion models with quenched disorder
We consider the one-dimensional partially asymmetric exclusion process with
random hopping rates, in which a fraction of particles (or sites) have a
preferential jumping direction against the global drift. In this case the
accumulated distance traveled by the particles, x, scales with the time, t, as
x ~ t^{1/z}, with a dynamical exponent z > 0. Using extreme value statistics
and an asymptotically exact strong disorder renormalization group method we
analytically calculate, z_{pt}, for particlewise (pt) disorder, which is argued
to be related to the dynamical exponent for sitewise (st) disorder as
z_{st}=z_{pt}/2. In the symmetric situation with zero mean drift the particle
diffusion is ultra-slow, logarithmic in time.Comment: 4 pages, 3 figure
A multi-species asymmetric simple exclusion process and its relation to traffic flow
Using the matrix product formalism we formulate a natural p-species
generalization of the asymmetric simple exclusion process. In this model
particles hop with their own specific rate and fast particles can overtake slow
ones with a rate equal to their relative speed. We obtain the algebraic
structure and study the properties of the representations in detail. The
uncorrelated steady state for the open system is obtained and in the ( limit, the dependence of its characteristics on the distribution of
velocities is determined. It is shown that when the total arrival rate of
particles exceeds a certain value, the density of the slowest particles rises
abroptly.Comment: some typos corrected, references adde
Reconstruction on trees and spin glass transition
Consider an information source generating a symbol at the root of a tree
network whose links correspond to noisy communication channels, and
broadcasting it through the network. We study the problem of reconstructing the
transmitted symbol from the information received at the leaves. In the large
system limit, reconstruction is possible when the channel noise is smaller than
a threshold.
We show that this threshold coincides with the dynamical (replica symmetry
breaking) glass transition for an associated statistical physics problem.
Motivated by this correspondence, we derive a variational principle which
implies new rigorous bounds on the reconstruction threshold. Finally, we apply
a standard numerical procedure used in statistical physics, to predict the
reconstruction thresholds in various channels. In particular, we prove a bound
on the reconstruction problem for the antiferromagnetic ``Potts'' channels,
which implies, in the noiseless limit, new results on random proper colorings
of infinite regular trees.
This relation to the reconstruction problem also offers interesting
perspective for putting on a clean mathematical basis the theory of glasses on
random graphs.Comment: 34 pages, 16 eps figure
Towards a model for protein production rates
In the process of translation, ribosomes read the genetic code on an mRNA and
assemble the corresponding polypeptide chain. The ribosomes perform discrete
directed motion which is well modeled by a totally asymmetric simple exclusion
process (TASEP) with open boundaries. Using Monte Carlo simulations and a
simple mean-field theory, we discuss the effect of one or two ``bottlenecks''
(i.e., slow codons) on the production rate of the final protein. Confirming and
extending previous work by Chou and Lakatos, we find that the location and
spacing of the slow codons can affect the production rate quite dramatically.
In particular, we observe a novel ``edge'' effect, i.e., an interaction of a
single slow codon with the system boundary. We focus in detail on ribosome
density profiles and provide a simple explanation for the length scale which
controls the range of these interactions.Comment: 8 pages, 8 figure
Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents
We propose a model for diffusion-limited annihilation of two species, or , where the motion of the particles is subject to a drift. For equal
initial concentrations of the two species, the density follows a power-law
decay for large times. However, the decay exponent varies continuously as a
function of the probability of which particle, the hopping one or the target,
survives in the reaction. These results suggest that diffusion-limited
reactions subject to drift do not fall into a limited number of universality
classes.Comment: 10 pages, tex, 3 figures, also available upon reques
Kinetics of A+B--->0 with Driven Diffusive Motion
We study the kinetics of two-species annihilation, A+B--->0, when all
particles undergo strictly biased motion in the same direction and with an
excluded volume repulsion between same species particles. It was recently shown
that the density in this system decays as t^{-1/3}, compared to t^{-1/4}
density decay in A+B--->0 with isotropic diffusion and either with or without
the hard-core repulsion. We suggest a relatively simple explanation for this
t^{-1/3} decay based on the Burgers equation. Related properties associated
with the asymptotic distribution of reactants can also be accounted for within
this Burgers equation description.Comment: 11 pages, plain Tex, 8 figures. Hardcopy of figures available on
request from S
Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes
We study the effect of quenched spatial disorder on the steady states of
driven systems of interacting particles. Two sorts of models are studied:
disordered drop-push processes and their generalizations, and the disordered
asymmetric simple exclusion process. We write down the exact steady-state
measure, and consequently a number of physical quantities explicitly, for the
drop-push dynamics in any dimensions for arbitrary disorder. We find that three
qualitatively different regimes of behaviour are possible in 1- disordered
driven systems. In the Vanishing-Current regime, the steady-state current
approaches zero in the thermodynamic limit. A system with a non-zero current
can either be in the Homogeneous regime, chracterized by a single macroscopic
density, or the Segregated-Density regime, with macroscopic regions of
different densities. We comment on certain important constraints to be taken
care of in any field theory of disordered systems.Comment: RevTex, 17pages, 18 figures included using psfig.st
Two-way traffic flow: exactly solvable model of traffic jam
We study completely asymmetric 2-channel exclusion processes in 1 dimension.
It describes a two-way traffic flow with cars moving in opposite directions.
The interchannel interaction makes cars slow down in the vicinity of
approaching cars in other lane. Particularly, we consider in detail the system
with a finite density of cars on one lane and a single car on the other one.
When the interchannel interaction reaches a critical value, traffic jam
occurs, which turns out to be of first order phase transition. We derive exact
expressions for the average velocities, the current, the density profile and
the - point density correlation functions. We also obtain the exact
probability of two cars in one lane being distance apart, provided there is
a finite density of cars on the other lane, and show the two cars form a weakly
bound state in the jammed phase.Comment: 17 pages, Latex, ioplppt.sty, 11 ps figure
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