623 research outputs found
Exact Results for the Asymmetric Simple Exclusion Process with a Blockage
We present new results for the current as a function of transmission rate in
the one dimensional totally asymmetric simple exclusion process (TASEP) with a
blockage that lowers the jump rate at one site from one to r < 1. Exact finite
volume results serve to bound the allowed values for the current in the
infinite system. This proves the existence of a gap in allowed density
corresponding to a nonequilibrium ``phase transition'' in the infinite system.
A series expansion in r, derived from the finite systems, is proven to be
asymptotic for all sufficiently large systems. Pade approximants based on this
series, which make specific assumptions about the nature of the singularity at
r = 1, match numerical data for the ``infinite'' system to a part in 10^4.Comment: 18 pages, LaTeX (including figures in LaTeX picture mode
When is a bottleneck a bottleneck?
Bottlenecks, i.e. local reductions of capacity, are one of the most relevant
scenarios of traffic systems. The asymmetric simple exclusion process (ASEP)
with a defect is a minimal model for such a bottleneck scenario. One crucial
question is "What is the critical strength of the defect that is required to
create global effects, i.e. traffic jams localized at the defect position".
Intuitively one would expect that already an arbitrarily small bottleneck
strength leads to global effects in the system, e.g. a reduction of the maximal
current. Therefore it came as a surprise when, based on computer simulations,
it was claimed that the reaction of the system depends in non-continuous way on
the defect strength and weak defects do not have a global influence on the
system. Here we reconcile intuition and simulations by showing that indeed the
critical defect strength is zero. We discuss the implications for the analysis
of empirical and numerical data.Comment: 8 pages, to appear in the proceedings of Traffic and Granular Flow
'1
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
Localized defects in a cellular automaton model for traffic flow with phase separation
We study the impact of a localized defect in a cellular automaton model for
traffic flow which exhibits metastable states and phase separation. The defect
is implemented by locally limiting the maximal possible flow through an
increase of the deceleration probability. Depending on the magnitude of the
defect three phases can be identified in the system. One of these phases shows
the characteristics of stop-and-go traffic which can not be found in the model
without lattice defect. Thus our results provide evidence that even in a model
with strong phase separation stop-and-go traffic can occur if local defects
exist. From a physical point of view the model describes the competition
between two mechanisms of phase separation.Comment: 14 pages, 7 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
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
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
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
Men, Women, and Ghosts in Science
Science suffers because, by favouring the self-confident of both sexes, we discriminate against women
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
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