2,547 research outputs found
Disordered asymmetric simple exclusion process: mean-field treatment
We provide two complementary approaches to the treatment of disorder in a
fundamental nonequilibrium model, the asymmetric simple exclusion process.
Firstly, a mean-field steady state mapping is generalized to the disordered
case, where it provides a mapping of probability distributions and demonstrates
how disorder results in a new flat regime in the steady state current--density
plot for periodic boundary conditions. This effect was earlier observed by
Tripathy and Barma but we provide treatment for more general distributions of
disorder, including both numerical results and analytic expressions for the
width of the flat section. We then apply an argument based on
moving shock fronts to show how this leads to an increase in the high current
region of the phase diagram for open boundary conditions. Secondly, we show how
equivalent results can be obtained easily by taking the continuum limit of the
problem and then using a disordered version of the well-known Cole--Hopf
mapping to linearize the equation. Within this approach we show that adding
disorder induces a localization transformation (verified by numerical scaling),
and maps to an inverse localization length, helping to give a new
physical interpretation to the problem.Comment: 13 pages, 16 figures. Submitted to Phys. Rev.
Real-space renormalisation group approach to driven diffusive systems
We introduce a real-space renormalisation group procedure for driven
diffusive systems which predicts both steady state and dynamic properties. We
apply the method to the boundary driven asymmetric simple exclusion process and
recover exact results for the steady state phase diagram, as well as the
crossovers in the relaxation dynamics for each phase.Comment: 10 pages, 5 figure
Quantum Scaling Approach to Nonequilibrium Models
Stochastic nonequilibrium exclusion models are treated using a real space
scaling approach. The method exploits the mapping between nonequilibrium and
quantum systems, and it is developed to accommodate conservation laws and
duality symmetries, yielding exact fixed points for a variety of exclusion
models. In addition, it is shown how the asymmetric simple exclusion process in
one dimension can be written in terms of a classical Hamiltonian in two
dimensions using a Suzuki-Trotter decomposition.Comment: 17 page
Non-universal coarsening and universal distributions in far-from equilibrium systems
Anomalous coarsening in far-from equilibrium one-dimensional systems is
investigated by simulation and analytic techniques. The minimal hard core
particle (exclusion) models contain mechanisms of aggregated particle
diffusion, with rates epsilon<<1, particle deposition into cluster gaps, but
suppressed for the smallest gaps, and breakup of clusters which are adjacent to
large gaps. Cluster breakup rates vary with the cluster length x as kx^alpha.
The domain growth law x ~ (epsilon t)^z, with z=1/(2+alpha) for alpha>0, is
explained by a scaling picture, as well as the scaling of the density of double
vacancies (at which deposition and cluster breakup are allowed) as 1/[t(epsilon
t)^z]. Numerical simulations for several values of alpha and epsilon confirm
these results. An approximate factorization of the cluster configuration
probability is performed within the master equation resulting from the mapping
to a column picture. The equation for a one-variable scaling function explains
the above results. The probability distributions of cluster lengths scale as
P(x)= 1/(epsilon t)^z g(y), with y=x/(epsilon t)^z. However, those
distributions show a universal tail with the form g(y) ~ exp(-y^{3/2}), which
disagrees with the prediction of the independent cluster approximation. This
result is explained by the connection of the vacancy dynamics with the problem
of particle trapping in an infinite sea of traps and is confirmed by
simulation.Comment: 30 pages (10 figures included), to appear in Phys. Rev.
Sample-Dependent Phase Transitions in Disordered Exclusion Models
We give numerical evidence that the location of the first order phase
transition between the low and the high density phases of the one dimensional
asymmetric simple exclusion process with open boundaries becomes sample
dependent when quenched disorder is introduced for the hopping rates.Comment: accepted in Europhysics Letter
Visualizing genetic constraints
Principal Components Analysis (PCA) is a common way to study the sources of
variation in a high-dimensional data set. Typically, the leading principal
components are used to understand the variation in the data or to reduce the
dimension of the data for subsequent analysis. The remaining principal
components are ignored since they explain little of the variation in the data.
However, evolutionary biologists gain important insights from these low
variation directions. Specifically, they are interested in directions of low
genetic variability that are biologically interpretable. These directions are
called genetic constraints and indicate directions in which a trait cannot
evolve through selection. Here, we propose studying the subspace spanned by low
variance principal components by determining vectors in this subspace that are
simplest. Our method and accompanying graphical displays enhance the
biologist's ability to visualize the subspace and identify interpretable
directions of low genetic variability that align with simple directions.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS603 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Smoothly-varying hopping rates in driven flow with exclusion
We consider the one-dimensional totally asymmetric simple exclusion process
(TASEP) with position-dependent hopping rates. The problem is solved,in a mean
field/adiabatic approximation, for a general (smooth) form of spatial rate
variation. Numerical simulations of systems with hopping rates varying linearly
against position (constant rate gradient), for both periodic and open boundary
conditions, provide detailed confirmation of theoretical predictions,
concerning steady-state average density profiles and currents, as well as
open-system phase boundaries, to excellent numerical accuracy.Comment: RevTeX 4.1, 14 pages, 9 figures (published version
Mean field and Monte Carlo studies of the magnetization-reversal transition in the Ising model
Detailed mean field and Monte Carlo studies of the dynamic
magnetization-reversal transition in the Ising model in its ordered phase under
a competing external magnetic field of finite duration have been presented
here. Approximate analytical treatment of the mean field equations of motion
shows the existence of diverging length and time scales across this dynamic
transition phase boundary. These are also supported by numerical solutions of
the complete mean field equations of motion and the Monte Carlo study of the
system evolving under Glauber dynamics in both two and three dimensions.
Classical nucleation theory predicts different mechanisms of domain growth in
two regimes marked by the strength of the external field, and the nature of the
Monte Carlo phase boundary can be comprehended satisfactorily using the theory.
The order of the transition changes from a continuous to a discontinuous one as
one crosses over from coalescence regime (stronger field) to nucleation regime
(weaker field). Finite size scaling theory can be applied in the coalescence
regime, where the best fit estimates of the critical exponents are obtained for
two and three dimensions.Comment: 16 pages latex, 13 ps figures, typos corrected, references adde
Spatially heterogeneous dynamics in granular compaction
We prove the emergence of spatially correlated dynamics in slowly compacting
dense granular media by analyzing analytically and numerically multi-point
correlation functions in a simple particle model characterized by slow
non-equilibrium dynamics. We show that the logarithmically slow dynamics at
large times is accompanied by spatially extended dynamic structures that
resemble the ones observed in glass-forming liquids and dense colloidal
suspensions. This suggests that dynamic heterogeneity is another key common
feature present in very different jamming materials.Comment: 4 pages, 3 figure
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