85 research outputs found
Variational approximations for stochastic dynamics on graphs
We investigate different mean-field-like approximations for stochastic
dynamics on graphs, within the framework of a cluster-variational approach. In
analogy with its equilibrium counterpart, this approach allows one to give a
unified view of various (previously known) approximation schemes, and suggests
quite a systematic way to improve the level of accuracy. We compare the
different approximations with Monte Carlo simulations on a reversible
(susceptible-infected-susceptible) discrete-time epidemic-spreading model on
random graphs.Comment: 29 pages, 5 figures. Minor revisions. IOP-style
Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory
We develop a mean-field theory for the totally asymmetric simple exclusion
process (TASEP) with open boundaries, in order to investigate the so-called
dynamical transition. The latter phenomenon appears as a singularity in the
relaxation rate of the system toward its non-equilibrium steady state. In the
high-density (low-density) phase, the relaxation rate becomes independent of
the injection (extraction) rate, at a certain critical value of the parameter
itself, and this transition is not accompanied by any qualitative change in the
steady-state behavior. We characterize the relaxation rate by providing
rigorous bounds, which become tight in the thermodynamic limit. These results
are generalized to the TASEP with Langmuir kinetics, where particles can also
bind to empty sites or unbind from occupied ones, in the symmetric case of
equal binding/unbinding rates. The theory predicts a dynamical transition to
occur in this case as well.Comment: 37 pages (including 16 appendix pages), 6 figures. Submitted to
Journal of Physics
Dynamical Transitions in a One-Dimensional KatzâLebowitzâSpohn Model
Dynamical transitions, already found in the high- and low-density phases of the Totally
Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the
rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond
to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional
KatzâLebowitzâSpohn model, a further generalization of the Totally Asymmetric Simple Exclusion
Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes
affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary
conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber
rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the
NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain
wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional
KatzâLebowitzâSpohn model, and discuss 2 new phenomena which are peculiar to this model
Interaction vs inhomogeneity in a periodic TASEP
We study the non-equilibrium steady states in a totally asymmetric simple exclusion process with periodic boundary conditions, also incorporating (i) an extra (nearest-neighbour) repulsive interaction and (ii) hopping rates characterized by a smooth spatial inhomogeneity. We make use of a generalized mean-field approach (at the level of nearest-neighbour pair clusters), in combination with kinetic Monte Carlo simulations. It turns out that the so-called shock phase can exhibit a lot of qualitatively different subphases, including multiple-shock phases, and a minimal-current shock phase. We argue that the resulting, considerably rich phase diagram should be relatively insensitive to minor details of either interaction or spatial inhomogeneity. As a consequence, we also expect that our results help elucidate the nature of shock subphases detected in previous studies
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