1,618 research outputs found
Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics
A numerical method based on Matrix Product Formalism is proposed to study the
phase transitions and shock formation in the Asymmetric Simple Exclusion
Process with open boundaries and parallel dynamics. By working in a canonical
ensemble, where the total number of the particles is being fixed, we find that
the model has a rather non-trivial phase diagram consisting of three different
phases which are separated by second-order phase transition. Shocks may evolve
in the system for special values of the reaction parameters.Comment: 8 pages, 3 figure
A Multi-Species Asymmetric Exclusion Model with an Impurity
A multi-species generalization of the Asymmetric Simple Exclusion Process
(ASEP) has been considered in the presence of a single impurity on a ring. The
model describes particles hopping in one direction with stochastic dynamics and
hard core exclusion condition. The ordinary particles hop forward with their
characteristic hopping rates and fast particles can overtake slow ones with a
relative rate. The impurity, which is the slowest particle in the ensemble of
particles on the ring, hops in the same direction of the ordinary particles
with its intrinsic hopping rate and can be overtaken by ordinary particles with
a rate which is not necessarily a relative rate. We will show that the phase
diagram of the model can be obtained exactly. It turns out that the phase
structure of the model depends on the density distribution function of the
ordinary particles on the ring so that it can have either four phases or only
one. The mean speed of impurity and also the total current of the ordinary
particles are explicitly calculated in each phase. Using Monte Carlo
simulation, the density profile of the ordinary particles is also obtained. The
simulation data confirm all of the analytical calculations.Comment: 20 pages,10 EPS figures; to appear in Physica
Shock in a Branching-Coalescing Model with Reflecting Boundaries
A one-dimensional branching-coalescing model is considered on a chain of
length L with reflecting boundaries. We study the phase transitions of this
model in a canonical ensemble by using the Yang-Lee description of the
non-equilibrium phase transitions. Numerical study of the canonical partition
function zeros reveals two second-order phase transitions in the system. Both
transition points are determined by the density of the particles on the chain.
In some regions the density profile of the particles has a shock structure.Comment: Contents modified and new references added, to appear in Physics
Letters
Multi shocks in Reaction-diffusion models
It is shown, concerning equivalent classes, that on a one-dimensional lattice
with nearest neighbor interaction, there are only four independent models
possessing double-shocks. Evolution of the width of the double-shocks in
different models is investigated. Double-shocks may vanish, and the final state
is a state with no shock. There is a model for which at large times the average
width of double-shocks will become smaller. Although there may exist stationary
single-shocks in nearest neighbor reaction diffusion models, it is seen that in
none of these models, there exist any stationary double-shocks. Models
admitting multi-shocks are classified, and the large time behavior of
multi-shock solutions is also investigated.Comment: 17 pages, LaTeX2e, minor revisio
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