135 research outputs found
The Asymmetric Avalanche Process
An asymmetric stochastic process describing the avalanche dynamics on a ring
is proposed. A general kinetic equation which incorporates the exclusion and
avalanche processes is considered. The Bethe ansatz method is used to calculate
the generating function for the total distance covered by all particles. It
gives the average velocity of particles which exhibits a phase transition from
an intermittent to continuous flow. We calculated also higher cumulants and the
large deviation function for the particle flow. The latter has the universal
form obtained earlier for the asymmetric exclusion process and conjectured to
be common for all models of the Kardar-Parisi-Zhang universality class .Comment: 33 pages, 3 figures, revised versio
Exact velocity of dispersive flow in the asymmetric avalanche process
Using the Bethe ansatz we obtain the exact solution for the one-dimensional
asymmetric avalanche process. We evaluate the velocity of dispersive flow as a
function of driving force and the density of particles. The obtained solution
shows a dynamical transition from intermittent to continuous flow.Comment: 12 page
The totally asymmetric exclusion process with generalized update
We consider the totally asymmetric exclusion process in discrete time with
generalized updating rules. We introduce a control parameter into the
interaction between particles. Two particular values of the parameter
correspond to known parallel and sequential updates. In the whole range of its
values the interaction varies from repulsive to attractive. In the latter case
the particle flow demonstrates an apparent jamming tendency not typical for the
known updates. We solve the master equation for particles on the infinite
lattice by the Bethe ansatz. The non-stationary solution for arbitrary initial
conditions is obtained in a closed determinant form.Comment: 11 pages, 3 figure
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