127 research outputs found
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
Critical Dynamics of Self-Organizing Eulerian Walkers
The model of self-organizing Eulerian walkers is numerically investigated on
the square lattice. The critical exponents for the distribution of a number of
steps () and visited sites () characterizing the process of
transformation from one recurrent configuration to another are calculated using
the finite-size scaling analysis. Two different kinds of dynamical rules are
considered. The results of simulations show that both the versions of the model
belong to the same class of universality with the critical exponents
.Comment: 3 pages, 4 Postscript figures, RevTeX, additional information
available at http://thsun1.jinr.dubna.su/~shche
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
Critical Behavior of the Sandpile Model as a Self-Organized Branching Process
Kinetic equations, which explicitly take into account the branching nature of
sandpile avalanches, are derived. The dynamics of the sandpile model is
described by the generating functions of a branching process. Having used the
results obtained the renormalization group approach to the critical behavior of
the sandpile model is generalized in order to calculate both critical exponents
and height probabilities.Comment: REVTeX, twocolumn, 4 page
Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry
Using the Bethe ansatz we obtain the determinant expression for the time dependent transition probabilities in the totally asymmetric exclusion process with parallel update on a ring. Developing a method of summation over the roots of Bethe equations based on the multidimensional analogue of the Cauchy residue theorem, we construct the resolution of the identity operator, which allows us to calculate the matrix elements of the evolution operator and its powers. Representation of results in the form of an infinite series elucidates connection to other results obtained for the ring geometry. As a byproduct we also obtain the generating function of the joint probability distribution of particle configurations and the total distance traveled by the particles
Non-contractible loops in the dense O(n) loop model on the cylinder
A lattice model of critical dense polymers is considered for the
finite cylinder geometry. Due to the presence of non-contractible loops with a
fixed fugacity , the model is a generalization of the critical dense
polymers solved by Pearce, Rasmussen and Villani. We found the free energy for
any height and circumference of the cylinder. The density of
non-contractible loops is found for and large . The
results are compared with those obtained for the anisotropic quantum chain with
twisted boundary conditions. Using the latter method we obtained for any
model and an arbitrary fugacity.Comment: arXiv admin note: text overlap with arXiv:0810.223
Three-leg correlations in the two component spanning tree on the upper half-plane
We present a detailed asymptotic analysis of correlation functions for the
two component spanning tree on the two-dimensional lattice when one component
contains three paths connecting vicinities of two fixed lattice sites at large
distance apart. We extend the known result for correlations on the plane to
the case of the upper half-plane with closed and open boundary conditions. We
found asymptotics of correlations for distance from the boundary to one of
the fixed lattice sites for the cases and .Comment: 16 pages, 5 figure
Transition from KPZ to Tilted Interface Critical Behavior in a Solvable Asymmetric Avalanche Model
We use a discrete-time formulation to study the asymmetric avalanche process
[Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact
expression for the average avalanche size of particles as a function of
toppling probabilities depending on parameters and . By mapping
the model below and above the critical line onto driven interface problems, we
show how different regimes of avalanches may lead to different types of
critical interface behavior characterized by either annealed or quenched
disorders and obtain exactly the related critical exponents which violate a
well-known scaling relation when .Comment: 10 page
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