2 research outputs found
New method to study stochastic growth equations: a cellular automata perspective
We introduce a new method based on cellular automata dynamics to study
stochastic growth equations. The method defines an interface growth process
which depends on height differences between neighbors. The growth rule assigns
a probability exp for a site to
receive one particle at a time and all the sites are updated
simultaneously. Here and are two parameters and
is a function which depends on height of the site and its neighbors. Its
functional form is specified through discretization of the deterministic part
of the growth equation associated to a given deposition process. In particular,
we apply this method to study two linear equations - the Edwards-Wilkinson (EW)
equation and the Mullins-Herring (MH) equation - and a non-linear one - the
Kardar-Parisi-Zhang (KPZ) equation. Through simulations and statistical
analysis of the height distributions of the profiles, we recover the values for
roughening exponents, which confirm that the processes generated by the method
are indeed in the universality classes of the original growth equations. In
addition, a crossover from Random Deposition to the associated correlated
regime is observed when the parameter is varied.Comment: 6 pages, 7 figure