Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-10-18
J. Phys. A: Math. Theor. 40 13245-13256 (2007)
Physics
Condensed Matter
Statistical Mechanics
6 pages, 7 figures
Scientific paper
10.1088/1751-8113/40/44/006
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 $p_{i}(t)=\rho$ exp$[\kappa \Gamma_{i}(t)]$ for a site $i$ to receive one particle at a time $t$ and all the sites are updated simultaneously. Here $\rho$ and $\kappa$ are two parameters and $\Gamma_{i}(t)$ is a function which depends on height of the site $i$ 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 $\kappa$ is varied.
Atman A. P. F.
Mattos T. G.
Moreira J. G.
No associations
LandOfFree
New method to study stochastic growth equations: a cellular automata perspective does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with New method to study stochastic growth equations: a cellular automata perspective, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New method to study stochastic growth equations: a cellular automata perspective will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-99352