Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Dec;66(6):061604. doi: 10.1103/PhysRevE.66.061604. Epub 2002 Dec 16.

Growth model with restricted surface relaxation.

Physical review. E, Statistical, nonlinear, and soft matter physics

T J da Silva, J G Moreira

PMID: 12513294 DOI: 10.1103/PhysRevE.66.061604

Abstract

We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the discrete surface relaxation model, but only within a distance s. If the local minimum is out from this distance, the particle evaporates through a refuse mechanism similar to the Kim-Kosterlitz nonlinear model. In d=1, the growth exponent beta, measured from the temporal behavior of roughness, indicates that in the coarse-grained limit, the linear term of the Kardar-Parisi-Zhang equation dominates in short times (low-roughness) and, in asymptotic times, the nonlinear term prevails. The crossover between linear and nonlinear behaviors occurs in a characteristic time t(c) which only depends on the magnitude of the parameter s, related to the nonlinear term. In d=2, we find indications of a similar crossover, that is, logarithmic temporal behavior of roughness in short times and power law behavior in asymptotic times.

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• Journal Article