Observation of nonuniversal scaling exponent in a novel erosion model

Abstract

In this present numerical work, we report a discrete erosion kind of model in (1 + 1)-dimension. Erosion and re-deposition phenomena with probabilities p and q(= 1 - p) are considered as two tunable parameters, which control the overall kinetic roughening behavior of the interface. Redeposition or diffusion dominated erosion like kinetic roughening model gives rise to nonuniversal growth exponent, which varies continuously with respect to erosion probability. However, universal character is restored for the roughness exponent with the value of 0.5 in (1 + 1)-dimension with respect to p. Due to nonuniversal nature of growth exponent, we observe a significant modification to the scaling behavior of surface width with respect to erosion probability. For low erosion probability (≲ 0.1) a power law like divergence has been observed of the correlation growth time. This can be argued as limiting behavior of a generalized functional behavior of crossover time with erosion probability.