Observation of nonuniversal scaling exponent in a novel erosion model

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 non-universal 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 (less than or similar to 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.