Surface properties and scaling behavior of a generalized ballistic deposition model in (1+1)-dimension

TL;DR

This paper investigates a generalized ballistic deposition model with variable stickiness, analyzing its surface scaling behavior and porosity, and demonstrating universal scaling laws dependent on sticking probability and system size.

Contribution

It introduces a new GBD model with variable stickiness and derives its surface width and porosity scaling exponents, expanding understanding beyond existing models.

Findings

Surface width exhibits scaling collapse with sticking probability and system size.

Porosity shows similar scaling behavior as surface width.

Scaling exponents are successfully determined for the GBD model.

Abstract

The surface exponents, the scaling behavior and the bulk porosity of a generalized ballistic deposition (GBD) model are studied. In nature, there exist particles with varying degrees of stickiness ranging from completely non-sticky to fully sticky. Such particles may adhere to any one of the successively encountered surfaces, depending on a sticking probability %should have the possibility of sticking to any of the %allowed points of contact on the surface with a sticking probability that is governed by the underlying stochastic mechanism. The microscopic configurations possible in this model are much larger than those allowed in existing models of ballistic deposition and competitive growth models that seek to mix ballistic and random deposition processes. In this article, we find the scaling exponents for surface width and porosity for the proposed GBD model. In terms of scaled width $\widetilde{W}$ and scaled time $\tilde{t}$, the numerical data collapse on to a single curve, demonstrating successful scaling with sticking probability p and system size L. Similar scaling behavior is also found for the porosity.