Conserved mass models with stickiness and chipping

TL;DR

This paper investigates a one-dimensional mass chipping model with stickiness, deriving steady state distributions for both symmetric and asymmetric cases using perturbation methods, applicable to different update schemes.

Contribution

It introduces a perturbation approach to analytically obtain steady state distributions for a novel mass chipping model with stickiness.

Findings

Steady state distributions are derived for both symmetric and asymmetric models.

Perturbation theory provides accurate steady state solutions in most cases.

Applicable to both parallel and random sequential update schemes.

Abstract

We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass sticks to the site. In the asymmetric version, the chipped off mass is distributed among the site and the right neighbour, whereas in the symmetric version the redistribution occurs among the two neighbours. The steady state mass distribution of the model is obtained using a perturbation method for both parallel and random sequential updates. In most cases, this perturbation theory provides a steady state distribution with reasonable accuracy.