Condensation and evaporation on a randomly occupied square lattice

TL;DR

This paper investigates particle dynamics on a square lattice with growth and culling rules, revealing new behaviors including hysteresis, through analytical and simulation methods for mobile and immobile cases.

Contribution

It introduces a novel lattice model for condensation and evaporation, analyzing both mobile and immobile particle scenarios with new findings on hysteresis.

Findings

Identification of hysteresis in particle occupation dynamics

Differences in behavior between mobile and immobile particle models

Comparison with existing surface condensation models

Abstract

We study the evolution of an initially random distribution of particles on a square lattice, under certain rules for `growing' and `culling' of particles. In one version we allow the particles to move laterally along the surface (mobile layer) and in the other version this motion is not allowed (immobile case). In the former case both analytical and computer simulation results are presented, while in the latter only simulation is possible. We introduce growth and culling probabilities appropriate for condensation and evaporation on a two-dimensional surface, and compare results with existing models for this problem. Our results show very interesting behaviour, under certain conditions quite different from earlier models. We find a possibility of hysteresis not reported earlier for such models. ~