Random Sequential Adsorption of Objects of Decreasing Size

TL;DR

This paper studies a model of random sequential adsorption where objects decrease in size over time, combining numerical simulations and analytical analysis to understand correlation functions and gap distributions.

Contribution

It introduces a model of decreasing-sized objects in RSA and provides numerical and analytical insights into correlation and gap distributions over time.

Findings

Correlation hole develops at finite times

Correlation functions vanish at contact in the model

Logarithmic divergence reappears at large times

Abstract

We consider the model of random sequential adsorption, with depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large time limit. Numerical Monte Carlo simulations of two-dimensional deposition of disks and one-dimensional deposition of segments are reported for the density-density correlation function and gap-size distribution function, respectively. Analytical considerations supplement numerical results in the one-dimensional case. We investigate the correlation hole - the depletion of correlation functions near contact and, for the present model, their vanishing at contact - that opens up at finite times, as well as its closing and reemergence of the logarithmic divergence of correlation properties at contact in the large time limit.