Jammed state characterization of the random sequential adsorption of segments of two lengths on a line

TL;DR

This paper analyzes the structure of the jammed state in a two-size segment adsorption process on a line, introducing a probabilistic model and validating it with simulations.

Contribution

It proposes a truncated exponential ansatz for the interparticle distance distribution and compares analytical results with Monte Carlo simulations.

Findings

The ansatz matches Monte Carlo results qualitatively.

Analytical cumulants agree with simulations without free parameters.

The model effectively characterizes the jammed state structure.

Abstract

We characterize the jammed state structure of the random sequential adsorption of segments of two different sizes on a line. To this end, we define the size ratio as a dimensionless quantity measuring the length of the large segments in terms of the smaller ones. We introduce a truncated exponential as an {\it ansatz} for the probability distribution function of the interparticle distance at the jammed state and use it to reckon the first four cumulants of the probability distribution function. The sole free parameter present in the various analytical expressions is tied to the mean interparticle distance from Monte Carlo simulations, while the remaining three cumulants are computed without any free parameter and compared to Monte Carlo results. We find that the proposed {\it ansatz} provides results in good qualitative agreement with Monte Carlo ones.