Gap-Size Distribution Functions of a Random Sequential Adsorption Model of Segments on the Line

TL;DR

This study investigates the structure of the jamming state in a two-segment size random sequential adsorption model on a line, analyzing how the size ratio influences gap distributions and structural patterns.

Contribution

It provides a detailed simulation-based analysis of gap-size distribution functions and structural characteristics at jamming for varying segment size ratios.

Findings

At low size ratios, the jamming state has short streaks of small and large segments.

At high size ratios, the jamming state features long streaks of small segments separated by large ones.

The study offers insights into minimizing interparticle distances and fluctuations in particle arrangements.

Abstract

We performed extensive simulations accompanied by a detailed study of a two-segment size random sequential model on the line. We followed the kinetics towards the jamming state, but we paid particular attention to the characterization of the jamming state structure. In particular, we studied the effect of the size ratio on the mean-gap size, the gap-size dispersion, gap-size skewness, and gap-size kurtosis at the jamming state. We also analyzed the above quantities for the four possible segment-to-segment gap types. We ranged the values of the size ratio from one to twenty. In the limit of a size ratio of one, one recovers the classical car-parking problem. We observed that at low size ratios the jamming state is constituted by short streaks of small and large segments, while at high values of the size ratio the jamming state structure is formed by long streaks of small segments separated by a single large segment. This view of the jamming state structure as a function of the size ratio is supported by the various measured quantities. The present work can help provide insight, for example, on how to minimize the interparticle distance or minimize fluctuations around the mean particle-to-particle distance.