Adsorption of Line Segments on a Square Lattice

TL;DR

This paper investigates the adsorption process of line segments on a square lattice, comparing Monte-Carlo simulations and time-series expansion to accurately estimate coverage, including the case of infinitely long segments.

Contribution

It introduces a combined approach using simulations and analytical expansion to accurately analyze coverage in line segment adsorption, especially for infinite lengths.

Findings

Monte-Carlo simulations and time-series expansion agree on coverage estimates.

Coverage at jamming can be accurately predicted for infinite segments.

The study provides a consistent method for analyzing adsorption limits.

Abstract

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte-Carlo simulations and by $7^{th}$-order time-series expansion are successfully compared. The non-trivial limit of adsorption of infinitely long segments is studied, and the lattice coverage is consistently obtained using these two approaches.