Monte Carlo simulation of entropy-driven pattern formation in two-dimensional system of rectangular particles

TL;DR

This study uses Monte Carlo simulations to explore how entropy influences pattern formation in a 2D system of rectangular particles, revealing that specific aspect ratios and particle types lead to distinct steady-state patterns.

Contribution

The paper introduces a simulation approach analyzing entropy-driven pattern formation in 2D rectangular particles, highlighting the effects of particle type and aspect ratio.

Findings

Steady state patterns depend on the aspect ratio of the system.

Pattern types differ between 'blind' and 'myopic' particles.

Patterns emerge only for certain aspect ratios and particle sizes.

Abstract

We simulated random walk of rectangular particles on a square lattice with periodic boundary conditions. Two kind of particles were investigated, viz., so-called `blind' and `myopic' particles. We found that steady state patterns occurred only for some values of the ratio $L_x/L_y$ where $L_x$ and $Ly$ are the linear sizes of the system and only for `needles', i.e., the particles of size $1 \times k$. Different patterns were observed for `blind' and `myopic' particles.