Soft disks in a narrow channel

TL;DR

This paper investigates how the pressure components of soft disks in a narrow 2D channel depend on channel width, revealing singularities related to the potential's nature and boundary conditions using analytical and simulation methods.

Contribution

It provides a detailed analysis of pressure singularities in soft disk systems in narrow channels, considering different boundary conditions and potential types, which was not previously explored.

Findings

Pressure components show singularities at specific channel widths related to the potential's singularity.

Boundary conditions influence the strength of pressure singularities, with periodic boundaries showing stronger effects.

Discontinuous potentials lead to stronger singularities than continuous power-law potentials.

Abstract

The pressure components of "soft" disks in a two dimensional narrow channel are analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics. Channels with either periodic or reflecting boundaries are considered. It is found that when the two-body potential, u(r), is singular at some distance r_0, the dependence of the pressure components on the channel width exhibits a singularity at one or more channel widths which are simply related to r_0. In channels with periodic boundary conditions and for potentials which are discontinuous at r_0, the transverse and longitudinal pressure components exhibit a 1/2 and 3/2 singularity, respectively. Continuous potentials with a power law singularity result in weaker singularities of the pressure components. In channels with reflecting boundary conditions the singularities are found to be weaker than those corresponding to periodic boundaries.