Universality of shocks in conserved driven single-file motions with bottlenecks

TL;DR

This paper uncovers a universal shape for shocks in driven single-file systems with bottlenecks, independent of parameters at high rates, revealing a fundamental property of such constrained transport phenomena.

Contribution

It demonstrates a previously unknown universality in shock shapes in cellular automata with conservation and bottlenecks, depending on system parameters.

Findings

Shock shapes are universal at high entry/exit rates and large particle numbers.

Shock shapes depend on parameters at low rates, lacking universality.

Boundary layers influence shock shape in certain regimes.

Abstract

Driven single-file motion, in which particles move unidirectionally along one-dimensional channels, sets the paradigm for wide variety of one-dimensional directed movements, ranging from intracellular transport and urban traffic to ant trails and controlled robot swarms. Motivated by the phenomenologies of these systems in closed geometries, regulated by number conservation and bottlenecks, we explore the domain walls (DWs) or shocks in a conceptual one-dimensional cellular automaton with a fixed particle number and a bottleneck. For high entry and exit rates of the cellular automaton, and with sufficiently large particle numbers, the DWs formed are independent of the associated rate parameters, revealing a {\em hitherto unknown universality} in their {\em shapes}, which are however enclosed by nonuniversal boundary layers. In contrast, the DWs do depend upon these parameters, if small, and hence have nonuniversal shapes, but without boundary layers. Nonuniversal delocalized DWs can be formed by additional tuning of the control parameters. Our predictions on the DWs are testable in model experiments.