Crystallization and melting of bacteria colonies and Brownian Bugs

TL;DR

This paper investigates pattern formation and phase transitions in a model of bacteria colonies and Brownian bugs, revealing a unique defect-mediated melting transition with similarities and differences to classical theories.

Contribution

It introduces a continuous Langevin equation for a discrete bacteria model and analyzes the spontaneous emergence of clusters and phase transitions in two dimensions.

Findings

Localized clusters of activity form spontaneously.

A melting/freezing transition from disordered to ordered hexagonal patterns occurs.

The transition is a non-standard, defect-mediated one, only partially understood.

Abstract

Motivated by the existence of remarkably ordered cluster arrays of bacteria colonies growing in Petri dishes and related problems, we study the spontaneous emergence of clustering and patterns in a simple nonequilibrium system: the individual-based interacting Brownian bug model. We map this discrete model into a continuous Langevin equation which is the starting point for our extensive numerical analyses. For the two-dimensional case we report on the spontaneous generation of localized clusters of activity as well as a melting/freezing transition from a disordered or isotropic phase to an ordered one characterized by hexagonal patterns. We study in detail the analogies and differences with the well-established Kosterlitz-Thouless-Halperin-Nelson-Young theory of equilibrium melting, as well as with another competing theory. For that, we study translational and orientational correlations and perform a careful defect analysis. We find a non standard one-stage, defect-mediated, transition whose nature is only partially elucidated.