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Crystallization and melting of bacteria colonies and Brownian bugs

Ramos, F.; López, C.; Hernández-García, E.; Muñoz, M.A.
Physical Review E 77, 021102(1-12) (2008)

Motivated by the existence of remarkably ordered cluster arrays of bacteria colonies growing in Petri dishes and other similar problems, we study the spontaneous emergence of clustering and patterns in a simple nonequilibrium model: 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 uncovered.