Morphology transition during non-equilibrium growth: I. Study of equilibrium shapes and properties

School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel
Physica A: Statistical Mechanics and its Applications (Impact Factor: 1.73). 02/1992; 181(1-2):136-155. DOI: 10.1016/0378-4371(92)90199-Z


We present a diffusion-transition scheme to study the penetration of a stable phase into a meta-stable one in systems described by a conserved order parameter. This approach is inspired by the specific example of solidification from supersaturated solution, for which we can take advantage of new experimental observations on surface kinetics. In this paper we present the approach and a study of solid-liquid equilibrium. The average shapes are compared with those evaluated by the Wulff construction. We calculate the fluctuations of the interface about the average shape as well as the temporal fluctuations in the diffusion field. Based on this, we propose a new strategy for experimental study of the kinetics of the phase transition. In part two we will present the morphologies observed in the simulations during non-equilibrium growth, focusing on the dense branching and dendritic morphologies, on their shape preserving envelope and on the transitions between them.

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    ABSTRACT: We present a study of interfacial pattern formation during diffusion-limited growth of Bacillus subtilis. It is demonstrated that bacterial colonies can develop patterns similar to morphologies observed during diffusion-limited growth in non-living (azoic) systems such as solidification and electro-chemical deposition. The various growth morphologies, that is the global structure of the colony, are observed as we vary the growth conditions. These include fractal growth, dense-branching growth, compact growth, dendritic growth and chiral growth. The results demonstrate the action of a singular interplay between the micro-level (individual bacterium) and macro-level (the colony) in selecting the observed morphologies as is understood for non-living systems. Furthermore, the observed morphologies can be organized within a morphology diagram indicating the existence of a morphology selection principle similar to the one proposed for azoic systems. We propose a phase-field-like model (the phase being the bacterial concentration and the field being the nutrient concentration) to describe the growth. The bacteria-bacteria interaction is manifested as a phase dependent diffusion constant. Growth of a bacterial colony presents an inherent additional level of complexity compared to azoic systems, since the building blocks themselves are living systems. Thus, our studies also focus on the transition between morphologies. We have observed extended morphology transitions due to phenotypic changes of the bacteria, as well as bursts of new morphologies resulting from genotypic changes. In addition, we have observed extended and heritable transitions (mainly between dense branching growth and chiral growth) as well as phenotypic transitions that turn genotypic over time. We discuss the implications of our results in the context of the evolving picture of genome cybernetics. Diffusion limited growth of bacterial colonies combined with new understanding of pattern formation in azoic systems provide new tools for the study of adaptive self-organization and mutation in the presence of selective pressures. We include brief reviews of both the recent developments in the study of interfacial pattern formation in non-living systems and the current trends in the view of mutation dynamics.
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