Morphological Instability and Dynamics of Fronts in Bacterial Growth Models with Nonlinear Diffusion
arXiv:cond-mat/0211463 · doi:10.1103/PhysRevE.65.061111
Abstract
It has been argued that there is biological and modeling evidence that a non-linear diffusion coefficient of the type D(b) = D_0 b^{k} underlies the formation of a number of growth patterns of bacterial colonies. We study a reaction-diffusion system with a non-linear diffusion coefficient introduced by Ben-Jacob et al. Due to the fact that the bacterial diffusion coefficient vanishes when the bacterial density b -> 0, the standard linear stability analysis for fronts cannot be used. We introduce an extension of the stability analysis which can be applied to such singular fronts, map out the region of stability in the D-k-plane and derive an interfacial approximation in some limits. Our linear stability analysis and sharp interface formulation will also be applicable to other examples of interface formation due to nonlinear diffusion, like in porous media or in the problem of vortex motion in superconductors.
References in corpus (7)
- Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
- Studies of Bacterial Branching Growth using Reaction-Diffusion Models for Colonial Development
- Lubricating Bacteria Model for Branching growth of Bacterial Colonies
- Modelling of spatio-temporal patterns in bacterial colonies
- Universal algebraic relaxation of fronts propagating into an unstable state
- Biscale Chaos in Propagating Fronts
- Breakdown of the standard Perturbation Theory and Moving Boundary Approximation for "Pulled" Fronts
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