Asymmetric spreading in highly advective, disordered environments

John H. Carpenter; Karin A. Dahmen

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arXiv · physics/0501123

Asymmetric spreading in highly advective, disordered environments

John H. Carpenter·Karin A. Dahmen

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Abstract

Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and super-diffusive spreading. A perturbation analysis yields a crossover time between diffusive and super-diffusive behavior. The time's dependence on the convection velocity and disorder is tested. Like the simplified equation, the full linear reaction-diffusion equation displays super-diffusive spreading perpendicular to the convection. However, for mean positive growth rates the full nonlinear reaction-diffusion equation produces symmetric spreading with a Fisher wavefront, whereas net negative growth rates cause an asymmetry, with a slower wavefront velocity perpendicular to the convection.

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John H. Carpenter, Karin A. Dahmen. 2005-01-22. Asymmetric spreading in highly advective, disordered environments. https://arxiv.org/abs/physics/0501123

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