Radial propagation in population dynamics with density-dependent diffusion.

Population dynamics that evolve in a radial symmetric geometry are investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate analytical solution to this equation is found.

Self-similar dynamics of bacterial chemotaxis.

Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in a bacterial colony is investigated theoretically through a continuum model that considers chemotaxis.

Self-similar solutions to a density-dependent reaction-diffusion model.

In this paper, we investigated a density-dependent reaction-diffusion equation, u(t)=(u(m))(xx)+u-u(m). This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation, which is widely used in population dynamics, combustion theory, and plasma physics. By employing a suitable transformation, this equation was mapped to the anomalous diffusion equation where the nonlinear reaction term was eliminated.

Mesoscale modeling technique for studying the dynamics oscillation of Min protein: pattern formation analysis with lattice Boltzmann method.

We presented an application of the Lattice Boltzmann method (LBM) to study the dynamics of Min proteins oscillations in Escherichia coli. The oscillations involve MinC, MinD and MinE proteins, which are required for proper placement of the division septum in the middle of a bacterial cell. Here, the LBM is applied to a set of the deterministic reaction diffusion equations which describes the dynamics of the Min proteins.