CLUSTERING OF ACTIVE WALKERS IN A 2-COMPONENT SYSTEM

This paper investigates the agglomeration of active walkers (component A) on a two-dimensional surface, described by a potential U(r,t), that determines the motion of the walkers. The walkers are able to change U(r,t) locally by producing a second component B, that decreases U(r,t) and which can diffuse and decompose. The nonlinear feedback between the spatio-temporal density distributions of both components results in a clustering of the walkers. The analytic description is based on a set of Langevin and Fokker-Planck equations for the active walkers, coupled by a reaction-diffusion equation for the component B. We investigate the stability of homogeneous solutions, the selection equation and an effective diffusion coefficient, which is negative in the case of the agglomeration process. Computer simulations demonstrate the time evolution of the surface potential at two different time scales: the scale of independent growth and of competition of the attraction regions. They also show the time-dependent distribution of the active walkers and spatio-temporal development of the effective diffusion coefficient.