Coupled-cellular-automata study on stochastic and pattern-formation dynamics under spatiotemporal fluctuation of temperature

Overdamped stochastic process under spatio-temporal fluctuation of temperature is investigated in terms of coupled cellular automata (CA). With this scheme, we study clustering of particles and its pattern formation on a flat substrate. To materialize such a CA, the heat conduction on the surface is represented in terms of hypothetical heat corpuscles (Bosons) that undergo diffusion. Chemical bonding emitts heat corpuscles to the substrate and dissociation absorbs, and thereby they interact with each other in a nonlinear manner. This nonlinear dynamics is treated by means of an interactive set of different CPU’s. The timing of message-exchange between the CPU’s practically determine a diffusion constant of the particles relative to that of the heat corpuscles. The first half of this paper is devoted to establishing the present coupled CA by examining the temperature dependence of the resultant diffusion constant and other quantities. Then, by comparing clustering dynamics on the substrates of fast and slow heat conductivity, we clarify and quantify the effects of spatiotemporal fluctuation of temperature on stochastic dynamics. Besides the spontaneous fluctuation of temperature, we explore the effects of rather artificial heat sources and sinks, the configurations of which can be varied in space-time to control the pattern formation.