Flux calculations of percolating particles in 2D space

Abstract

We model the percolation of particles through an H x W barrier region (β) using rules in a cellular automata (CA) model. Barriers are introduced in β with probability ρ ε[0,1). Particles are free to move from one site downwards to an unoccupied site simulating the fall of particles with constant velocity. Particles cannot move to a blocked site but can alternatively move to either the left or right diagonal bottom with equal chances if both are possible. We introduce a constant influx of particles at the topmost part of β. The outflux Φ(t) of particles at the bottom of β per iteration time t is analyzed for different height H and barrier density ρ. We fit the resulting Φ(t) with the Hill function and we relate the function parameters to system parameters: a) saturation value, b) delay time before the half-maximum flux, and c) degree of cooperation between blocked cells.