Collision avoidance strategies for a game with three players, two pursuers and one evader, are constructed by determining the semi-permeable curves that form the barrier. The vehicles are assumed to have the same capabilities, speed and turn-rates. The game is assumed to be played on a two-dimensional plane. The usable part and its boundary are first determined along with the strategy along the...

The diffusion equation is the primary tool to study movement dynamics of a free Brownian particle, but when spatial heterogeneities in form permeable interfaces are present, no fundamental has been derived. Here we obtain such an from microscopic description using lattice random walk model. sought after Fokker-Planck and corresponding backward Kolmogorov employed investigate first-passage local...