Compartment-based stochastic diffusion

Compartment-based stochastic diffusion represents molecular motion by nearest-neighbour jumps on a spatial lattice. Jump rates of order $D/h^2\pm v/(2h)$ converge to an advection--diffusion equation as compartment width $h$ tends to zero.

The asymmetric simple exclusion process permits at most one particle per lattice site and biases jumps in one direction. A mean-field hydrodynamic limit has advective flux proportional to $c(1-c)$ because both an occupied departure site and vacant arrival site are required.