Figure 1.

Schematics for (a) the pseudo-compartment method and the (b) the ghost cell method. The green line represents the PDE solution, the blue boxes the number of particles in the mesoscopic region of the respective hybrid methods, and the yellow dots denote the Brownian particles. These particles are shown with a volume, but in the simulations do not have a mass or volume. In the scenario illustrated, the particles reside on the one-dimensional line, but have been illustrated in the plane in order to show the directions and magnitudes of their next movement clearly (black arrows). The green boxes in (a) denote the number of particles in the pseudo-compartment, and similarly, the yellow boxes in (b) are the number of particles in the ghost cell, with each box representing a single particle. In each case, the red line denotes the point interface between the two regimes.