Figure 12.

Left: 100 rounds of drift potential-stepping ring evolution using an explicit tau-leaping inner Gillespie simulator with N=200; nodal redistribution is performed every ten reverse ring integration (coarse Euler) steps. The ring is initially centered at (−1,−1). Fifty replica Gillespie simulation runs are performed, each run with 10 000 particles and the explicit tau-leaping parameter ϵ=0.03. For the reverse integration ΔV=5×10⁻². Contours of the function V(x,y) [defined in Eq. 3.9] are shown. Right: 3D view of reverse ring integration shown left with estimated potential of each node shown according to the color bar. Evolving ring nodes with x<−1.2 are omitted for clarity. Contours of the function V(x,y) [defined in Eq. 3.9] are shown in 3D. Points on a single representative potential contour (as computed using reverse integration) are plotted as black symbols in the V(x,y)=−10 plane at the base of the figure; points along the actual potential contour are shown as red symbols.