FIG. 3.

Rate-equation relaxation vs RD relaxation for A + A → 0 with fixed reaction parameters and varying initial conditions. All systems have k_a = 100 μm²/s, D_tot = 2 μm²/s, σ = 1 nm, and N_A = 1000 particles. Black curves are Smoluchowski prediction from Eq. (4). Solid purple, red, and magenta curves are numerical solutions using FPR, repeated for 50 trajectories, as V changes from 0.25 μm², 1 μm², and 4 μm². Dashed lines are solutions that are best-fit to the rate equation using a fixed rate constant, where the best fit was defined such that A(t)/A₀ = 0.5. The time-dependence deviates from the RD behavior, and the best-fit rate decreases as the volume increases.