Figure 2.

Capture times for a random walker in the presence of one target but no traps. (a) Log-log plot of the Montroll capture time t_M as a function of the target concentration C_T = 1/N for the two-dimensional case (triangular and square lattices) and the three-dimensional case (simple cubic lattice), from Eqs. 6 and 7 with coefficients given in the text. For the two-dimensional lattices, the theoretical results and the numerical results of Kozak are indistinguishable on the scale of this figure. (b) Scaled Monte Carlo capture times for the cubic lattice t_M(3D)/N as a function of log N, and least-squares fit Eq. 7. Horizontal line, theoretical asymptotic limit imposed by Eq. 7.