Mathematical modeling and numerical computation of narrow escape problems.

摘要: The narrow escape problem refers to the of calculating mean first passage time (MFPT) needed for an average Brownian particle leave a domain with insulating boundary containing N small well-separated absorbing windows, or traps. This satisfies Poisson partial differential equation subject mixed Dirichlet-Neumann condition on boundary, Dirichlet corresponding In limit total trap size, common asymptotic theory is presented calculate MFPT in two-dimensional domains and unit sphere. formulas depend mutual locations, allowing global optimization locations. Although was developed asymptotically radii, under assumption that traps are well-separated, comprehensive study involving comparison full numerical simulations shows results within 1% accuracy even when size only moderately small, may be rather close together. agreement between at finite, not necessarily values clearly illustrates one key side benefits based systematic analysis. addition, sphere, given optimal configuration collection surface sphere minimizes MFPT. case identical pattern two different sizes considered. effect fragmentation also discussed.