The Narrow Capture Problem with Partially Absorbing Targets and Stochastic Resetting

We consider a particle undergoing diffusion with stochastic resetting in bounded domain for . The is perforated by set of partially absorbing spherical targets within which the may be absorbed at rate Each target assumed to much smaller than , allows us use asymptotic and Green’s function methods solve equation Laplace space. In particular, we construct an inner solution interior local exterior each match it outer bulk This yields expansion transformed flux into powers respectively, where nondimensionalized size. fluxes determine how mean first passage time (MFPT) absorption depends on reaction For range parameter values, MFPT unimodal minimum optimal that configuration.