Search for a small egg by spermatozoa in restricted geometries

摘要: The search by swimmers for a small target in bounded domain is ubiquitous cellular biology, where prominent case that of the spermatozoa an egg uterus. This one severest selection processes animal reproduction. We present here mathematical model search, its analysis, and numerical simulations. In proposed swimmers’ trajectories are rectilinear speed constant. When trajectory hits obstacle or boundary, it reflected at random angle continues with same speed. Because hitting rare event, asymptotic approximations stochastic simulations needed to estimate mean time various geometries. consider searches disk, convex planar domains, domains cusps. exploration parameter space motion different uterus geometries leads scaling laws process.