Abstract

We consider a system of nonoverlapping Brownian needles in two dimensions. Unlike point particles, the needles’ size and shape influence the system’s evolution. We explore the effects of excluded volume and anisotropy at the population level. Since needles exclude less volume if aligned, can excluded-volume effects alone induce order in the system? Starting from the stochastic particle system, we derive a nonlocal nonlinear partial differential equation for the population density using the methods of matched asymptotic expansions and conformal mapping. Finally, we show some numerical simulations and two model reductions.