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Excluded volume and order in a system of Brownian needles

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We consider a system of hard-core interacting Brownian needles. Unlike point particles, the finite size and shape of each needle 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 an integro-differential equation for the population density using the method of matched asymptotic expansions and conformal mapping. We present numerical simulations and discuss the limit of large rotational diffusion.

This talk is part of the Fluid Mechanics (DAMTP) series.

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