Computing the distribution of displacements due to swimming microorganisms
نویسنده
چکیده
with n = N/V the number density of swimmers. This is nonzero (and might diverge) in the limit V → ∞, reflecting the cumulative effect of multiple swimmers. Note that this expression is exact, within the problem assumptions: it doesn’t even require N to be large. It is not at all clear that (4) leads to diffusive behavior, but it does [2–4]: the “support” of the drift function ∆(η, t) typically grows in time: that is, the longer we wait, the larger the number of particles displaced by the swimmer. The rate of convergence to Gaussian can be estimated from
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