Review of Levy Flights

If Levy flights occur, the variance increases faster than just linearly with time. The variance denotes the typical size of a group of random walkers, and is the average of the squares of the distance moved minus square of the average of the distance moved. D is the rate at which the variance grows. Diffusion is faster in watery hemolymph (large diffusion constant) than in hemolymph of high osmolality (small diffusion constant). Volume changes in the hemocoel complicate these relationships.

If variance equals time raised to some exponent, the exponent being one for normal diffusion, this exponent is larger than one, but usually less than two, during a Levy flight. Superdiffusion is when the exponent is greater than one but less than two. Having an exponent of two would mean that all random walkers were moving apart from each other at a constant rate as might occur in an explosion. We still must learn what role, if any, Levy flight dynamics and superdiffusion play in the bee's hemocoel (Ref: Levy Flight Dynamics).

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