Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis.
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Olsen et al. (2024) studied this question.
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