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Abstract: We analyze a pair of diffusion equations which are derived in the infinitesystem-size limit from a microscopic, individual-based, stochastic model.Deviations from the conventional Fickian picture are found which ultimatelyrelate to the depletion of resources on which the particles rely. Themacroscopic equations are studied both analytically and numerically, and areshown to yield anomalous diffusion which does not follow a power law with time,as is frequently assumed when fitting data for such phenomena. These anomaliesare here understood within a consistent dynamical picture which applies to awide range of physical and biological systems, underlining the need for clearlydefined mechanisms which are systematically analyzed to give definitepredictions.

Author: Duccio Fanelli, Alan J. McKane

Source: https://arxiv.org/

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