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    Fractional diffusion equation for an n-dimensional correlated Lévy walk. 
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    Fractional diffusion equation for an n-dimensional correlated Lévy walk.

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    Accepted version (342.1Kb)
    Volume
    94
    Pagination
    012104 - ?
    DOI
    10.1103/PhysRevE.94.012104
    Journal
    Phys Rev E
    Issue
    1-1
    Metadata
    Show full item record
    Abstract
    Lévy walks define a fundamental concept in random walk theory that allows one to model diffusive spreading faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion equation for an n-dimensional correlated Lévy walk remained elusive. Starting from a fractional Klein-Kramers equation here we use a moment method combined with a Cattaneo approximation to derive a fractional diffusion equation for superdiffusive short-range auto-correlated Lévy walks in the large time limit, and we solve it. Our derivation discloses different dynamical mechanisms leading to correlated Lévy walk diffusion in terms of quantities that can be measured experimentally.
    Authors
    Taylor-King, JP; Klages, R; Fedotov, S; Van Gorder, RA
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/13058
    Collections
    • Mathematics [1264]
    Language
    eng
    Licence information
    http://arxiv.org/abs/1606.03395
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