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Renormalizing chaotic dynamics in fractal porous media with application to microbe motility
Author(s) -
Park Moongyu,
Kleinfelter Natalie,
Cushman John H.
Publication year - 2006
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2005gl024606
Subject(s) - fractal , intermittency , physics , statistical physics , chaotic , diffusion , trajectory , microscale chemistry , classical mechanics , turbulence , mechanics , mathematical analysis , mathematics , computer science , astronomy , artificial intelligence , thermodynamics , mathematics education
Motivated by the need to understand the movement of microbes in natural porous systems and the evolution of their genetic information, a renormalization procedure for motile particles in media with fractal functionality between upper and lower cutoffs is developed and applied to Lévy particles. On the micro scale, particle trajectories are the solution to an integrated stochastic ordinary differential equation (SODE) with Markov, stationary, ergodic drift subject to Lévy diffusion. The Lévy diffusion allows for self‐motile particles. On the meso scale, the trajectory is the solution to an integrated SODE with Lévy drift and diffusion arising from the microscale asymptotics. Lévy drift is associated with the fractal character of the Lagrangian velocity. On the macro scale, the process is driven by the asymptotics of the mesoscale drift without additional diffusion. Renormalized dispersion equations are presented on the meso and macro scales.