Levy Motions and Microbial Dynamics in Fractal Porous Media

Dr. Moongyu Park

Department of Earth and Atmospheric Sciences
Purdue University

February 10, 2006
202 Madison Hall
1:00 PM (Coffee and Cookies at 12:30)

Abstract

My research is motivated by the need to understand the movement of microbes in natural porous systems and the evolution of their genetic information. Many researchers are studying cell scale phenomena of the problems and publishing many papers. But the global effect has not been studied. Therefore, our group has been developing upscaling procedures for motile particles in media with fractal functionality between upper and lower cutoffs and applied to Levy 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 Levy diffusion. The Levy diffusion allows for self-motile particles. On the meso scale, the trajectory is the solution to an integrated SODE with Levy drift and diffusion arising from the micro scale asymptotics. Levy drift is associated with the fractal character of the Lagrangian velocity. On the macro scale, the process is driven by the asymptotics of the meso scale drift without additional diffusion. The upscaled dispersion equation contains a fractional derivative term.