HR: 0800h
AN: H11C-0655    [Abstracts]
TI: Markov processes for Advection-Diffusion Transport in Non-Smooth Media: Skew Brownian Motion and the Generalized Taylor-Aris Formula.
AU: * Ramirez, J M
EM: jramirez@math.arizona.edu
AF: Department of Mathematics, The University of Arizona, 617 N. Santa Rita Ave. P.O. Box 210089, Tucson, AZ 85721–0089, United States
AU: Thomann, E
EM: thomann@science.oregonstate.edu
AF: Department of Mathematics, Oregon State University, 368 Kidder Hall, Corvallis, OR 97331, United States
AU: Waymire, E
EM: waymire@math.oregonstate.edu
AF: Department of Mathematics, Oregon State University, 368 Kidder Hall, Corvallis, OR 97331, United States
AU: Wood, B
EM: Brian.Wood@oregonstate.edu
AF: Chemical, Biological and Environmental Engineering, Oregon State Universtiy, 102 Gleeson Hall, Corvallis, OR 97331, United States
AU: Chastanet, J
EM: Juliette.Chastanet@imft.fr
AF: Institut de Mécanique des Fluides, 1 allée du Professeur Camille Soula, Toulouse, 31400, France
AU: Haggerty, R
EM: haggertr@science.oregonstate.edu
AF: Geosciences Department, Oregon State University, 104 Wilkinson Hall, Corvallis, OR 97331, United States
AB: Markov processes are used to study advective-diffusive transport of passive solutes in media with non-smooth diffusion tensor D and drift coefficient U. The classical Taylor-Aris formula for the effective dispersion in a cylinder is generalized to the case where U is bounded and D is bounded positive definite; both functions depending only on the transversal spatial coordinate. In the particular case of a two-dimensional arrangement of layers of constant D parallel to the direction of flow, we identify the Markov process modeling the motion of individual particles: in the transversal direction the motion is a generalization of skew Brownian motion; longitudinally the motion is an Itô process with paths depending on the transversal process. At an interface between layers where D takes two different values, the diffusing particles are more likely to go into the medium with the higher value of D. This feature is analytically characterized by the sample path properties of skew Brownian motion. The results are applied to give theoretical foundation to classical particle tracking methods for mass transfer in porous media.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1849 Numerical approximations and analysis
DE: 1869 Stochastic hydrology
DE: 3265 Stochastic processes (3235, 4468, 4475, 7857)
SC: Hydrology [H]
MN: 2007 Fall Meeting