title: Spatial Markov model of anomalous transport through random lattice networks.
abstract: Flow through lattice networks with quenched disorder exhibits a strong correlation in the velocity field, even if the link transmissivities are uncorrelated. This feature, which is a consequence of the divergence-free constraint, induces anomalous transport of passive particles carried by the flow. We propose a Lagrangian statistical model that takes the form of a continuous time random walk with correlated velocities derived from a genuinely multidimensional Markov process in space. The model captures the anomalous (non-Fickian) longitudinal and transverse spreading, and the tail of the mean first-passage time observed in the Monte Carlo simulations of particle transport. We show that reproducing these fundamental aspects of transport in disordered systems requires honoring the correlation in the Lagrangian velocity.
authors: Massachusetts Institute of Technology, 77 Massachusetts Ave, Building 48, Cambridge, Massachusetts 02139, USA.
authors: Peter K
authors: PK
authors: Kang
authors: Marco
authors: M
authors: Dentz
authors: Tanguy
authors: T
authors: Le Borgne
authors: Ruben
authors: R
authors: Juanes
mesh_terms: D001692:Biological Transport; D003198:Computer Simulation; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D013997:Time Factors