| Abstract
| - The article presents studies on the Taylor transport in disordered systems. We assume that a moving particlecan exist in different states and that for each state its transport properties are described by a different linearevolution operator. The transition from one state to another is described by a Markov process in continuoustime. The transition rates of the Markov process depend on a set of variable parameters that are randomlyselected from a known probability density. This type of transport model is of interest in connection with thestudy of multiphasic transport, for example, in the case of chromatographic separation, neutron migration innuclear reactions, or neutrino flow in astrophysical problems. We consider two different types of effectivemedium approximations: (1) a global approach, which consists of solving the Taylor problem for a given setof values of the of the random parameters, followed by averaging the result, and (2) a local approach, forwhich the averaging is done for small macroscopic regions of the system, which leads to a system of age-dependent master equations. We show that the averaging in the global approach induces an artificial collectivebehavior that results in ballistic diffusion. The local approach may lead either to normal or dispersive transport.We apply our theory to the experiment of Drazer and Zanette (Phys. Rev. E.1999, 60, 5858) and show thatthat the local approach is in agreement with experimental data.
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