Non‐Fickian (or anomalous) transport of contaminants has been observed at field and
laboratory scales in a wide variety of porous and fractured geological formations. Over many …

Almost a century ago, Lévy (1925) first explored stable distributions in his study of sums of
random terms. The basic mathematical facts about stable laws were described in the …

Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

Two distinct but interconnected approaches can be used to model diffusion in fluids; the first
focuses on dynamics of an individual particle, while the second deals with collective …

Over the last few decades a number of powerful approaches have been developed to
intelligently reduce the number of degrees of freedom in very complex heterogeneous …

Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik,
2000a, b) were fi rst used in the time domain; they are here considered in the space domain …

Coherent structures/motions in turbulence inherently give rise to intermittent signals with
sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the …

In this paper we consider multicomponent mass transport in porous media for non-dilute
solutions. This process is described by coupled, nonlinear transport equations that must be …

In paper I [Phys. Fluids 13, 75 (2001)] we provided a theory for simulating anomalous
dispersion which relied on the self-part of the intermediate scattering function. Here we …

Spatially nonlocal transport describes the evolution of solute concentration due to mass
transfer over long ranges. Such long-range mass transfer, present in many flow situations …