Fractal mobile/immobile solute transport

By R. Schumer, David A. Benson, Mark M. Meerschaert, Boris Baeumer. 2003

556 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/cc82c098814051da309ff6124d38e87fc41bb242

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In Civil and Structural Engineering

In Environmental Engineering

Citations in the corpus

A finite element solution for the fractional advection–dispersion equation (2008, background): “Several attempts have been made to model the anomalous transport, including the mobile–immobile (MIM) model [9,44], the multiple-rate and fractal MIM [39,16], the continuous time random walk (CTRW) [5,4], the non-local stochastic transport theories [30,31], and the fractional advection–dispersion eq”
Fractional dispersion in a sand bed river (2010, unknown): “Some of this material may have washed over to the right side of the channel and may be visible in Figure 3 at 170.1 h as a bump in the concentration profile behind the peak at about 100 feet (30.5 m). Modeling dispersive transport with extended rest periods may require a differential equation that i”
Modeling non‐Fickian transport in geological formations as a continuous time random walk (2006, background): “[225] In contrast to the temporal FDE a spatial FDE assumes a transition time distribution y(t) with a finite first moment and a transition length distribution p(s) with a diverging second moment.”
A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations (2009, methodology): “[31] we write the MRMT equations of contaminant transport:”
Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model (2015, methodology): “…a/mkv r @2cmðr; tÞ @r2 50: (17) It has been shown that the MRMT model is equivalent to CTRW models characterized by uncoupled transition length and time distributions, and to time fractional advection-dispersion models [Dentz and Berkowitz, 2003; Schumer et al., 2003; Benson and Meerschaert, 2009].”
FracFit: A robust parameter estimation tool for fractional calculus models (2017, methodology): “The goal of this paper is to describe a new toolbox for fractional advection-dispersion models [Liu et al., 2003; Schumer et al., 2003; Meerschaert et al., 2008].”
Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations (2016, background): “1), and to [21, 28] for that of the multi-term (i.”
Non‐Fickian transport in homogeneous unsaturated repacked sand (2004, background): “[15] It has recently been shown that multiple-rate, or power law waiting time, MIM models are equivalent to CTRW [Dentz and Berkowitz, 2003; Schumer et al., 2003] when the transition length and time distribution density decouple [Dentz and Berkowitz, 2003].”
Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, methodology): “Previous research [20,47,128] established a connection between CTRW and MRMT models.”