Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests

By David A. Benson, R. Schumer, Mark M. Meerschaert, S. Wheatcraft. 2001

476 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/3425cb5dd9c0a0c7ed1df8693a91c6b99ac86f05

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In Civil and Structural Engineering

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Citations in the corpus

Possible problems of scale dependency in applications of the three‐dimensional fractional advection‐dispersion equation to natural porous media (2002, methodology): “…explanation for the observed scale dependence of the traditional dispersivity is that the resulting dispersion is based on the mechanics of Brownian motion [Benson et al., 2000, 2001], while macroscopic random trajectories in heterogeneous porous media may be better described by Levy motion.”
Parameter estimation for fractional transport: A particle‐tracking approach (2009, methodology): “Note that the simulated conductivity field is multiscale lognormal, while the MADE conductivity field exhibits heavier tails [Benson et al., 2001].”
Multiscaling fractional advection‐dispersion equations and their solutions (2003, methodology): “The meaning of the parameters in a compound Poisson process, a subset of CTRWs, is used to develop a physical interpretation of the equation variables.”
Fractional advection‐dispersion equations for modeling transport at the Earth surface (2009, background): “The diffusion term Z(t) = t1/aSa (0, 1, a, b) exhibits nonFickian scaling, a characteristic often seen in laboratory and field studies [Benson et al., 2000a, 2000b, 2001].”
VECTOR GRÜNWALD FORMULA FOR FRACTIONAL DERIVATIVES (2004, background): “Introduction Fractional derivatives have been around for centuries [22, 26] but recently they have found new applications in physics [2, 6, 7, 9, 15, 18, 19, 29], hydrology [1, 4, 5, 10, 14, 28], and finance [24, 25, 27].”
TEMPERED FRACTIONAL CALCULUS (2015, background): “…and Probability, Michigan State University, East Lansing, MI 48823, United States b School of Sciences, Jimei University, Xiamen, Fujian, 361021, China a r t i c l e i n f o a b s t r a c t Article history: Received 17 February 2014 Received in revised form 3 April 2014 Accepted 7 April 2014…”
Fractional conservation of mass (2008, background): “applications of fractional calculus to flow and transport in porous media [ 3 ,5,11] suggest that a reflects the degree of heterogeneity in the porous medium.”