Proceedings of the Workshop "Ongoing Paleoclimatic Studies in the Northern Great Basin," Reno, Nevada, May 1993

Benson, Larry

doi:10.3133/cir1119

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1999

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“…Di usion equations that use fractional derivatives are attractive because they describe a wealth of continuous time random walks (CTRW 1]) that are good models of transport in real systems 2,3,4,5]. Solutions to the fractional di usion equations are L evy motions, a generalization of Brownian motion using -stable distributions 6].…”

Section: Introductionmentioning

confidence: 99%

Multidimensional advection and fractional dispersion

1999

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Extension of the fractional diffusion equation to two or three dimensions is not as simple as extension of the second-order equation. This is revealed by the solutions of the equations: unlike the Gaussian, the most general stable vector cannot be generated with an atomistic measure on the coordinate axes. A random combination of maximally skewed stable variables on the unit sphere generates a stable vector that is a general model of a diffusing particle. Subsets are symmetric stable vectors that have previously appeared in the literature and the well-known multidimensional Brownian motion. A multidimensional fractional differential operator is defined in the process.

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Section: Introductionmentioning

confidence: 99%