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November 2013 Advection–Dispersion Across Interfaces
Jorge M. Ramirez, Enrique A. Thomann, Edward C. Waymire
Statist. Sci. 28(4): 487-509 (November 2013). DOI: 10.1214/13-STS442

Abstract

This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with formulations in terms of partial differential equations governing the conservative, advective-dispersive transport of mass concentrations in divergence form, the specific interfacial heterogeneities are introduced in terms of (spatial) discontinuities in the diffusion coefficient across a lower-dimensional hypersurface. A pathway to an equivalent stochastic formulation is then developed with special attention to the interfacial effects in various functionals such as first passage times, occupation times and local times. That an appreciable theory is achievable within a framework of applications involving one-dimensional models having piecewise constant coefficients greatly facilitates our goal of a gentle introduction to some rather dramatic mathematical consequences of interfacial effects that can be used to predict structure and to inform modeling.

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Jorge M. Ramirez. Enrique A. Thomann. Edward C. Waymire. "Advection–Dispersion Across Interfaces." Statist. Sci. 28 (4) 487 - 509, November 2013. https://doi.org/10.1214/13-STS442

Information

Published: November 2013
First available in Project Euclid: 3 December 2013

zbMATH: 1331.60003
MathSciNet: MR3161584
Digital Object Identifier: 10.1214/13-STS442

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.28 • No. 4 • November 2013
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