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Advection–Dispersion Across Interfaces

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https://ir.library.oregonstate.edu/concern/articles/qj72p930v

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  • 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.
  • This is the publisher’s final pdf. The published article is copyrighted by the Institute of Mathematical Statistics and can be found at: http://www.imstat.org/sts/.
  • Keywords: Mathematical ecology, Insect dispersion, Interface, Local time, Solute transport, Heterogeneous dispersion, River network dispersion, Breakthrough curve, Occupation time, Skew Brownian motion, Ocean upwelling
  • Keywords: Mathematical ecology, Insect dispersion, Interface, Local time, Solute transport, Heterogeneous dispersion, River network dispersion, Breakthrough curve, Occupation time, Skew Brownian motion, Ocean upwelling
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  • 28
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  • 4
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  • Professor Enrique Thomann acknowledgesfellowship support of the NSF Institute forMathematics and its Applications at the University ofMinnesota during the academic year 2012–2013. Theauthors Thomann and Waymire were supported in partby NSF Grants DMS-11-22699 and DMS-10-31251.
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