Advection-Dispersion Across Interfaces
arXiv:1310.7643 · 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.
Published in at http://dx.doi.org/10.1214/13-STS442 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (6)
- On the constructions of the skew Brownian motion
- Green's functions for Sturm-Liouville problems on directed tree graphs
- A uniqueness theorem for the martingale problem describing a diffusion in media with membranes
- Numerical Methods for Linear Diffusion Equations in the Presence of an Interface
- Interfacial Phenomena and Natural Local Time
- On The Drift Paradox in a Regime-Switching Model