Recent results on the mathematical and experimental analysis of the transport of contaminants suspended in highly heterogeneous media demonstrate surprising consequences for the structure of passage times and breakthrough curves. The location of these discontinuities, referred to as interfaces, are described as hypersurfaces in the corresponding spatial domain. As a result, specific asymmetries appear in the breakthrough curves that were rigorously shown by the authors to result from the interface condition. On the other hand, the same interfacial principles are not generally applicable to other examples, leading to considerations of a richer class of possible interfacial conditions and, as a result, other consequences for the structure of the basic passage time functionals. Other examples, including dispersion of larvae in river networks, butterfly dispersal in patchy floral environments, and localized patterns of chlorophyll blooms associated with the upwelling due to sharp coastal shelf break will also be illustrated in this context.
Keywords: first passage time; interface; heterogeneity; skew Brownian motion
Biography: Professor Ed Waymire is a Professor of Mathematics and of Statistics at Oregon State University. He works in areas of stochastic processes and their applications in the physical and biological sciences.