A RESUME OF NONLOCAL TRANSPORT THEORIES

Analysis from a number of different perspectives has shown diffusion a nd dispersion in natural porous formations to generally be nonlocal in character, i.e., the mass balance involves integro-partial differenti al equations. Only in certain asymptotic limits do these laws localize to classical partial differential equations. Compiled within is a res ume of nonlocal laws that our group has developed over the last few ye ars for systems with physical, chemical and biological heterogeneity. Analytical tools used to obtain these laws are nonequilibrium and equi librium statistical mechanics, and first-order spectral-perturbation m ethods. This paper is an expansion of the material presented at the Wa terloo conference held in the memory of Dr. Unny.