GREEN'S FUNCTION FORMALISM IN GENERALIZED TAYLOR DISPERSION THEORY†

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Abstract
Green's function formalism is applied to obtain the asymptotically long-time solution of the multidimensional, phase-space, convective-diffusion equation governing transport and temporal evolution of the conditional probability density P of a Brownian tracer particle. In the long-time limit, P (as well as its infinite sequence of polyadic moments) is shown to be derivable from a pair of time-independent scalar fields characterizing the local-space transport process. These two functions are employed to obtain the global phenomenological coefficients occurring in the physical-space (global) equation governing the asymptotically long-time, locally-averaged, conditional probability density distribution

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