Solution of Transport Schemes on Fractals by Means of Green Function Renormalization — Application to Integral Quantities

Abstract

Green function renormalization is applied to obtain exact recursions for integral quantities and integral transforms of concentration fields, involving a summation over a manifold of lattice sites or over the entire lattice. Definition of the Fourier transform of the Green functions, to some extent equivalent to the dynamic structure factor, is extremely useful to obtain quantitative information on the spatial behavior of concentration profiles and eigenfunctions. Some preliminary results on sorption properties of product lattices are presented. The application of anisotropic lattice models to study the volume-to-surface effects in adsorption and reaction is discussed. The properties of the Green function generating function are also analyzed.