ESTIMATING EFFECTIVE PROPERTIES OF COMPOSITES FROM CROSS-SECTIONAL PHOTOGRAPHS

An algorithm is presented for the rapid evaluation of certain function als of three-point correlation functions, measured in a plane. This si mplifies the estimation of effective physical properties of composite materials from cross-sectional photographs via bounds. More precisely, Fourier coefficients of a reduced three-point correlation function ar e expressed as inner products of polyharmonic fields. The polyharmonic fields are evaluated with a polyharmonic version of the fast multipol e method with a CPU requirement proportional to the number p of fields included and to the number N of points in a discretization of the com ponent interfaces. The Fourier coefficients are related to structural parameters which are used in third-order bounds on conductivity and el astic properties. Inclusion of p polyharmonic fields gives structural parameters with an error decaying at least as 1/p(3). In a simple appl ication for disks with p = 10, superalgebraic convergence in 1/N, and a high-order Gaussian quadrature rule for the inner products, the algo rithm gives an error of typically 0.05%. A previous algorithm, involvi ng Monte Carlo integration, gives structural parameters with an error of typically 2%. (C) 1995 Academic Press, Inc.