A CONTINUED-FRACTION REPRESENTATION FOR THE EFFECTIVE CONDUCTIVITY OFA 2-DIMENSIONAL POLYCRYSTAL

A continued fraction representation for the effective conductivity ten sor sigma of a two-dimensional polycrystal is derived. This represent ation is in terms of a sequence of positive definite symmetric matrice s which characterize the underlying geometric structure of the materia l. The proof is accomplished by considering a particular basis for the Hilbert space of fields in the composite in which the linear operator s relevant to determining the effective conductivity take simple forms as infinite matrices. These infinite matrices are then used in the va riational definition of the effective conductivity to formulate the co ntinued fraction. This continued fraction is used to derive upper and lower bounds on sigma. (C) 1997 American Institute of Physics.