S-continued fractions for complex transport coefficients of two-phase composites - Tokarzewski, Stanisław; Telega, Józef Joachim (Computer Assisted Methods in Engineering and Science, 2023)
We examine S-continued fraction bounds on the effective dielectric constant ee of a two-phase composite for the case where the dielectric coefficients e1 and e2 are complex. The starting point for our study is a power series expansion of e(z) at Z = 0, Z = e2/e 1-1. The S-continued fractions to the expansions of e(z) have an interesting mathematical structure. Its convergents represent the best bounds derived earlier by Milton [24-25], and independently by Bergman [5] . Specific examples of calculation of complex S-continued fraction bounds on ee are provided.