S-continued fractions for complex transport coefficients of two-phase composites
Abstract
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.
Keywords
References
[1] G.A. Baker. Essentials of Padé Approximants. Academic Press, London, 1975.[2] G.A. Baker, P. Graves-Morris. Padé Approximants, Part I: Basic Theory. Encyclopedia of Mathematics and its Applications, 13, Addison- Wesley Publ. Co., London, 1981.
[3] G.A. Baker, P. Graves-Morris. Padé Approximants, Part II: Extensions and Applications. Encyclopedia of Math· ematics and its Applications, 14, Addison-Wesley Publ. Co., London, 1981.
[4] D.J. Bergman. The dielectric constant of a composite material - A problem in classical physics, Phys. Rep., 43: 377- 407, 1978.
[5] D.J . Bergman. Rigorous bounds for the complex dielectric constant of a two-component composite. Ann. Phys., 138: 78-114, 1982.
Published
Jul 14, 2023
How to Cite
TOKARZEWSKI, Stanisław; TELEGA, Józef Joachim.
S-continued fractions for complex transport coefficients of two-phase composites.
Computer Assisted Methods in Engineering and Science, [S.l.], v. 3, n. 2, p. 109-119, july 2023.
ISSN 2956-5839.
Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1449>. Date accessed: 31 dec. 2024.
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