S-continued fractions for complex transport coefficients of two-phase composites

Computer Assisted Mechanics and Engineering Sciences

Volumn 3, Issue 2, 1996, Pages 109-119

  Tokarzewski, Stanislaw ^a   Telega, Józef Joachim ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; MICROSTRUCTURE; PERMITTIVITY;

POWER SERIES EXPANSION; S CONTINUED FRACTIONS;

COMPOSITE MATERIALS;

EID: 0029715818     PISSN: 1232308X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

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 Mathematics 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.
6. D.J. Bergman. Hierarchies of Stieltjes functions and their application to the calculation of bounds for the dielectric constant of a two-components composite medium. SIAM J. Appl. Math., 53: 915-930, 1993.
7. D.J. Bergman. The effective electric coefficient of a composite medium: Rigorous bounds from analytic properties. In: J.L. Ericksen, D. Kinderlehrer, R. Kohn, J.L. Lions, eds., Homogenization and Effective Moduli of Materials and Media, 27-51, Springer-Verlag, New York, 1986.
8. D.J. Bergman. Bounds for the complex dielectric constant of a two-component composite material. Phys. Rev. B, 23: 3058-3065, 1981.
9. D.J. Bergman. The dielectric constant of a simple cubic array of identical spheres. J. Phys. C, 12: 4947-4960, 1979.
10. D.J. Bergman. Bulk physical properties of composite media, In: Les Méthodes de l Homogénéisation: Théorie et Applications en Physique, pp. 1-128, Ed. Eyrolles, Paris, 1985.
11. D.J. Bergman, K.J. Dunn. Bulk effective dielectric constant of a composite with periodic microgeometry. Phys. Rev. B, 45: 3262-13271, 1992.
12. B. Cichocki, B.U. Felderhof. Electrostatic spectrum and dielectric constant of nonpolar hard sphere fluids. J. Chem. Phys., 90: 4960-4967, 1989.
13. K.E. Clark, G.W. Milton. Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional composites. Proc. Roy. Soc. London A, 448: 161-190, 1995.
14. A.M. Dykhne. Conductivity of a two-dimensional two-phase system (in Russian). Zh. Eksp. Teor. Fiz., 59: 110-115, 1970.
15. B.U. Felderhof. Bounds for the complex dielectric constant of a two-phase composite. Physica A, 126: 430-442, 1984.
16. J. Gilewicz. Approximants de Padé. Springer-Verlag, Berlin, 1978.
17. K. Golden. Bounds on the complex permittivity of a multi-components material. J. Mech. Phys. Solids, 34: 333-358, 1986.
18. K. Golden and G. Papanicolaou. Bounds for effective parameters of heterogeneous media by analytic continuation. Comm. Math. Phys., 90: 473-491, 1983.
19. Z. Hashin, S. Shtrikman. A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys., 33: 3125-3131, 1962.
20. J.B. Keller. A theorem on the conductivity of a composite medium. J. Math. Phys., 5: 548-549, 1964.
21. S. May, S. Tokarzewski, A. Zachara, B. Cichocki. Continued fraction representation for the effective thermal conductivity coefficient of a periodic two component composite. Int. J. of Heat and Mass Transf., 37: 2165-2173, 1994.
22. R.C. McPhedran, G.W. Milton. Bounds and exact theories for the transport properties of inhomogeneous media. Appl. Phys. A, 26 207-220, 1981.
23. K.S. Mendelson. A theorem on the effective conductivity of two-dimensional heterogeneous medium. J. Appl. Phys., 46: 4740-4741, 1975.
24. G.W. Milton. Bounds on the complex permittivity of a two-component composite material. J. Appl. Phys., 52: 5286-5293, 1981.
25. G.W. Milton. Bounds on the transport and optical properties of two-component material. J. Appl. Phys., 52: 5294-5304, 1981.
26. K. Schulgasser. On a phase interchange relationship for composite materials. J. Math. Phys., 17: 378-381, 1976.
27. S. Tokarzewski, J. Blawzdziewicz, I.V. Andrianov. Effective conductivity of densely packed highly conducting cylinders. Appl. Phys., A 59: 601-604, 1994.
28. S.Tokarzewski, J.J.Telega. S-continued fraction bounds for real effective moduli of two-phase composite materials (submitted).
29. S. Tokarzewski, J.J. Telega. S-continued fraction representation for effective transport coefficients of two-phase media, IFTR Reports, 16/95.
30. H.S. Wall. Analytic Theory of Continued Fractions. New York, Van Nostrand, 1948.
31. O. Wiener. Abhandlungen der mathematisch-physischen Klasse der königlichen sachsischen Gesellschaft der Wissenschaften. Abh. Sächs. Akad. Wiss. Leipzig Math.-Naturwiss. Kl, 32: 509, 1912.