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Z. Hashin, S. Shtrikman (1962)
A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase MaterialsJournal of Applied Physics, 33
K. Golden, G. Milton (1985)
Thermal Conductivity
G. Milton (1981)
Bounds on the complex permittivity of a two‐component composite materialJournal of Applied Physics, 52
G. A. Baker, P. Graves-Morris (1981)
Padé Approximants, Part I: Basic Theory
S. May, S. Tokarzewski, A. Zachara, B. Cichocki (1994)
Continued fraction representation for the effective thermal conductivity coefficient of a regular two-component compositeInternational Journal of Heat and Mass Transfer, 37
D. J. Bergman (1985)
Les méthodes de l'homogénéisation: théorie et applications en physique
D. Bergman (1979)
The dielectric constant of a simple cubic array of identical spheres
G. Milton, K. Golden (1985)
Thermal Conduction in Composites
J. Gilewicz (1978)
Approximants de PadéMathematics of Computation, 35
D. J. Bergman (1986)
Homogenization and Effective Moduli of Materials and Media
D. Bergman (1993)
Hierarchies of Stieltjes Functions and Their Application to the Calculation of Bounds for the Dielectric Constant of a Two-Component Composite MediumSIAM J. Appl. Math., 53
D. Bergman (1981)
Bounds for the complex dielectric constant of a two-component composite materialPhysical Review B, 23
G. A. Baker, P. Graves-Morris (1981)
Padé Approximants, Part II: Extensions and Applications
B. Felderhof (1984)
Bounds for the complex dielectric constant of a two-phase compositePhysica A-statistical Mechanics and Its Applications, 126
G. Baker (1975)
Essentials of Padé approximants
K. Golden (1986)
Bounds on the complex permittivity of a multicomponent materialJournal of The Mechanics and Physics of Solids, 34
T. B., H. Wall (2000)
Analytic Theory of Continued Fractions
G. Milton (1981)
Bounds on the transport and optical properties of a two‐component composite materialJournal of Applied Physics, 52
J. Keller (1964)
A Theorem on the Conductivity of a Composite MediumJournal of Mathematical Physics, 5
K. Clark, G. Milton (1995)
Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional compositesProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 448
D. Bergman (1978)
The dielectric constant of a composite material—A problem in classical physicsPhysics Reports, 43
K. Mendelson (1975)
A theorem on the effective conductivity of a two‐dimensional heterogeneous mediumJournal of Applied Physics, 46
O. Wiener (1912)
Abhandlungen der mathematisch-physischen Klasse der königlichen sachsischen Gesellschaft der WissenschaftenAbh. Sächs. Akad. Wiss., Leipzig Math.-Naturwiss. Kl., 32
K. Golden, G. Papanicolaou (1983)
Bounds for effective parameters of heterogeneous media by analytic continuationCommunications in Mathematical Physics, 90
B. Cichocki, B. Felderhof (1989)
Electrostatic spectrum and dielectric constant of nonpolar hard sphere fluidsJournal of Chemical Physics, 90
A. Dykhne (1971)
Conductivity of a Two-dimensional Two-phase SystemJournal of Experimental and Theoretical Physics, 32
D. Bergman, K. Dunn (1992)
Bulk effective dielectric constant of a composite with a periodic microgeometry.Physical review. B, Condensed matter, 45 23
G. W. Milton (1981)
Bounds on the transport and optical properties of two-component materialJ. Appl. Phys., 52
K. Schulgasser (1976)
On a phase interchange relationship for composite materialsJournal of Mathematical Physics, 17
A. M. Dykhne (1970)
Conductivity of a two-dimensional two-phase systemZh. Eksp. Teor. Fiz., 59
D. Bergman (1982)
Rigorous bounds for the complex dielectric constant of a two-component compositeAnnals of Physics, 138
R. McPhedran, G. Milton (1981)
Bounds and exact theories for the transport properties of inhomogeneous mediaApplied Physics A, 26
The aim of this contribution is to examine the S-continued fraction method of obtaining bounds on the effective dielectric constant εe of a two-phase composite for the case where the dielectric coefficients ε1and ε2 of both components are either complex or real. The starting point for our study is a power expansion of εe (z) at(z)=0 (z)=ε2/ε1-1. The obtained S-continued fraction bounds have an interesting mathematical structure convenient for theoretical and numerical investigations of εe. They also agree with the earlier estimations reported by Bergman and Milton. Specific examples of calculation of bounds on εe by theS-continued fraction method are also provided.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 15, 2004
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