Bounds for effective parameters of multicomponent media by analytic continuation

Recently D. Bergman introduced a method for obtaining bounds for the effective dielectric constant (or conductivity) of a two-component medium. This method does not rely on a variational principle but instead exploits the properties of the effective parameter as an analytic function of the ratio of the component parameters. We extend the method to multicomponent media using techniques of several complex variables.

[1]  D. J. Bergman,et al.  Bounds for the complex dielectric constant of a two-component composite material , 1981 .

[2]  Graeme W. Milton,et al.  Bounds on the complex permittivity of a two‐component composite material , 1981 .

[3]  S. Shtrikman,et al.  A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials , 1962 .

[4]  R. McPhedran,et al.  A comparison of two methods for deriving bounds on the effective conductivity of composites , 1982 .

[5]  Graeme W. Milton,et al.  Bounds on the transport and optical properties of a two‐component composite material , 1981 .

[6]  Graeme W. Milton,et al.  Bounds on the Electromagnetic, Elastic, and Other Properties of Two-Component Composites , 1981 .

[7]  On a phase interchange relationship for composite materials , 1976 .

[8]  G. Milton,et al.  Thermal Conduction in Composites , 1985 .

[9]  David J. Bergman,et al.  Rigorous bounds for the complex dielectric constant of a two-component composite , 1982 .

[10]  D. Bergman.  Resonances in the bulk properties of composite media — theory and applications , 1982 .

[11]  G. A. Baker.  Best Error Bounds for Padé Approximants to Convergent Series of Stieltjes , 1969 .

[12]  B. U. Felderhof.  Bounds for the complex dielectric constant of a two-phase composite , 1984 .

[13]  G. A. Baker.  Essentials of Padé approximants , 1975 .

[14]  A. Korányi,et al.  Holomorphic functions with positive real part on polycylinders , 1963 .

[15]  Joseph B. Keller,et al.  A Theorem on the Conductivity of a Composite Medium , 1964 .

[16]  Holonomic functions in a polycircle with nonnegative imaginary part , 1974 .

[17]  David J. Bergman,et al.  The dielectric constant of a simple cubic array of identical spheres , 1979 .

[18]  Kenneth M. Golden,et al.  Bounds on the complex permittivity of a multicomponent material , 1986 .

[19]  N. Akhiezer,et al.  The Classical Moment Problem. , 1968 .

[20]  F. Smithies.  Theory of Linear Operators in Hilbert Space. By N. I. Akhiezer and I. M. Glazman. Vol. 1, 50s. Vol. 2, 60a. 1964. (Constable) , 1966 .

[21]  H. Wenzel.  W. Rudin, Function Theory in Polydiscs. IX + 188 S. New York/Amsterdam 1969. W. A. Benjamin, Inc. Preis geb. £12.50 , 1973 .

[22]  David R. Smith,et al.  Thermal Conductivity 18 , 1985 .

[23]  George Papanicolaou,et al.  Bounds for effective parameters of heterogeneous media by analytic continuation , 1983 .

[24]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[25]  David J. Bergman,et al.  Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material , 1980 .

[26]  I. M. Glazman,et al.  Theory of linear operators in Hilbert space , 1961 .

[27]  W. Rudin.  Function theory in polydiscs , 1969 .

[28]  Graeme W. Milton,et al.  Bounds on the complex dielectric constant of a composite material , 1980 .

[29]  Graeme W. Milton,et al.  Bounds on the elastic and transport properties of two-component composites , 1982 .

[30]  David J. Bergman,et al.  The dielectric constant of a composite material—A problem in classical physics , 1978 .

[31]  David J. Bergman,et al.  Theory of resonances in the electromagnetic scattering by macroscopic bodies , 1980 .

[32]  D. Bergman,et al.  Improved rigorous bounds on the effective elastic moduli of a composite material , 1984 .