Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. VII. Comparison of different approaches

Journal Article · Tue Mar 01 00:00:00 EST 1977 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523293· OSTI ID:7124009

Hori, M

A general analysis is given for the theoretical evaluation of the effective permittivity of random heterogeneous materials that are statistical homogeneous. The perturbative and variational formulations presented in Papers I--VI in this series of work are reconstructed from a slightly different point of view and compared with recent approaches developed by other authors. Perturbation expansions for the effective permittivity are derived through electric field, electric displacement, Lorentz field, and T matrix. The validity of various approximate solutions involving the effective-medium approximation and the cumulant expansion method is discussed with the aid of a diagrammatic representation of the perturbation series. It is confirmed that, at the present stage, the cumulant theory is the best approximation for a three-dimensional system, while the effective-medium theory is the best for a two-dimensional system. The meaning and applicability of variational approaches are also reviewed.

• Research Organization: Department of Applied Physics, Tokyo Institute of Technology, Meguroku, Tokyo 152, Japan
• OSTI ID: 7124009
• Journal Information: J. Math. Phys. (N.Y.); (United States), Vol. 18:3
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
PERMITTIVITY
MATHEMATICAL MODELS
SOLIDS
DIELECTRIC PROPERTIES
ELECTRIC CONDUCTIVITY
ERGODIC HYPOTHESIS
THERMAL CONDUCTIVITY
ELECTRICAL PROPERTIES
HYPOTHESIS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
656000* - Condensed Matter Physics