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J.F. Douglasa and E.J. Garboczib
aPolymers and bBuilding Materials Divisions
National Institute of Standards and Technology
Gaithersburg, Maryland 20899
The intrinsic viscosity  and the electric e and magnetic m polarizabilities of objects having general shape are required in the calculation of some of the most basic properties of solid-solid composites and fluid-solid mixtures. Specifically, the leading order virial coefficients of diverse properties (viscosity, refractive index, dielectric constant, magnetic permeability, thermal and electrical conductivity, and others) can often be expressed in terms of these functionals of object shape. These virial coefficients also provide basic input into effective medium theories describing higher concentration mixtures. The electric and magnetic polarizability tensors have independent interest in numerous applications involving the scattering of electromagnetic and pressure waves from objects of general shape. We present an argument that the ratio of  and < e > / Vp (the average polarizability tensor trace per unit object volume) is an invariant to a good approximation. Many analytical and numerical finite element results for a variety of shapes are presented to support the conjectured relation. Our approximate relation between  and < e > / Vp complements the exact relation between the hydrodynamic virtual mass W and the magnetic polarizability e tensors.
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