Anisotropic ellipsoidal inclusion with an anisotropic shell in an isotropic medium subjected to a uniform electric field

Generalized effective-field approximation for inhomogeneous medium with inclusions in multilayered shells

“…in the x 1 x 2 x 3 coordinate system [26]. Similarly (51), there is a relation of these tensors to the same tensors in the coordinate system x…”

“…The coordinate transformation associated with the transformation T i has the form i+1 ; denote their half-axes as a i,1 ′ , a i,2 ′ , a i,3 ′ and a i+1,1 ′ , a i+1,2 ′ , a i+1,3 ′ . The matrix T i of this transformation is related to the permittivity tensor ε i of the ith shell layer by the relation [26]:…”

“…Consider the ith layer of the kth inclusion, which we will consider isolated in an infinite comparison environment. The electric field potential in it has the form (the upper index denoting the inclusion number is omitted everywhere, because the dependence will be the same for all inclusions) [26]…”