Polya hypothesis and variational inequalities for polarizabilities of dielectric bodies

Concept of dipole polarizability matrices for a system of wires and examples of their calculations and variational estimates

“…1 This statement can be interpreted as the Dirichlet principle for the problem on the dipole wire polarizability. We note that the Thomson principle is used to estimate from above the polarizability tensor, and the Dirichlet principle allows estimates from below to be obtained [7]. The absence in the scientific literature of the dipole polarizability concept for a wire system has motivated the present work.…”

“…A short review of precisely solved problems on the polarizability tensor of separate wires having relatively simple geometrical shapes was presented in [7]. The polarizability tensor is positively determined and symmetric.…”

“…We note that the potential ϕ in this case is created only by the wire charges[7]. In this formulation of the Dirichlet principle, ϕ is only the component of the total system potential.…”