Singular Behavior of Electric Field of High Contrast Concentrated Composites

A heterogeneous medium of constituents with vastly different mechanical properties, whose inhomogeneities are in close proximity to each other, is considered. The gradient of the solution to the corresponding problem exhibits singular behavior (blow up) with respect to the distance between inhomogeneities. This paper introduces a concise procedure for capturing the leading term of gradient's asymptotics precisely. This procedure is based on a thorough study of the system's energy. The developed methodology allows for straightforward generalization to heterogeneous media with a nonlinear constitutive description

The asymptotics for the perfect conductivity problem with stiff C^1,α-inclusions

This paper is devoted to an investigation of blow-up phenomena occurring in high-contrast fiber-reinforced composites. When the distance between perfect conductors or between the conductors and the matrix boundary tends to zero, the electric field may appear blow-up. The major objective of this paper is to give a precise description for the singular behavior of such a high concentration in the presence of C1,α-inclusions with extreme conductivities. Our results contain the boundary and interior asymptotics of the concentrated field in all dimensions. In particular, the blow-up factor for each dimension is accurately captured.</p

Effective permittivity of random plasmonic composites

An effective-medium theory (EMT) is developed to predict the effective permittivity \epsilon_eff of dense random dispersions of high optical-conductivity metals such as Ag, Au and Cu. Dependence of \epsilon_eff on the volume fraction \phi, a microstructure parameter \kappa related to the static structure factor and particle radius a is studied. In the electrostatic limit, the upper and lower bounds of \kappa correspond to Maxwell-Garnett and Bruggeman EMTs respectively. Finite size effects are significant when |\beta^2(ka/n)^3| becomes O(1) where \beta, k, and n denote the nanoparticle polarizability, wavenumber and matrix refractive index respectively. The coupling between the particle and effective medium results in a red-shift in the resonance peak, a non-linear dependence of \epsilon_eff on \phi, and Fano resonance in \epsilon_eff.Comment: Manuscript submitted to J. Opt. Soc. Am. B. 33 page