Related papers: A limitation of the Bruggeman formalism for homoge…
The Bruggeman formalism provides an estimate $\eps^{Br}_{hcm}$ of the relative permittivity of a homogenized composite material (HCM), arising from two component materials with relative permittivities $\eps_a$ and $\eps_b$. It can be…
The Bruggeman formalism provides an estimate of the effective permittivity of a composite material comprising two constituent materials, with each constituent material being composed of electrically small particles. When one of the…
Two different formalisms for the homogenization of composite materials containing oriented ellipsoidal particles of isotropic dielectric materials are being named after Bruggeman. Numerical studies reveal clear differences between the two…
The Bruggeman formalism is implemented to estimate the refractive index of an isotropic, dielectric, homogenized composite medium (HCM). Invoking the well--known Hashin--Shtrikman bounds, we demonstrate that the group velocity in certain…
The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials…
Two different formalisms for the homogenization of composite materials containing ellipsoidal inclusions based on Bruggeman's original formula for spherical inclusions can be found in the literature. Both approximations determine the…
The Bruggeman formalism for the homogenization of particulate composite materials is used to predict the effective permittivity dyadic of a two-constituent composite material with one constituent having the ability to display the Pockels…
An effective-medium theory is proposed for random weakly nonlinear dielectric media. It is based on a new gaussian approximation for the probability distributions of the electric field in each component of a multi-phase composite. These…
Implementations of the Bruggeman and Maxwell Garnett homogenization formalisms were developed to estimate the relative permittivity dyadic of a homogenized composite material (HCM), namely $\underline{\underline{\epsilon}}^{\rm HCM}$,…
Influence of number of particles considered in numerical simulations on complex dielectric permittivity of binary dilute dielectric mixtures in two-dimensions are reported. In the simulations, dodecagons (polygons with 12-sides) were used…
We report on a strategy for achieving negative phase velocity (NPV) in a homogenized composite medium (HCM) conceptualized using the Bruggeman formalism. The constituent material phases of the HCM do not support NPV propagation. The HCM and…
Two active dielectric materials may be blended together to realize a homogenized composite material (HCM) which exhibits more gain than either component material. Likewise, two dissipative dielectric materials may be blended together to…
A many-particle theory is presented for the effective quasistatic permittivity of macroscopically homogeneous and isotropic systems of inhomogeneous dielectric particles with different degrees of penetrability. The theory is based upon our…
In a long wavelength regime, the effective properties of particulate composites, including nanocomposites, may be estimated using one of various homogenization formalisms, such as the Bruggeman and Maxwell Garnett formalisms, and the…
We study in this paper compression effects in heterogeneous media with maximal packing constraint. Starting from compressible Brinkman equations, where maximal packing is encoded in a singular pressure and a singular bulk viscosity, we show…
Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the…
The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density,…
Dynamic homogenization theories are powerful tools for describing and understanding the behavior of heterogeneous media such as composites and metamaterials. However, a major challenge in the dynamic homogenization theory is determining…
In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…