Depolarization volume and correlation length in the homogenization of anisotropic dielectric composites

In conventional approaches to the homogenization of random particulate composites, both the distribution and size of the component phase particles are often inadequately taken into account. Commonly, the spatial distributions are characterized by volume fraction alone, while the electromagnetic response of each component particle is represented as a vanishingly small depolarization volume. The strong-permittivity-fluctuation theory (SPFT) provides an alternative approach to homogenization wherein a comprehensive description of distributional statistics of the component phases is accommodated. The bilocally-approximated SPFT is presented here for the anisotropic homogenized composite which arises from component phases comprising ellipsoidal particles. The distribution of the component phases is characterized by a two-point correlation function and its associated correlation length. Each component phase particle is represented as an ellipsoidal depolarization region of nonzero volume. The effects of depolarization volume and correlation length are investigated through considering representative numerical examples. It is demonstrated that both the spatial extent of the component phase particles and their spatial distributions are important factors in estimating coherent scattering losses of the macroscopic field.Comment: Typographical error in eqn. 16 in WRM version is corrected in arxiv versio

Electrical control of the linear optical properties of particulate composite materials

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 effect. Scenarios wherein the constituent particles are randomly oriented, oriented spheres, and oriented spheroids are numerically explored. Thereby, homogenized composite materials (HCMs) are envisaged whose constitutive parameters may be continuously varied through the application of a low-frequency (dc) electric field. The greatest degree of control over the HCM constitutive parameters is achievable when the constituents comprise oriented and highly aspherical particles and have high electro-optic coefficients

Ankylosing spondylitis and sarcoidosis — Coincidence or association?

We report a 25-year-old woman presenting with sarcoidosis and bilateral sacroiliitis. Her sarcoidosis related symptoms (malaise, cough and dyspnoea) improved dramatically under treatment with steroids but severe back pain persisted. Only seven similar cases have been described over the last 40 years and the question of a possible association between the two diseases has been raised. However, prevalence data from the literature and the apparent lack of genetic links are better arguments for coincidence than for association

Depolarization regions of nonzero volume in bianisotropic homogenized composites

In conventional approaches to the homogenization of random particulate composites, the component phase particles are often treated mathematically as vanishingly small, point-like entities. The electromagnetic responses of these component phase particles are provided by depolarization dyadics which derive from the singularity of the corresponding dyadic Green functions. Through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. We present an extension to the strong-property-fluctuation theory in which depolarization regions of nonzero volume and ellipsoidal geometry are accommodated. Therein, both the size and spatial distribution of the component phase particles are taken into account. The analysis is developed within the most general linear setting of bianisotropic homogenized composite mediums (HCMs). Numerical studies of the constitutive parameters are presented for representative examples of HCM; both Lorentz-reciprocal and Lorentz-nonreciprocal HCMs are considered. These studies reveal that estimates of the HCM constitutive parameters in relation to volume fraction, particle eccentricity, particle orientation and correlation length are all significantly influenced by the size of the component phase particles

Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales

A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conformal block is related to geometric configuration of the interfaces and what is the physical meaning of mixed conformal blocks. We illustrate the general ideas on concrete computations, with applications to percolation and the Ising model.Comment: 40 pages, 6 figures. V2: well, it looks better with the addresse

Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs and Alkali-mediated Interactions

Starting from a model of rigid interacting C60 polymer chains on an orthorhombic lattice, we study the mutual orientation of the chains and the stability of the crystalline structures Pmnn and I2/m. We take into account i) van der Waals interactions and electric quadrupole interactions between C60 monomers on different chains as well as ii) interactions of the monomers with the surrounding alkali atoms. The direct interactions i) always lead to an antiferrorotational structure Pmnn with alternate orientation of the C60 chains in planes (001). The interactions ii) with the alkalis consist of two parts: translation-rotation (TR) coupling where the orientations of the chains interact with displacements of the alkalis, and quadrupolar electronic polarizability (ep) coupling, where the electric quadrupoles on the C60 monomers interact with induced quadrupoles due to excited electronic d states of the alkalis. Both interactions ii) lead to an effective orientation-orientation interaction between the C60 chains and always favor the ferrorotational structure I2/m where C60 chains have a same orientation. The structures Pmnn for KC60 and I2/m for Rb- and CsC60 are the result of a competition between the direct interaction i) and the alkali-mediated interactions ii). In Rb- and CsC60 the latter are found to be dominant, the preponderant role being played by the quadrupolar electronic polarizability of the alkali ions.Comment: J.Chem.Phys., in press, 14 pages, 3 figures, 8 table