Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

In vitro evaluation of cytotoxic and inflammatory properties of silica nanoparticles of different sizes in murine RAW 264.7 macrophages

The biological response to four well-characterized amorphous silica nanoparticles was investigated in RAW 264.7 macrophages in view of their potential application as drug carriers to sites of inflammation. All silica nanoparticles-induced cell membrane damage, reduced metabolic activity, generated ROS and released various cytokines, but to different extents. Two silica nanoparticles of 34 nm (A and B) with different zetapotentials were more cytotoxic than (aggregated) 11 and 248 nm nanoparticles, while cytokines were mostly induced by the (aggregated) 11 nm and only one of the 34 nm nanoparticles (34A). The results indicate that specific silica nanoparticles may have counterproductive effects, for example when used as carriers of anti-inflammatory drugs. The physicochemical properties determining the response of nanoparticles vary for different responses, implying that a screening approach for the safe development of nanoparticles needs to consider the role of combinations of (dynamic) physicochemical properties and needs to include multiple toxicity endpoints.     

Effect of Mn on the magnetic properties of Fe3B/Nd2Fe14B nanocomposites

The magnetic properties of Nd_4.5Fe_77−xMn_xB_18.5 (x=0, 1 and 2) nanocomposites prepared by the crystallization of amorphous precursors were investigated. Addition of Mn is found to decrease the crystallization temperature of the amorphous ribbons. The intrinsic coercivity _iH_c and maximum energy product (BH)_max increase from 2.6 kOe and 9.1 MGOe for x=0 to 3.1 kOe and 10.3 MGOe for x=1, respectively, and the remanence ratio M_r/M_s increases from 0.70 to 0.72. The effect of Mn on Curie temperature T_C and the thermal stability of M_r and _iH_c were also studied. ⁵⁷Fe Mössbauer spectra have been recorded for x=0, 1 and 2 ribbons at room temperature and site preference of the Mn atoms in Fe₃B and Nd₂Fe₁₄B phases is discussed using the Mössbauer spectroscopy.     

The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.     

TheB 2Σ-X 2Σ system of the CaF molecule

The spectrum of theB ²Σ-X ²Σ system of the CaF molecule has been photographed in the second order of a 10.6 m concave grating spectrograph with 0.33 Å/mm dispersion. The rotational structure of the (0, 0) and (1, 0) bands has been analysed and the precise molecular constants have been obtained. Using the constants so determined the band origins of a large number of bands with 0 <v′,v″ < 10 have been calculated and used to obtain the accurate vibrational constants forB andX states and these are presented.     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Classification of graded Hecke algebras for complex reflection groups

The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well as complex reflection groups. Received: July 25, 2001