Scattering theorems for dyadic chiral fields

A time-harmonic plane dyadic electromagnetic field is scattered by a chiral body in a chiral environment. The body is either a perfect conductor or a dielectric. The incident field is a linear combination of left-circularly polarized and right-circularly polarized dyadic electromagnetic fields, each of which has a different wave number. We prove reciprocity and scattering theorems in dyadic form, which incorporate as special cases the corresponding known theorems for vector electromagnetic waves. Specializing to the same direction of incidence and observation in the general scattering theorems we obtain forward scattering theorems.     

Induced Projective Modules Over Group von Neumann Algebras

Let G be a group and k a subring of the field of complex numbers. In this paper we study the additive map in reduced K-theory, which is associated with the inclusion of the group algebra kG into the group von Neumann algebra G, and obtain necessary and sufficient conditions for it to be identically zero (or zero modulo torsion). Our results complete the work of Eckmann [Comm. Math. Helvet. 71 (1996), 453–462; Arch. Math. 76 (2001), 241–249] and Schafer [K-theory 19 (2000), 211–217], while reducing to Swan’s theorem on induced representations [Ann. Math. 71 (1960), 552–578], in the case where the group G is finite. (Received: January 2005) Research supported by University of Athens grant Pythagoras 70/3/7298.     

Harmonic Analysis on Chord Arc Domains

In the present paper we study the solvability of the Dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients which are small perturbations of given operators in rough domains beyond the Lipschitz category. In our approach, the development of the theory of tent spaces on these domains is essential.     

Assembly of quantum dots on peptide nanostructures and their spectroscopic properties

We present a chemical process for the decoration of self-assembled two-dimensional peptide fibrils with two different sizes of CdSe@ZnS core–shell quantum dots (Qdots) capped with trioctylphosphine oxide molecules. The attachment of the semiconducting nanoparticles to the fibrils is directed via disulfide bond between the quantum dot and cysteine aminoacids that are deliberately impeded in the peptide structures. A significant red shift in the emission spectra of the quantum dots is observed and attributed to the synergistic interaction between adjacent nanoparticles arranged on peptide film templates extending over hundreds of nanometers.     

Balance in complete cohomology

The balance of complete cohomology for modules that admit complete resolutions has been established by Christensen and Jorgensen (2013), as well as by Enochs, Estrada and Iacob (2012), by using two types of constructions on a given bicomplex. In this paper, we show that these constructions are closely related to each other. We also present an alternative proof of balance, which is based on the corresponding assertion for ordinary cohomology.     

Light wave propagation in periodic tilted liquid crystal structures: a periodic beam propagation method

Periodically deformed liquid crystal profiles are commonly encountered either spontaneously under the influence of an external excitation, or intentionally, with the introduction of relief type gratings on the supporting surfaces. These types of periodicity are often characterized by a pitch around one micron or less. As the pitch is directly comparable to the optical wavelength, it is necessary to develop rigorous numerical methods to predict light wave propagation within such structures. A wide angle periodic beam propagation method (BPM) is proposed for the simulation of light propagation in purely bend/splay periodic director deformations. A common occurrence of this type of deformation is encountered in smectic A materials under the Helfrich effect. More importantly, bistable nematic cells with zenithal deformation have been developed for interesting display applications. Both aforementioned deformations are examined to verify the applicability of the proposed periodic BPM.     

LC–UV determination of atrazine and its principal conversion products in soil after combined microwave-assisted and solid-phase extraction

A multiresidue method developed for the analysis of atrazine and its principal conversion products, deisopropylatrazine (DIA), deethylatrazine (DEA) and hydroxyatrazine (HA), in soil is presented. The method is based on the microwave-assisted extraction (MAE) of soil with aqueous methanol followed by solid-phase extraction (SPE) of the extracts and subsequent analysis by LC–UV with a diode array detector. MAE operational parameters (extraction solvent, extractant volume) were optimized with respect to extraction efficiency of the target compounds from soils with 2.5% organic matter (OM) content. Recoveries above 80% were obtained for all solutes. Soil OM content did not affect analyte recoveries. Recoveries from fresh and aged residues, the latter weathered under cold storage conditions, were not statistically different. Finally, MAE was found to be superior in terms of extraction efficiency, sample throughput, and solvent consumption to conventional flask-shaking extraction.     

Wetting of a multiarm star-shaped molecule

The equilibrium contact angles and line tensions of macroscopic droplets, composed of star-shaped polystyrene (PS) macromolecules, on silicon oxide substrates, are shown to be smaller than their linear analogs, by up to approximately 1 and 2 orders of magnitude, respectively, depending on the size and functionality of the star-shaped molecule. A precursor layer, of lateral dimensions and of thicknesses on the order of nanometers, surrounds each droplet of low molecular weight linear PS chains. Droplets composed of star-shaped molecules possessing a sufficient number of arms, reside on a layer adsorbed to the substrate.     

Computational techniques for the analysis and design of dielectric-loaded plasmonic circuitry

The finite element and the beam propagation method, two widely used methods in photonics, are utilized for the analysis of plasmonic components based on the dielectric-loaded plasmonic waveguide. Two components are chosen as examples and are subsequently numerically investigated by employing the aforementioned methods, in order to demonstrate their applicability in plasmonics. Specifically, a microring resonator add-drop filter and a Mach–Zehnder interferometric switch are analyzed by means of the finite element and the beam propagation method, respectively. The formulation adopted is clearly presented in both cases and the case-dependent implementation details are thoroughly discussed.     

Time-dependent potential scattering in chiral media

Electromagnetic waves propagating in a homogeneous three-dimensional unbounded chiral medium are considered. We define a chiral operator and study potential scattering relative to this operator. A spectral analysis of associated operators is obtained, based on the Plancherel theory of the Fourier transform. Using the generalised eigenfunction expansion theory, we give an integral representation of the solution. A discussion of asymptotic equality of solutions is provided and the associated wave operator introduced.