Boundary Element Methods for Maxwell Transmission Problems in Lipschitz Domains

Summary. We consider the Maxwell equations in a domain with Lipschitz boundary and the boundary integral operator A occuring in the Calderón projector. We prove an inf-sup condition for A using a Hodge decomposition. We apply this to two types of boundary value problems: the exterior scattering problem by a perfectly conducting body, and the dielectric problem with two different materials in the interior and exterior domain. In both cases we obtain an equivalent boundary equation which has a unique solution. We then consider Galerkin discretizations with Raviart-Thomas spaces. We show that these spaces have discrete Hodge decompositions which are in some sense close to the continuous Hodge decomposition. This property allows us to prove quasioptimal convergence of the resulting boundary element methods. Mathematics Subject Classification (2000):65N30     

Computer simulation of a carbon-deposition plasma in CH4

A transport and reaction model of a low-pressure, high-frequency (13.56 MHz) CH₄ plasma used for diamondlike carbon (a-C:H) deposition was developed. The model includes reactions among four molecular species (CH₄, C₂ H₆, C₂H₄, and H₂), five radicals and atom (CH₃, CH₂, CH, C₂H₅, and H), and four ions (CH₄⁺ , CH₃⁺, CH₅⁺, and C ₂H₅⁺). It also accounts for the influence of the sticking coefficient of species at the walls. Calculated values of the dissociation degree for several flow rates are in good agreement with experimental measurements made by quadrupole mass spectroscopy. A simple surface-model based on the hydrogen coverage of surface and ion flux and energy at the substrate surface was established. This model permitted the calculation of the deposition rate on the powered electrode as a function of the power applied to this electrode. Good agreement between experimental and calculated growth rates was obtained when CH₃, C₂H₅, and CH₂ were assumed to participate in film formation, and when hydrogen removal by ion bombardment with variable energy as a function of the power was included in the model     

A Fair Allocation of County Cricket Opponents

Each team in the English County Cricket Championship plays against some other teams twice a year, and others only once. This paper describes a case study whose aim was to overcome this inherent unfairness by producing a four-year schedule of opponents which was as fair as possible, and could be easily seen to be fair, while still allowing for traditional rivalries. The schedule also needed to be satisfactory in regard to several other constraints and objectives. Various simple heuristics were used; these are described in some detail. Of particular interest is the effectiveness of a ‘local non-worsening’ approach when the objective is to find any feasible solution. This is equivalent to simulated annealing at a constant temperature of absolute zero.     

The sense of smell,its signalling pathways,and the dichotomy of cilia and microvilli in olfactory sensory cells

Smell is often regarded as an ancillary perception in primates, who seem so dominated by their sense of vision. In this paper, we will portray some aspects of the significance of olfaction to human life and speculate on what evolutionary factors contribute to keeping it alive. We then outline the functional architecture of olfactory sensory neurons and their signal transduction pathways, which are the primary detectors that render olfactory perception possible. Throughout the phylogenetic tree, olfactory neurons, at their apical tip, are either decorated with cilia or with microvilli. The significance of this dichotomy is unknown. It is generally assumed that mammalian olfactory neurons are of the ciliary type only. The existence of so-called olfactory microvillar cells in mammals, however, is well documented, but their nature remains unclear and their function orphaned. This paper discusses the possibility, that in the main olfactory epithelium of mammals ciliated and microvillar sensory cells exist concurrently. We review evidence related to this hypothesis and ask, what function olfactory microvillar cells might have and what signalling mechanisms they use.     

Temperature Dependence for Fluorescence of β-NADH in Glycerol/Water Solution and in Trehalose/Sucrose Glass

Fluorescence imaging of cells and tissue can be used to evaluate β-NADH redox and location. At low temperature, β-NADH fluorescence intensity increases and therefore sensitivity of imaging increases. In this paper, the temperature dependence of fluorescence was evaluated for β-NADH in glycerol/water solution and in trehalose/sucrose glass. The average fluorescence lifetime for NADH in glycerol/water is 0.66 ns, compared with 5.3 ns in trehalose/ sucrose at 20°C. Emission spectra were recorded from 290 to 12 K. The fluorescence of β-NADH in glycerol/water increases ∼16 fold and the emission shifts about 35 nm to the blue as temperature decreases. Much smaller change is seen for fluorescence of β-NADH in sugar glass. Below 77 K, the β-NADH spectral features did not change significantly with temperature change, and so no increase in sensitivity is obtained by going to very low temperatures. It is suggested that the sensitivity of β-NADH fluorescence is related to water relaxation around the excited state molecule. Differences in water in various tissues may contribute to β-NADH fluorescence changes when cells are altered.     

Subwavelength-resolution near-field Raman spectroscopy

The resolution capabilities of near-field Raman spectroscopy based on a giant enhancement of the electric field near a nanosized metal probe are studied. As a test sample, bundles of single-walled carbon nanotubes deposited on glass substrates are used. It is shown that this method ensures a subwavelength spatial resolution of about 50 nm and demonstrates a Raman scattering enhancement of the order of 10⁴.     

A convergent star product for linear Poisson structures

An explicit star product ⋆ _α ^Γ on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between this star product and the Kontsevich star product in [K₁] is given and diverse properties of the star product ⋆ _α ^Γ are studied. It is also proved that the star product ⋆ _α ^Γ provides a convergent deformation quantization in the sense of Rieffel [R₁].     

Microporated PEG Spheres for Fluorescent Analyte Detection

Poly(ethylene glycol) (PEG) hydrogels have been used to encapsulate fluorescently labeled molecules in order to detect a variety of analytes. The hydrogels are designed with a mesh size that will retain the sensing elements while allowing for efficient diffusion of small analytes. Some sensing assays, however, require a conformational change or binding of large macromolecules, which may be sterically prohibited in a dense polymer matrix. A process of hydrogel microporation has been developed to create cavities within PEG microspheres to contain the assay components in solution. This arrangement provides improved motility for large sensing elements, while limiting leaching and increasing sensor lifetime. Three hydrogel compositions, 100% PEG, 50% PEG, and microporated 100% PEG, were used to create pH-sensitive microspheres that were tested for response time and stability. In order to assess motility, a second, more complex sensor, namely a FITC-dextran/TRITC-Con A glucose-specific assay was encapsulated within the microspheres.