Quadratic Lagrangians and the Reissner-Nordström-de Sitter metric

The purpose of this note is to point out that the Einstein-Maxwell equations with cosmological constant can be derived from the quadratic Lagrangians R² and F F . The linear combination R R + ²+k ₂F F leads to field equations not satisfied by the Reissner-Nordström-de Sitter metric.     

Cation–anion interactions in triphenyl telluronium salts. The crystal structures of (Ph3Te)2[MCl6] (M=Pt, Ir), (Ph3Te)[AuCl4], and (Ph3Te)(NO3)·HNO3

Triphenyltelluronium hexachloroplatinate (1), hexachloroiridate (2), tetrachloroaurate (3), and tetrachloroplatinate (4) were prepared from Ph₃TeCl and potassium salts of the corresponding anions. Upon recrystallization of 4 from concentrated nitric acid, K₂[PtCl₆] and (Ph₃Te)(NO₃)·HNO₃ (5) were obtained. The crystal structures of 1–3 and 5 are reported. Compounds 1 and 2 are isostructural. They are triclinic, P , Z=2 (the asymmetric unit contains two formula units). Compound 1: a=10.7535(2), b=17.2060(1), c=21.4700(3) Å, =78.9731(7), β=77.8650(4), γ=78.8369(4)°. Compound 2: a=10.7484(2), b=17.1955(2), c=21.4744(2) Å, =78.834(1), β=77.649(1), γ=78.781(1)°. Compound 3 is monoclinic, P2₁/c, Z=4, a=8.432(2), b=14.037(3), c=17.306(3) Å, β=93.70(3)°. Compound 5 is monoclinic. P2₁/n, Z=4, a=9.572(2), b=14.050(3), c=13.556(3) Å, β=90.76(3)°. The primary bonding in the Ph₃Te⁺ cation in each salt is a trigonal AX₃E pyramid with Te---C bond lengths in the range 2.095(8)–2.14(2) Å and the bond angles 94.1(6)–100.9(5)°. The weak TeCl (1–3) and TeO (5) secondary interactions expand the coordination sphere. In 1 and 2 the cation shows a trigonal bipyramidal AX₃YE coordination with one primary Te---C bond and the shortest secondary TeCl contact in axial positions and the two other Te---C bonds and the lone-pair in equatorial positions. The cation in 3 shows a distorted octahedral AX₃Y₃E environment and that in 5 is a more complex AX₃Y₃Y′₂ arrangement. In both latter salts the structure is a complicated three-dimensional network of cations and anions.     

Dispersion Theory of Liquids Containing Optically Linear and Nonlinear Maxwell Garnett Nanoparticles

Kramers-Kronig relations and sum rules for effective linear permittivity of the Maxwell Garnett liquid-nanosphere system were obtained using complex analysis and general expression of the effective permittivity. When reflectance from optically linear and nonlinear Maxwell Garnett nanoparticles was calculated it was observed that the reflectance, in the case of attenuated total reflection, depends on the fill fraction of the nanospheres and their nonlinear susceptibility. According to simulations a good sensitivity of the nonlinear contribution on the reflectance can be obtained by using a probe wavelength corresponding to the resonance frequency of the nanosphere system. In Kretchmann#x0027;s configuration it was observed that the surface-plasmon-resonance angle depends on the fill fraction and on the intensity of the incident light. By using reflectance, it is possible to detect optically nonlinear nanospheres in liquids.     

The effect of facet reflections in index-coupled distributed feedback lasers with coated facets

The effect of facet reflections and different grating parameters on side-mode suppression ratio in index-coupled distributed feedback lasers without a phase-shift section is analyzed. The effect of uncontrollable facet positions on side-mode suppression ratio is studied when the grating coupling coefficient, the grating filling factor, the grating order, the device length and the facet reflectivities are varied. The single-mode device yield and the facet reflectivities needed for achieving a high yield are evaluated, the reflectivity of the anti-reflection coated facet is optimized as a function of the coupling strength and the effect of facet reflections on the other laser characteristics is shown.     

Heuristic for a new multiobjective scheduling problem

We consider a telecommunication problem in which the objective is to schedule data transmission to be as fast and as cheap as possible. The main characteristic and restriction in solving this multiobjective optimization problem is the very limited computational capacity available. We describe a simple but efficient local search heuristic to solve this problem and provide some encouraging numerical test results. They demonstrate that we can develop a computationally inexpensive heuristic without sacrificing too much in the solution quality.     

Kramers-Kronig analysis on the real refractive index of porous media in the terahertz spectral range

We present a terahertz time-domain experimental technique for the detection of scattering from porous media. The method for detection of the scattering enables one to make a decision when Fresnel or Kramers-Kronig (K-K) analysis can be applied for a porous medium. In this study the real refractive index of a tablet is calculated using the conventional K-K dispersion relation and also using a singly subtractive K-K relation, which are applied to the extinction coefficient obtained from the Beer-Lambert law. The advantage of the K-K analysis is that one gets estimates both for absolute refractive index and also dispersion of the porous tablet, whereas Fresnel analysis provides only the absolute value of the index.     

Aqueous dispersion, surface thiolation, and direct self-assembly of carbon nanotubes on gold

We report the efficient aqueous dispersion of pristine HiPco single-walled carbon nanotubes (SWNTs) with ionic liquid (IL)-based surfactants 1-dodecyl-3-methylimidazolium bromide (1) and 1-(12-mercaptododecyl)-3-methylimidazolium bromide (2), the thiolation of nanotube sidewalls with 2, and the controlled self-assembly of positively charged SWNT-1,2 composites on gold. Optical absorption spectra and resonance Raman (RR) data of obtained aqueous SWNT-1,2 dispersions are consistent with debundled and noncovalently functionalized nanotubes whose electronic properties have not been disturbed. Additionally, the dispersion of pristine nanotube material with surfactants 1 and 2 leads to a high degree of purification from carbonaceous particles. The chiralities of the 14 smallest semiconducting HiPco SWNTs in resonance with Raman excitation at 1064 nm (1.165 eV) were determined in SWNT-2 aqueous dispersion using UV-vis-NIR and RR spectra. X-ray photoelectron spectroscopy (XPS) and surface-enhanced resonance Raman scattering (SERRS) spectroscopy of SWNT-2 submonolayers on gold verified the encapsulation of individualized SWNTs with IL surfactants, the cleavage of S-S disulfide bonds formed in aqueous SWNT-2 suspensions, and the direct chemisorption of the SWNT-2 composite on bare gold via the Au-S bond. Aqueous dispersions of SWNTs with IL-based surfactants add biofunctionality to carbon nanotubes by imparting the positive surface charge necessary for interactions with cell membranes. Our technique, which purifies pristine nanotube material and produces water-soluble, positively charged nanotubes with pendent surface-active thiol groups, may also be translated to other carbon nanotubes and carbon nanostructures. Self-assembled, positively charged submonolayers of SWNTs can be further used for applications in cell biology and sensor technology.     

Behaviour of Extractives in Norway Spruce (Picea abies) Bark during Pile Storage

The current practices regarding the procurement chain of forest industry sidestreams, such as conifer bark, do not always lead to optimal conditions for preserving individual chemical compounds. This study investigates the standard way of storing bark in large piles in an open area. We mainly focus on the degradation of the most essential hydrophilic and hydrophobic extractives and carbohydrates. First, two large 450 m³ piles of bark from Norway spruce (Picea abies) were formed, one of which was covered with snow. The degradation of the bark extractives was monitored for 24 weeks. Samples were taken from the middle, side and top of the pile. Each sample was extracted at 120 °C with both n-hexane and water, and the extracts produced were then analysed chromatographically using gas chromatography with flame ionisation or mass selective detection and high-performance liquid chromatography. The carbohydrates were next analysed using acidic hydrolysis and acidic methanolysis, followed by chromatographic separation of the monosaccharides formed and their derivatives. The results showed that the most intensive degradation occurred during the first 4 weeks of storage. The levels of hydrophilic extractives were also found to decrease drastically (69% in normal pile and 73% in snow-covered pile) during storage, whereas the decrease in hydrophobic extractives was relatively stable (15% in normal pile and 8% in snow-covered pile). The top of the piles exhibited the most significant decrease in the total level of extractives (73% in normal and snow-covered pile), whereas the bark in the middle of the pile retained the highest amount of extractives (decreased by 51% in normal pile and 47% in snow-covered pile) after 24-week storage.     

Phase retrieval of reflectance for nanoparticle optical identification

We present a method for optical identification of dielectric and metal nanoparticles in a liquid matrix using phase retrieval of reflectance with TE- and TM-polarized light. A formula is derived for extracting the effective complex dielectric function of a nanoparticle colloid based on different complex reflectance components. The phase retrieval is performed using the maximum entropy method. We observe excellent accuracy both for dielectric and metallic nanoparticles with volume fractions up to 10%.