Upper limits on a stochastic background of gravitational waves

The Laser Interferometer Gravitational-Wave Observatory has performed a third science run with much improved sensitivities of all three interferometers. We present an analysis of approximately 200 hours of data acquired during this run, used to search for a stochastic background of gravitational radiation. We place upper bounds on the energy density stored as gravitational radiation for three different spectral power laws. For the flat spectrum, our limit of omega0 < 8.4 x 10(-4) in the 69-156 Hz band is approximately 10(5) times lower than the previous result in this frequency range.     

Preface

Preface

Preface     

Synthese und Röntgenstrukturanalyse des Additionsproduktes von Schwefeltrioxid an Tetraschwefeltetranitrid (S4N4· SO3)

Synthesis and X-ray Structure Analysis of the Addition Compound of Sulfurtrioxide and Tetrasulfurtetranitride (S₄N₄· SO₃) S₄N₄ · SO₃ was obtained by reaction of S₄N₄ with SO₃ in CH₂Cl₂ and by solvent free reaction of S₄N₄ with Fluorosulfonic acid anhydride. The structure of the adduct could be determined by single crystal X-ray structure analysis. The “cage” of the S₄N₄ is analogous to the structure of S₄N₄ · SbCl₅ reconvoluted into a deformated saddle conformation with nearly C_s-symmetry. The S? N bond lengths in the S₄N₄ ring vary from 1.51 to 1.69 Å. The C_s-symmetry is significantly disturbed by the position of the SO₃ group. In the crystal structure with monoclinic unit cell of space group P2₁/n the molecules are packed into columns, which are arranged pseudohexagonally.     

Ultrasonic characterization of ceramic fibres at ambient and elevated temperatures

A non-destructive laser-generated ultrasonic inspection system has been developed to evaluate the elastic properties of ceramic fibres. The approach uses a pulsed Nd:YAG laser to excite ultrasonic signals in fibres. The signal is detected by a piezoelectric acoustic emission transducer to obtain the appropriate frequency response suitable for an elastically one-dimensional sample. By using a differential time-of-flight system, a very accurate measure of the velocity can be obtained in the fibre, with a total scatter of less than 0.5%. This approach has been used to investigate the Young's modulus of polycrystalline carbon and boron fibres as a function of stress. Both types of fibres were found to have a Young's modulus increase as greater applied loads were imposed. The carbon and boron fibres, along with silicon carbide fibres, were evaluated at elevated temperatures up to 700 °C. The carbon fibres were found to have an immediate decrease in the Young's modulus as the temperature was increased, due to oxidation of the carbon. The Young's modulus of the boron fibres decreased only at temperatures higher than 200 °C, probably the result of a microstructural transformation or relaxation. The silicon carbide fibres were found to have no significant change in the elastic properties up to 700 °C. The ultrasonic technique was also applied to polycrystalline alumina fibres and fibre tows between ambient temperature and 1200 °C in a specially designed furnace. Using this technique, it was possible to distinguish the changes in the elasticity of the alumina fibres as they were processed into -alumina. The change in the Young's modulus was readily apparent during phase transformations to -alumina. In addition, the ultrasonic velocity can be used to infer information concerning any coatings that were applied to the alumina fibres. This can be used to aid in the quantification of the coating thickness and uniformity. The application of the ultrasonic inspection system has demonstrated the ability to determine rapidly and non-destructively the elastic properties in ceramic fibres. The information gained from the measurements can be used as a quality assurance technique, or can be modified to be a real-time process control/process monitoring system.     

The bidentate behaviour of tetrahydroborate towards copper(II) and group(IV) metals in heterobimetallic complexes

Summary New heterobimetallic complexes of the type [Cu(TETA)-BH₄)₂M(BH₄)₂] (TETA = triethylene tetramine; M = Si, Ge, Sn, Ti and Zr) were prepared by the interaction of [Cu(TETA)Cl₂MCl₂] with an excess of KBH₄ in THF. The results indicate that the complexes are nonelectrolytes and the tetrahydroborate group links to the copper(II) atom and the group(IV) metal in a bidentate manner adopting C _2v symmetry.     

An analytical technique for solving a class of strongly nonlinear conservative systems

Recently, an analytical technique has been developed to determine approximate solutions of strongly nonlinear differential equations containing higher order harmonic terms. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. Previously such algebraic equations for the Duffing equation were solved in powers of a small parameter; but the solutions measure desired results when the amplitude is an order of 1. In this article different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. Moreover, two or three terms of this power series solution measure a good result when the amplitude is an order of 1. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the Duffing oscillator but it is also useful for many other nonlinear problems.     

Mechanochemical Synthesis of High Crystalline Cerium Hexaboride Nanoparticles from CeO2‐B2O3‐Mg Ternary System

High crystalline cerium hexaboride (CeB₆) nanoparticles (NPs) were synthesized using mixture of mag‐ nesium (Mg), cerium oxide (CeO₂) and boron oxide (B₂O₃) via the mechanochemical process at room tem‐ perature. Based on the results, magnesiothermic reduction of B₂O₃ occurred after about 2 h of milling in a mechanically induced self‐sustaining reaction (MSR). The significant amount of heat produced by the reduction reaction resulted in CeO₂ reduction to elemental Ce which finally reacted with elemental B and formed CeB₆ compound. According to XRD analyses, the degree of crystallinity and lattice parameter of the product was calculated about 93 % and 4.1458 Å, respectively. The morphology observations revealed that the synthesized CeB₆ had semi‐cubic shape with the range of size 25–60 nm. The synthesis of CeB₆ during the thermal treatment was studied by simultaneous thermal analysis (STA) technique. It was found that the reduction of B₂O₃ took place after melting of Mg meanwhile, no CeB₆ phase achieved even up to 1100 °C.     

The relaxation of the structure of RADP in an electric field

X-ray scattering measurements have been made to study the behaviour of the ferroelectric glass of Rb_1–x(NH₄)_xH₂PO₄ withx0.22 in the presence of an electric field. The results showed that the system has very long relaxation times, characteristic of competing interactions. The change in the intensity of the x-ray scattering from the incommensurate modulation and the ferroelectric phase have a roughly linear relationship with time.     

The Condensation Phase Transition in Random Graph Coloring

Based on a non-rigorous formalism called the “cavity method”, physicists have put forward intriguing predictions on phase transitions in diluted mean-field models, in which the geometry of interactions is induced by a sparse random graph or hypergraph. One example of such a model is the graph coloring problem on the Erd?s–Renyi random graph G(n, d/n), which can be viewed as the zero temperature case of the Potts antiferromagnet. The cavity method predicts that in addition to the k-colorability phase transition studied intensively in combinatorics, there exists a second phase transition called the condensation phase transition (Krzakala et al. in Proc Natl Acad Sci 104:10318–10323, 2007). In fact, there is a conjecture as to the precise location of this phase transition in terms of a certain distributional fixed point problem. In this paper we prove this conjecture for k exceeding a certain constant k₀.