Upper limits on the mechanical loss of silicate bonds in a silicon tuning fork oscillator

Silicon optics suspended by silicon ribbons or silicon fibers and kept at low temperature are being considered, because of promising optical and mechanical properties, for the test masses of third generation interferometric gravitational-wave detectors. To interconnect the suspension elements the technique of hydroxide catalysis (or silicate) bonding can be used. In order to estimate the bond loss a tuning fork was fabricated from silicon ribbons, which were then silicate bonded. The temperature dependence of mechanical loss of this tuning fork was measured in the temperature range of 95–295 K. The ratio of the energy stored in the bond layer to the total energy of the tuning fork was calculated by numerical simulation. This provided an upper limit of the bond loss as a function of the temperature. It is $(5\pm 2)\times {10}^{?3}$ at 123 K, a proposed operating temperature of cryogenically operating ground based interferometric gravitational-wave detectors.     

Phase Separation in Random Cluster Models I: Uniform Upper Bounds on Local Deviation

This is the first in a series of three papers that addresses the behaviour of the droplet that results, in the percolating phase, from conditioning the planar Fortuin-Kasteleyn random cluster model on the presence of an open dual circuit Γ₀ encircling the origin and enclosing an area of at least (or exactly) n ². (By the Fortuin-Kasteleyn representation, the model is a close relative of the droplet formed by conditioning the Potts model on an excess of spins of a given type.) We consider local deviation of the droplet boundary, measured in a radial sense by the maximum local roughness, MLR(Γ₀), this being the maximum distance from a point in the circuit Γ₀ to the boundary ∂ of the circuit’s convex hull; and in a longitudinal sense by what we term maximum facet length, MLF(Γ₀), namely, the length of the longest line segment of which the polygon ∂ is formed. The principal conclusion of the series of papers is the following uniform control on local deviation: that there are constants 0 < c < C < ∞ such that the conditional probability that the normalized quantity n ^−1/3(log n )^−2/3MLR lies in the interval [c, C] tends to 1 in the high n-limit; and that the same statement holds for n ^−2/3 (log n )^−1/3 MLF. In this way, we confirm the anticipated n ^1/3 scaling of maximum local roughness, and provide a sharp logarithmic power-law correction. This local deviation behaviour occurs by means of locally Gaussian effects constrained globally by curvature, and we believe that it arises in many radially defined stochastic interface models, including growth models belonging to the Kardar-Parisi-Zhang universality class.     

The Synthesis of B2(SIDip)2 and its Reactivity Between the Diboracumulenic and Diborynic Extremes

A new compound with the formula L‐B₂‐L wherein the stabilizing ligand (L) is 1,3‐bis[diisopropylphenyl]‐4,5‐dihydroimidazol‐2‐ylidene (SIDip) has been synthesized, isolated, and characterized. The π‐acidity of the SIDip ligand, intermediate between the relatively non‐acidic IDip (1,3‐bis[diisopropylphenyl]imidazol‐2‐ylidene) ligand and the much more highly acidic CAAC (1‐[2,6‐diisopropylphenyl]‐3,3,5,5‐tetramethylpyrrolidin‐2‐ylidene) ligand, gives rise to a compound with spectroscopic, electrochemical, and structural properties between those of L‐B₂‐L compounds stabilized by CAAC and IDip. Reactions of all three L‐B₂‐L compounds with CO demonstrate the differences caused by their respective ligands, as the π‐acidities of the CAAC and SIDip carbenes enabled the isolation of bis(boraketene) compounds (L(OC)B‐B(CO)L), which could not be isolated from reactions with B₂(IDip)₂. However, only B₂(IDip)₂ and B₂(SIDip)₂ could be converted into bicyclic bis(boralactone) compounds.     

In-beam spectroscopy of 253, 254No

In-beam conversion electron spectroscopy experiments have been performed on the transfermium nuclei ^{253, 254}No using the conversion electron spectrometer SACRED in nearly collinear geometry in conjunction with the gas-filled separator RITU at the University of Jyv?skyl?. The experimental setup is discussed and the spectra are compared to Monte Carlo simulations. The implications for the ground-state configuration of ²⁵³No are discussed. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: rdh@ns.ph.liv.ac.uk RID="b" ID="b"Present address: GANIL, F-14021 Caen, France. RID="c" ID="c"Permanent address: IReS Strasbourg, IN2P3-CNRS, F-67037-Strasbourg, France. RID="d" ID="d"Present address: CEA/DIF DCRE/SDE/LDN F-91680 Bruyeres-le-Chatel. RID="e" ID="e"Present address: Daresbury Laboratory, Daresbury WA4 4AD, UK. RID="f" ID="f"Permanent address: IPN Lyon, IN2P3-CNRS, F-69037 Lyon, France.     

Magnetic charge type equations from torsion

It is shown that torsion can be built from two independent vector fields, and that these vector fields obey, for the Lagrangian chosen, the equations of electromagnetism with magnetic charge from the two photon formalism. The equation of motion follows from the Bianchi identity ofU ₄ spacetime, and finally the interpretation of these fields is discussed.     

Isolation and Component Structure in Spaces of Composition Operators

We establish a condition that guarantees isolation in the space of composition operators acting between H^p(B_N) and H^q(B_N), for 0 < p ≤ ∞, 0 < q < ∞, and N ≥ 1. This result will allow us, in certain cases where 0 < q < p ≤ ∞, completely to characterize the component structure of this space of operators.     

Angle resolved ESCA analysis of plasma modified polysterene

Summary Plasma treatment can be used to modify the surface properties of polymers. In the present paper angle resolved ESCA studies were carried out to determine the influence of a H₂O plasma on polysterene. Contrary to an O₂ plasma we observed a thinner reaction layer. On the other hand the H₂O plasma treatment induces higher concentrations of carbonate and ester linkages. An additional H₂ plasma treatment demonstrated that the highly oxidized constituents were reduced more effectively. The plasma reactions were carried out in a reactor that was already attached to the ESCA spectrometer.

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Winkelabhängige ESCA-Messungen an plasmabehandeltem Polystyrol

Zusammenfassung Die Oberflächeneigenschaften von Kunststoffen können durch Plasmareaktionen gezielt verändert werden. In der vorliegenden Arbeit wurde mit Hilfe von winkelabhängigen ESCA-Messungen der Einfluß eines H₂O-Plasmas auf Polystyrol untersucht. Im Gegensatz zum O₂-Plasma bildet sich eine dünne Reaktionsschicht aus. Außerdem entstehen verstärkt Carbonat und Estergrappen. Eine anschließende Behandlung im H₂-Plasma zeigt, daß bevorzugt die Gruppen mit höherem Oxidationszustand reduziert wurden. Die Plasmareaktionen erfolgten in einem Reaktor, der direkt an das Spektrometer angeschlossen war.

     

The essential equivalence of pairwise and mutual conditional independence

For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown to be essentially equivalent — i.e., equivalent to up to null sets. Unlike in the finite setting, a large collection of random variables remains essentially conditionally independent under further conditioning. The essential equivalence of pairwise and multiple versions of exchangeability also follows as a corollary. Our result relies on an iterated extension of Bledsoe and Morse's completion of the product of two measure spaces. Part of this work was done while Peter Hammond was visiting the National University of Singapore in March–April 2004. The final version was completed while Yeneng Sun was on sabbatical leave at the University of Illinois at Urbana–Champaign and Stanford University in October 2004 – May 2005.