Observation of discrete vortex solitons in optically induced photonic lattices

We report on the first experimental observation of discrete vortex solitons in two-dimensional optically induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.     

A study on the primary and secondary nucleation of ice by power ultrasound

Several different investigations have been carried out to study the primary and secondary nucleation of ice by sonocrystallisation. Firstly, the primary nucleation of discrete ice crystals in a supercooled sucrose solution has been observed. For increasing concentrations of sucrose solutions from 0 to 45 wt%, the nucleation temperature consistently occurs at a higher nucleation temperature in the presence of ultrasound. The nucleation temperature also increases as the power output and duty cycle of a commercial ultrasonic horn are increased. Snap shot images of the bubble clouds obtained from the ultrasonic horn also show that the number of bubbles appears to increase as the ultrasonic output is increased. This suggests that the nucleation of ice is related to the power output and number of cavitation bubbles. The effect of a single bubble on the sonocrystallisation of ice is discussed. High-speed movies (1120 fps) have shown that the crystallisation appears to occur in the immediate vicinity of the single bubble. In most cases, many crystals are observed and it is not known whether a single ice crystal is being fragmented by the bubble or whether many crystals are being initiated. The bubble appears to undergo a dancing regime, frequently splitting and rejoining and also emitting some small microbubbles. A study on the secondary nucleation of ice in sucrose solutions has been carried out using a unique ultrasonic cold stage device. Images taken using a microscope system show that the pre-existing ice dendrite crystals can be broken up into smaller fragments by an ultrasonic field. Cavitation bubbles appear to be important during the fragmentation process, possibly melting any ice crystals in their path. Flow patterns around cavitation bubbles have also been observed, and these may be responsible for the fragmentation of ice crystals.     

The geometry of 1-based minimal types

In this paper, we study the geometry of a (nontrivial) 1-based rank-1 complete type. We show that if the (localized, resp.) geometry of the type is modular, then the (localized, resp.) geometry is projective over a division ring. However, unlike the stable case, we construct a locally modular type that is not affine. For the general 1-based case, we prove that even if the geometry of the type itself is not projective over a division ring, it is when we consider a 2-fold or 3-fold of the geometry altogether. In particular, it follows that in any -categorical, nontrivial, 1-based theory, a vector space over a finite field is interpretable.

     

On the problem of coupling of ultrasonic receivers to layered structures for process control

Different layers in the construction of ultrasonic receiving transducers have been identified as a significant factor in the frequency response of these transducers. The discussion has been extended to the reception of signals through the layers of a process vessel-wall to determine whether the resulting system can be made independent of frequency over a significant spectral range and whether a system can be identified that is essentially independent, in its spectral response, to the thickness of one of the layers (the couplant to the vessel). While the present results are limited to a frequency range of 0–2 MHz, they can readily be extended to other frequency ranges. These computations have as variables the backing material, the transducer material, a wear plate, one or two quarter wavelength layers, the couplant and the structure of the vessel wall. The effect of thin bonding layers for the quarter wavelength plates is also briefly considered. As may have been expected each extra layer introduced into the system produces its own series of resonances. The case of a number of quarter wavelength layers can give a flat frequency response over almost a megahertz of bandwidth but great care needs to be taken with the bonding layers. A system in which the thickness of the couplant had little effect on the overall spectral response was not found.     

A multiple nomogram for ultrasonic propagation calculations

A multiple nomogram is presented for the evaluation of wavelength λ in a given medium, the acoustic radius ka of a scatterer or source, and the near-field length of a circular piston source. The nomogram may be used for velocities between 100 and 10⁴ ms^?1, for frequencies between 10⁴ and 10⁹ Hz, and for linear dimensions between 1 μm and 100 mm.     

Chemistry of pnictogen(III)-nitrogen ring systems

This critical review covers significant recent advances in the chemistry of pnictogen(III)-nitrogen ring systems, also known as cyclopnict(III)azanes. The synthetic methodologies and reactions of the heavier pnictogen systems are compared with the well-developed chemistry of cyclophosph(III)azanes. Particular attention is focused on ring-oligomerization processes and the use of four-membered E(2)N(2) rings as building blocks for the synthesis of macrocyclic molecules. Main-group element and transition-metal complexes are also discussed (95 references).     

Ring and Cluster Structures of {Li[C(NtBu)2(HNtBu)]}2·(THF) and {Li2[C(NtBu)3]}2, Containing the Novel Anions [C(NtBu)2(HNtBu)]−- and [C(NtBu)3]2−

The reaction of tert.-butyl carbodiimide with one equivalent of LiNH^tBu in tetrahydrofuran at-78 °C produces {Li[C(N^tBu)₂(HN^tBu)]}₂-(THF) (1), which is an eight-membered Li₂C₂N₄ ring; the deprotonation of (1) with two equivalents of n-BuLi in tetrahydrofuran at -78 °C and recrystallisation of the product from n-pentane yielded the unsolvated dimer {Li₂[C(N^tBu)₃]}₂ (2), which adopts the structure of a distorted hexagonal prism.