Lateral interactions and nonequilibrium in adsorption and desorption. Part 2. A kinetic lattice gas model for (2 × 2)-(3O + NO)/Ru(0 0 1)

A kinetic lattice gas model is set up to study nonequilibrium effects in thermal desorption caused by limited mobility in the adsorbate. Treating the theoretical desorption spectra as input data we show that nonequilibrium effects must show up when different types of Arrhenius analyses, such as threshold and isosteric methods, are applied. We obtain estimates of the lateral NO interaction energies. The theory developed here has broader applicability beyond the present system.     

An unusual intramolecular Diels-Alder reaction

The diene-ester (2) on heating undergoes an intramolecular Diels-Alder reaction via the intermediate (3). The β-alkyl furan moiety in 3 reacts as the dienophile adding to the cyclohexadiene unit to give 4.     

Some isoperimetric norm bounds for solutions of the helmholtz equation

Summary Previous results of the authors [2] relating theL ₁ andL ₂ integrals of the first eigenfunction in the two dimensional fixed membrane problem are here extended to the analogous problem in higher dimensions.

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Zusammenfassung Frühere Resultate der Verfasser [2], welche eine Beziehung zwischen demL ₁- und demL ₂-Integral der ersten Eigenfunktion einer zweidimensionalen eingespannten Membran ergaben, werden hier auf das analoge Problem in höheren Dimensionen erweitert.

     

The preparation of multimode glass- and liquid-core optical fibres

A preform technique for drawing cladded-glass and hollow fibres suitable for application to optical communications is described. The parameters which need to be controlled are discussed and the preparation of the preforms is described. The resulting fibres have a high geometric uniformity and a probe beam remains largely at the same angle to the axis after more than 10⁶ reflections at the core/cladding interface. Fibre attenuations of 150, 60 and 5.8 dB km^–1 have been obtained with commercial glasses, preforms made from a special melt at Sheffield University [5], and a commercial liquid, respectively. The fibre drawing process does not appear to introduce any additional impurities and heat treatment has produced a significant reduction of transmission loss in glass fibres.     

Effects of residual single-quantum coherences in intermolecular multiple-quantum coherence studies

Intermolecular multiple-quantum coherences (iMQCs) have been reported to offer a sensitivity to sample structure at a specific user-defined length scale down to the order of 10 microm. When assessing this novel contrast mechanism in controlled phantom experiments, we have observed three different mechanisms whereby residual single-quantum coherences (SQCs) arising from intense high spatial frequencies, stimulated echoes and strong spatially encoding gradients can produce significant changes in signal contrast at particular length scales. These changes which only appear when components arising from SQCs and iMQCs are both present in the detected signal, are similar to changes previously attributed to iMQCs alone. We demonstrate each mechanism by which these residual SQCs arise and describe methods for their suppression.     

Surface diffusion: the low activation energy path for nanotube growth

We present the temperature dependence of the growth rate of carbon nanofibers by plasma-enhanced chemical vapor deposition with Ni, Co, and Fe catalysts. We extrapolate a common low activation energy of 0.23-0.4 eV, much lower than for thermal deposition. The carbon diffusion on the catalyst surface and the stability of the precursor molecules, C2H2 or CH4, are investigated by ab initio plane wave density functional calculations. We find a low activation energy of 0.4 eV for carbon surface diffusion on Ni and Co (111) planes, much lower than for bulk diffusion. The energy barrier for C2H2 and CH4 dissociation is at least 1.3 eV and 0.9 eV, respectively, on Ni(111) planes or step edges. Hence, the rate-limiting step for plasma-enhanced growth is carbon diffusion on the catalyst surface, while an extra barrier is present for thermal growth due to gas decomposition.     

The synthesis of some azuleno[c]furans

Azuleno[5,6-c]furan and 4-chloroazuleno[4,5-c]furan have been prepared by a tandem cycloaddition-cycloreversion strategy. These azulenofurans are qualitatively more stable than isobenzofuran and were characterised spectroscopically and as their Diels-Alder adducts with N-methylmaleimide.     

Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing

We propose a method to achieve quantum entanglement of two Fock states with perfectly efficient, ultraslow propagation enhanced four-wave mixing. A cold atomic medium is illuminated with a two-mode cw control laser to produce coherent mixtures of excited states. An ultraslowly propagating, single-photon quantum probe field completes the four-wave mixing with 100% photon flux conversion efficiency, creating a depth dependent entanglement of two Fock states. We show that at a suitable propagation distance, a maximum entangled state is created with a single-photon wave-packet state that has 50% probability of being in each of two product-type Fock states.     

On maximum principles for a class of nonlinear second-order elliptic equations

In a recent paper [3] the authors derived maximum principles which involved $\text{u(x)}\text{and}\text{q = ¦}\text{grad}\text{u¦}$, where u(x) is a classical solution of an alliptic differential equation of the form ($\text{g(q}{}^2\text{)u}{}_{\mathrm{,i}}\text{)}{}_{\mathrm{,i}}\text{+ ?(u) ?(q}{}^2\text{) = 0}$. In this paper these results are extended to the more general case in which $\text{g = g(u, q}{}^2\text{)}\text{and}\text{?(u) ?(q}{}^2\text{)}$ is replaced by h(u, q²).