The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901

We study the linearized stability of n-vortex (n∈ℤ) solutions of the magnetic Ginzburg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ± 1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n|≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]). Received: 16 November 1998 / Accepted: 3 January 2000 RID="*" ID="*"Research on this paper was supported by NSERC under grant N7901 RID="**" ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.&para;E-mail: gustaf&commat;cims.nyu.edu     

The growth of the thermal boundary layer in laminar flow between parallel flat plates

Summary The problem considered is that of the heat transfer occurring at the inlet to a parallel plate channel. Instead of separating variables, the energy equation is solved, after transformation, in the form of a power series. This method supplies information concerning the initial growth of the thermal boundary layer which is not obtainable by previous methods using eigen-function expansions. A sufficient number of coefficients of the series is computed to allow the present solution to be joined to the asymptotic eigen-function solution, thus completing the treatment of the problem for all values of the longitudinal variable.     

Oxidation of the hydrogenated diamond (100) surface

The surface composition and structure of natural diamond (100) surfaces subsequently oxidized with activated oxygen at T_sub≤35°C were investigated with high-resolution electron energy loss spectroscopy (HREELS), Auger electron spectroscopy, electron loss spectroscopy (ELS) and low-energy electron diffraction (LEED). Complete surface oxidation (oxygen coverage θ=1 ML) required doses of hundreds of kilolangmuirs of O₂. HREELS vibrational spectra permitted identification of the specific surface oxygen species, and also provided information about the diamond surface states. Most surface sites lost their hydrogen at least once before becoming oxidized. The oxygen coverage θ increased quickly at first, and then more slowly as saturation was approached; different mechanisms or sites may have accounted for the decreased rate. The relative distribution of oxygen species varied with the oxidation conditions. Ether, carbonyl and hydroxyl groups appeared during the initial stages of oxidation, but the hydroxyl groups disappeared at higher coverages. Bridge-bonded ether groups dominated at saturation coverage, although smaller amounts of carbonyl and hydroxyl were still observed. The carbonyl and C---H stretch frequencies increased with oxygen dose due to formation of higher oxidation states and/or hydrogen bonding between adjacent groups. ELS revealed only a low concentration of C=C dimers on the oxidized surfaces, and no evidence of graphitization.

Surfaces generated by oxygen addition and then desorption were more reactive than surfaces generated by hydrogen desorption. Oxidized surfaces that were heated in vacuum and then rehydrogenated did not recover the sharp LEED patterns and HREELS spectra of the original plasma-smoothed surface. This effect was presumably due to surface roughening caused by oxygen desorption as CO and CO₂, and creation of reactive high-energy sites that quickly bonded to available background gases and prevented large areas of organized surface reconstruction.     

2]Pseudorotaxanes, [2]rotaxanes and metal-organic rotaxane frameworks containing tetra-substituted dibenzo[24]crown-8 wheels

[2]Pseudorotaxanes, [2]rotaxanes and metal-organic rotaxane framework materials that utilise DB24C8 as the wheel component are well known and structural variations based on changing the axle component are common. Studies in which the DB24C8 wheel is structurally modified are much more limited. Herein, is described the synthesis of symmetrical DB24C8 analogues containing four CH(2)OR (R = CH(2)CH(2)CH(3), CH(2)(C(6)H(5)), C(6)H(5) and C(6)H(4)(4-COOEt)) substituents on the 4 and 5 positions of the aromatic rings. The effect of these molecular appendages on the stability and structures of the interpenetrated and interlocked molecules derived from these new wheels is described. The major effects are an increase in association constants for the formation of [2]pseudorotaxanes relative to DB24C8, the crystal packing of [2]rotaxanes and a change on the internal structure of a 2D MORF (R = C(6)H(5)) compared to DB24C8.     

Corannulene and its penta-tert-butyl derivative co-crystallize 1:1 with pristine C60-fullerene

The first X-ray structural determinations of pristine fullerene C(60), cocrystallized 1:1 with corannulene and with its pentaalkyl-substituted derivative, 1,3,5,7,9-penta-tert-butyl-corannulene, have now been achieved.     

The effect of Lewis number variation on combustion waves in a model with chain-branching reaction

In this paper we investigate the linear stability and properties of the travelling premixed combustion waves in a model with two-step chain-branching reaction mechanism in the adiabatic limit in one spatial dimension. It is shown that the Lewis number for fuel has a significant effect on the properties and stability of premixed flames, whereas the Lewis number for the radicals has only quantitative (but not qualitative) effect on the combustion waves. We demonstrate that when the Lewis number for fuel is less than unity the flame speed is unique and is a monotonically decreasing function of the dimensionless activation energy. The combustion wave is stable and exhibits extinction for finite values of activation energy as the flame speed decreases to zero. For fuel Lewis number greater than unity the flame speed is a double-valued function. The slow solution branch is shown to be unstable whereas the fast solution branch is either stable or exhibits the onset of pulsating instabilities via the Hopf bifurcation. The evolution of these instabilities leads to flame extinction.     

Electron-impact induced oxygen migration in the mass spectra of β-ketoalkylidenephosphoranes

The mass spectra of six β-ketoalkylidenephosphoranes have been examined. The spectra all exhibit an electron-impact induced migration of oxygen to phosphorus reminiscent of their thermal decomposition.