Singularities in cascade models of the Euler equation

The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial large-scale energy distribution, the energy rushes towards smaller scales, forming a universal front independent of initial conditions. The front results in a singularity of the vorticity in finite time, and has scaling form as function of the time difference from the singularity. Using a simplified model, we compute the values of the exponents and the shape of the front analytically. The results are in good agreement with numerical simulations.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

FEM study of palladium and molybdenum clusters on an alumina covered field emitter

Palladium and molybdenum polycrystalline layers (clusters) have been deposited in a stainless steel UHV system onto a layer of alumina (Al₂O₃). This layer has been prepared by high temperature oxidation of an aluminium layer. The interaction of this system with nitrogen has been investigated at room temperature by an FEM technique. Under these conditions nitrogen spillover from molybdenum to palladium has been observed.     

Hydroxyl ion conduction in ytterbium-doped strontium cerate at T<580 K in H2O/air atmosphere

Open circuit voltage (OCV) measurements in H₂O/air concentration cells at T<580 K using Yb-doped SrCeO₃ electrolyte indicate that under these conditions, protons are transported through the electrolyte as -ve ions, possibly as hydroxyl (OH⁻) ions. The H⁺ ionic transport, which is generally reported, becomes the dominant mode for H₂O/air concentration cells at temperatures greater than 750 K or when H₂O/air electrodes are replaced by H₂/Ar, and the anomalous OCV sign disappears. The combination of low temperature and the presence of hydrogen and oxygen as provided by the H₂O/air system appears to be necessary for the postulated hydroxyl ion electrode reactions to take place. In addition to OCV measurements, results from impedance spectroscopy are used to provide evidence in support of the suggested hydroxyl ion mode of protonic transport under the specified conditions. These findings are directly relevant in the development of novel humidity sensors in the temperature range 450–580K and is reported in a separate paper in this conference. Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996     

Adiabatic passage Hartmann-Hahn cross polarization in NMR under magic angle sample spinning

We have recently demonstrated that polarization transfer using an adiabatic passage through the Hartmann-Hahn condition (APHH-CP) by a variation of the radio-frequency amplitude can substantially improve the transfer efficiency over Hartmann-Hahn cross polarization. Here we show that APHH-CP can be combined with fast magic angle sample spinning (MAS). The heteronuclear dipolar order, established in the course of the transfer, can indeed be created and preserved.     

Alloying by high dose ion implantation of iron into magnesium and aluminium

Alloys of the systems Fe–Al (mixable over the whole concentration range) and Fe–Mg (insoluble with each other) were produced by implantation of Fe ions into Al and Mg, respectively. The implantation energy was 200 keV and the ion doses ranged from 1 × 10₁₄ to 9 × 10₁₇cm^-2The obtained implantation profiles were determined by Auger electron spectroscopy depth profiling. Maximum iron concentrations reached were up to 60 at.% for implantation into Al and 94 at.% for implantation into Mg. Phase analysis of the implanted layers was performed by conversion electron Mössbauer spectroscopy and X‐ray diffraction. For implantation into Mg, two different kinds of Mössbauer spectra were obtained: at low doses paramagnetic doublets indicating at least two different iron sites and at high doses a dominant ferromagnetic six‐line‐pattern with a small paramagnetic fraction. The X‐ray diffraction pattern concluded that in the latter case a dilated αiron lattice is formed. For implantation into Al, the Mössbauer spectra were doublet structures very similar to those obtained at amorphous Fe–Al alloys produced by rapid quenching methods. They also indicated at least two different main iron environments. For the highest implanted sample a ferromagnetic six‐line‐pattern with magnetic field values close to those of Fe₃Al appeared.     

Evolved gas analysis (EGA) of brick clays

Using a system based on non-dispersive infrared (NDIR) detectors, evolved gas analysis (EGA) was able to identify and quantify the principal volatiles produced by heating powdered samples of UK brick clays. From these results, atmospheric emissions likely to result from brick production can be predicted. In addition, EGA results for extruded brick clay test pieces are significantly different from those of powdered samples. Within an extruded brick clay body, evolved gases are contained within a pore system and evolved gas-solid phase reactions also occur. This EGA study provides further evidence on the nature of firing reactions within brick clay bodies. The qualitative and quantitative influence of heating rate — a key process condition in brick manufacture — on gas release is also outlined.Dedicated to Dr. Robert Mackenzie on the occasion of his 75th birthday