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     

Mössbauer study of Martian regolith analogues

Terrestrial basalt rocks considered to be a good analogues of the Martian regolith were studied by using the Mössbauer spectroscopy and X-ray diffraction. The weathering of basalts was followed by the changes of the Fe²⁺/Fe³⁺ ratio. The basalt rock undergoes alteration from primary mineral composition (olivine+pyroxene+plagioclase) through smectite to kaolinite clay with oxides and hydroxides with the increase of the Fe²⁺/Fe³⁺ ratio.     

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     

129Xe NMR study of the homogeneity and the size distribution of small sodium metal particles in NaY zeolite

NaY zeolite samples loaded with sodium metal by vapor phase deposition have been investigated using¹²⁹Xe NMR spectroscopy. At low sodium concentration, the¹²⁹Xe NMR spectrum showed three resonance lines which clearly indicate the existence of distinct domains in the zeolite sample. Such an observation suggests that the diffusion of the xenon atoms into each domain only occurs with respect to the NMR time scale (2.9 ms). As the sodium concentration increases, observation of a single broad line indicate a macroscopic homogenization of the system. The shift of this line is explained in part due to a paramagnetic interaction between the xenon atoms and the unpaired electrons of particles containing an odd number of sodium atoms. The linewidth is due to the distribution of the local magnetic fields partially averaged by the rapid motion of the xenon atoms and to the statistical distribution of the sodium particles in the supercage cavities. The paramagnetic interaction vanishes with the oxidation of the sample leading to a narrowing and a shift of the line to higher magnetic fields.     

Thoms Effect as Influenced by the Concentration and Molecular Parameters of the Cationic Copolymer of Acrylamide

The Thoms effect observed with water-soluble cationic copolymer of acrylamide was studied in relation to the concentration, molecular weight, and molecular weight polydispersity of the polymeric additive, with its composition and composition polydispersity being constant.     

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.