Exact solution of a vertex model ind dimensions

We consider a class of vertex models describing directed lines on a lattice in arbitraryd dimensions, and solve the model exactly for the Cartesian lattice and in the case that each loop of lines carries a fugacity - 1. Our analysis, which can be carried out for arbitrary lattices, is based on an equivalence of the vertex model with a dimer problem. The dimer problem is, in turn, solved using the method of Pfaffians. It is found that the system is frozen below a critical temperatureT _cwith the critical exponent = (3 –d)/2.     

Surface studies on polycrystalline YBa2Cu3O7−δ with Auger electron and low-energy electron energy-loss spectroscopy

Chemical and electronic properties of scrapecleaned YBa₂Cu₃O_7–(YBCO) ceramics, which were also annealed in vacuum or exposed to H atoms or O₂ molecules, were studied at room temperature by applying Auger electron (AES) and low-energy electron energy-loss spectroscopy (LEELS). Scanning electron micrographs showed such scraped surfaces to consist mainly of small, fractured YBCO crystallites, i.e. of clean YBCO surfaces. With only one exception, all low-energy AES lines were found to be shifted in energy compared to data recorded with surfaces of metallic Cu and Y. The analysis of the high-energy AES lines indicated the existence of non-stoichiometric material in grain boundaries. At least 25 different LEELS features were recorded. The 24.9-eV energy loss, which is due to the excitation of bulk valence-electron plasmons, indicates an enhanced oxygen deficit _s 0.8 at scrape-cleaned YBCO surfaces. Annealing of scraped YBCO samples at approximately 700 K in vacuum and also their exposure to hydrogen atoms resulted in an additional oxygen depletion within a few atomic layers near to the surfaces. These oxygen deficiencies were found to increase the intensity ratios of low-and high-energy AES lines of Cu, Ba, and Y and to intensify the energy-loss peak at 4.4 eV which has been attributed to O–Cu–O dumbbells.     

Relaxation and phonons in viscous and glassy orthoterphenyl by neutron scattering

We present an extended set of incoherent neutron scattering measurements on the van der Waals liquido-terphenyl, obtained by time-of-flight and backscattering spectroscopy. In the supercooled liquid regime, data from three instruments are combined and analysed in terms of the selfcorrelationS(Q, t). In the time range 1...100 ps, the crossover from -to -relaxation is well described by the masterfunction of mode coupling theory, and fitted parameters are consistent with the previously established critical temperatureT _c [Z. Phys. B83, 175 (1991)]. In the glassy regime, vibrations are harmonic and can be described by a density of states. Deviations at lowQ are quantitatively explained by a multiple scattering simulation. Throughout the article, experimental difficulties are discussed in some detail.     

The level structure of92Ru up to high spin values

The level structure of⁹²Ru has been studied by means of γ-ray spectroscopy. The nucleus was produced by the⁵⁸Ni(⁴⁰Ca, α2p)⁹²Ru reaction at beam energies of 147 and 187 MeV. The NORDBALL detector system including particle selection was used. A large number of new levels with excitation energies up to 11.3 MeV and spin values up to 22 or 23 units of angular momentum have been established. The level scheme is compared with recent shell model calculations using¹⁰⁰Sn as a core. Some systematics of the g ₉ ^2/?2 configuration is discussed and a strong correlation between the levels in⁹⁰Mo and⁹²Ru is found.     

Additive pulse mode-locked Nd: YAG laser

Additive pulse mode locking applied to lamppumped Nd: YAG lasers results in an attractive source of picosecond pulses at 1.06 m or 1.32 m with average powers at the Watt level. We provide detailed information on construction and operation and give data on performance. A modified active stabilization scheme allows not only improved stability of operation but also insight into the dynamics of pulse formation.     

Depth-profiling of organic layers on microparticles with SNMS

Summary Previous work on the quantification and localization of organically bound elements with plasma-based SNMS for the characterization of microparticles has been continued. Relative detection factors for 10 elements have been determined. Except for lead and bromine a principle proportionality to atomic ionization probabilities is shown. A moderate matrix dependence of less than 40% variation was found even when inorganic and organic materials are included. For depth calibration, erosion rates of organic materials were determined from the time interval necessary to sputter through planar single-layers and Langmuir-Blodgett multi-layer systems with known thickness, as well as from gravimetric powder measurements. Depth propagation rates were 0.7 nm·sec^–1 for polymers and 2.3 nm·sec^–1 for aromatic compounds, when 400 eV argon ion bombardment with 0.7 mA·cm^–2 was used. A depth resolution of 30 nm has been obtained. Model particles of 5 m size have been coated with fluoranthene. Inspection with SNMS revealed an incomplete coating covering only 20% of the microparticle surface with an average thickness of the partial coating of 300 nm. Subsequent characterization using laser-induced fluorimetry confirmed the amount of fluoranthene coating measured by SNMS.     

The critical exponent of degenerate parabolic systems

The Cauchy problemu _t=u +v ^p ,v _t =v +u ^q is studied, wherex R ^N , 0 <t < and ,,p andq, are positive exponents. It is proved that ifp,q 1 and 1 <pq < 1 + 2 max(p + ,q + )/n then every nontrivial non-negative solution is not global in time; whereaspq > 1 + 2 max(p + , q + )/n then there exist both positive global solutions and non-global solutions. In addition, the decaying in time of solutions tou _t,=u inR ⁿ × (0, ), an equation which occurs naturally in our study of above systems, is studied and solutions with the fastest decaying in time are constructed.     

The generation and classification of tile-k-transitive tilings of the Euclidean plane,the sphere and the hyperbolic plane

Algorithms based on the theory of Delaney-Dress symbols are discussed that can be used to recursively produce all possible equivariant types of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane, for any (reasonable)k. A number of results can be obtained using computer implementations of the algorithms.     

Reaction-diffusion model for combustion with fuel consumption: II. Robin boundary conditions

A model, derived in a previous paper, for the reaction betweena gaseous oxidant and a solid porous fuel is analysed furtherfor general Robin boundary conditions. Numerical solutions areobtained and the effects of varying the dimensionless parameters,particularly the Frank-Kamenetskii parameter and the Lewisnumber L, are discussed in detail and compared with resultsobtained previously when Dirichlet boundary conditions are applied.Analytic solutions are obtained for the small-time developmentand for large values of . This latter solution shows the existenceof a propagating reaction-diffusion burning wave, and has featureswhich are qualitatively different to those derived earlier.