Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Clumping Data in 2-Way Tables: A User-Orientated Perspective

Following a critique of existing algorithms, an algorithm is presented which will re-organize a 2-way data table to bring like rows together, and like columns together. Extensions of the method are described, and justified, to accommodate distances measured in modular arithmetic, and with bipolar columns/rows, as in repertory grid analysis. One value of the algorithms is that the user can see relationships in the tables without the data in the cells themselves ever having been transformed. Thus, users will continue to feel they own their data.     

Refining the Diffusion Approximation for the <Emphasis Type="Italic">GI</Emphasis><Superscript><Emphasis Type="Italic">x</Emphasis></Superscript><Emphasis Type="Italic">/G/c</Emphasis> Queue

This paper deals with the GI ^x /G/c queueing system in a steady state. We refine a diffusion approximation method incorporating the constraint of traffic conservation for general queueing systems. An approximate expression for the distribution of the number of customers is obtained. Numerical results are presented to show that the refined model provides improved performance.     

Spin coupling in distorted high-valent Fe(IV)-porphyrin radical complexes

In order to study structural influences on the interaction of Fe(IV) (S=1) and porphyrin cation radical (S=1/2) in high-valent iron porphyrin complexes of the type ¦X-(TMP)Fe=O¦⁺(Cl^–), X=I, Br₂, Br₄ were generated by mCPBA oxidation of corresponding Fe(III) porphyrins. The halogen substitution at the peripheral positions of the porphyrin leads to distortion of the planar porphyrin ring of ¦(TMP)Fe=O¦⁺. The new species have beeen investigated by temperature-dependent EPR and field-dependent Mössbauer spectroscopy; for the evaluation of spectra, we adopted the spin-Hamiltonian formalism including exchange interaction explicitly. As in ¦(TMP)Fe=O¦⁺, strong ferromagnetic spin coupling was observed with|J₀|D=0.9–1 and a zero-field spltting ofD32 cm^–1. For consistent parametrization of EPR and Mössbauer results, anisotropic coupling had to be introduced. Compared to ¦(TMP)Fe=O¦⁺ [1], analysis of the spectroscopic data shows that zero-field splitting and spin coupling is only slightly affected by the halogen distortion of the porphyrin structure.     

Mössbauer and PAC studies of nanocrystalline Fe

High-purity Fe powder was mechanically milled under argon at ambient temperature using an SPEX 8000 mill. The local atomic and magnetic structure was studied using⁵⁷Co/Fe Mössbauer and¹¹¹In/Cd perturbed angular correlations (PAC) spectroscopies. After 32 hours of milling, X-ray diffraction revealed effective grain diameters of 18 nm and energy-dispersive X-ray analysis indicated a Cr impurity concentration of 5%, presumably introduced by mechanical attrition of steel ball bearings used for milling. In addition to a spectral component very similar to bulk iron metal, the Mössbauer spectra exhibited hyperfine field shifts attributed to the Cr impurities. PAC spectra on Fe milled for 5 h, with no contamination, exhibited two components: (1) A slightly broadened magnetic interaction attributed to interior, defect-free sites of In/Cd probes with a mean hyperfine field slightly greater than in macroscopic grains. The defect-free site fraction grew appreciably during milling, even though In is essentially insoluble in Fe. (2) An indistinct signal due to mixed magnetic and quadrupole interactions attributed to probes at surface or other defect sites.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Investigations of the interlayer coupling in high-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> cuprates

Low-field magnetizationM(H) measurements can be used to probe the nature of the screening currents and the interlayer coupling in high-T _c cuprates. Here we compare theM(H) behaviour of single crystals of Bi₂Sr₂CaCu₂O₈ and fully oxygenated and oxygen reduced YBa₂Cu₃O_7??. In YBa₂Cu₃O₇, theM(H) behaviour is consistent with anisotropic 3D superconductivity whilst in Bi₂Sr₂CaCu₂O₈, the surface screening currents are strongly affected by the presence of vortices, implying that the CuO₂ planes are coupled via a weak Josephson interaction. In oxygen-deficient YBa₂Cu₃O_6.7 (T _c =63K), theM(H) behaviour at low temperatures is similar to that found for Bi₂Sr₂CaCu₂O₈, implying that the removal of oxygen from the chains has resulted in a dimensional crossover of the superconducting state in YBa₂Cu₃O_7??. As the temperature approachesT _c , the 3D behaviour is eventually restored as thec-axis coherence length ξ _c becomes comparable with the interlayer spacingd.     

Transport studies in boron-ion implanted type II<Emphasis Type="Italic">a</Emphasis> diamond

We have investigated low-temperature electrical transport mechanisms in the surface layer of a type IIa diamond which has been heavily implanted with boron-ions at low temperatures and then annealed at high temperatures. The boron atoms occupy substitutional sites giving rise to a heavily doped wide-bandgap semiconductor. The dc-conductivity results suggest that for the maximum boron doping that has been achieved, the diamond sample is close to the insulator-metal transition. A model to account for the observed increase in activated boron centres with ion dose is presented. On the insulating side of the transition, the data are interpreted in terms of variable-range hopping laws.