Co-rich decagonal Al-Co-Ni: predicting structure, orientational order, and puckering

We apply systematic methods previously used by Mihalkovic et al. to predict the structure of the `basic' Co-rich modification of the decagonal Al70 Co20 Ni10 layered quasicrystal, based on known lattice constants and previously calculated pair potentials. The modelling is based on Penrose tile decoration and uses Monte Carlo annealing to discover the dominant motifs, which are converted into rules for another level of description. The result is a network of edge-sharing large decagons on a binary tiling of edge 10.5 A. A detailed analysis is given of the instability of a four-layer structure towards $c$-doubling and puckering of the atoms out of the layers, which is applied to explain the (pentagonal) orientational order.Comment: IOP LaTex; 7 pp, 2 figures. In press, Phil. Mag. A (Proc. Intl. Conf. on Quasicrystals 9, Ames Iowa, May 2005

The Cauchy Operator for Basic Hypergeometric Series

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator $T(bD_q)$. Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the $q$-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big $q$-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic

Scattering on two Aharonov-Bohm vortices with opposite fluxes

The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations

Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

Numerical study of molten and semi-molten ceramic impingement by using coupled Eulerian and Lagrangian method

Large temperature gradients are present within ceramic powder particles during plasma spray deposition due to their low thermal conductivity. The particles often impinge at the substrate in a semi-molten form which in turn substantially affects the final characteristics of the coating being formed. This study is dedicated to a novel modeling approach of a coupled Eulerian and Lagrangian (CEL) method for both fully molten and semi-molten droplet impingement processes. The simulation provides an insight to the deformation mechanism of the solid core YSZ and illustrates the freezing-induced break-up and spreading at the splat periphery. A 30 μm fully molten YSZ particle and an 80 μm semi-molten YSZ particle with different core sizes and initial velocity ranging from 100 to 240 m/s were examined. The flattened degree for both cases were obtained and compared with experimental and analytical data