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

Marginally Trapped Surfaces in the Nonsymmetric Gravitational Theory

We consider a simple, physical approach to the problem of marginally trapped surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach to a particular spherically symmetric, Wyman sector gravitational field, consisting of a pulse in the antisymmetric field variable. We demonstrate that marginally trapped surfaces do exist for this choice of initial data.Comment: REVTeX 3.0 with epsf macros and AMS symbols, 3 pages, 1 figur

Laser-assisted photothermal imprinting of nanocomposite

We report on a laser-assisted photothermal imprinting method for directly patterning carbon nanofiber-reinforced polyethylene nanocomposite. A single laser pulse from a solid state Nd:YAG laser (10 ns pulse, 532 nm and 355 nm wavelengths) is used to melt/soften a thin skin layer of the polymer nanocomposite. Meanwhile, a fused quartz mold with micro-sized surface relief structures is pressed against the surface of the composite. Successful pattern transfer is realized upon releasing the quartz mold. Although polyethylene is transparent to the laser beam, the carbon nanofibers in the high density polyethylene (HDPE) matrix absorb the laser energy and convert it into heat. Numerical heat conduction simulation shows the HDPE matrix is partially melted or softened, allowing for easier imprinting of the relief pattern of the quartz mold.Mechanical Engineerin

Characterisation of microstructure, defect and high-cycle-fatigue behaviour in a stainless steel joint processed by brazing

We report the characterisation of microstructures and high-cycle-fatigue (HCF) properties of Type 304 stainless steel joints processed by brazing. Pure copper was applied as the filler metal for brazing at 1120 °C. A two-phase microstructure was obtained within the joint region: the star-shaped precipitates and copper matrix. The precipitates with an average size of 0.43 μm were rich in iron and chromium. A fixed orientation relationship was found between the precipitates and copper matrix. The joint exhibited much higher tensile strength and HCF life when compared to pure copper. The strength enhancement can be attributed to the presence of precipitates. Furthermore, the effect of joint interface roughness as well as defects was critically investigated. The joint interface roughness showed little influence on the HCF lives. Post-examinations revealed that fatigue crack initiation and propagation occurred entirely within the joint region, hence being consistent with the similar HCF lives regardless of the pre-defined interface roughness conditions. In addition, it was found that the HCF lives decreased exponentially with the increase of initial defect area. Fractography analysis revealed that fatigue striation spacings near the crack initiation zone increased with the increase of defect area, suggesting that the larger defects result in higher crack growth rate, hence shorten the overall fatigue life.</div

Classification of spacelike surfaces in spacetime

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of trapped, umbilical and extremal surfaces, which split into several different classes. The classification raises new important questions and opens many possible new lines of research. These, together with some applications and examples, are briefly considered.Comment: 42 pages, 10 tables, many diagram

The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

The renormalisation group approach is applied to the study of the short-time critical behaviour of the $d$-dimensional Ginzburg-Landau model with long-range interaction of the form $p^{\sigma} s_{p}s_{-p}$ in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents $\theta^{\prime}$ and $\theta$ of the order parameter and the response function respectively, are calculated to the second order in $\epsilon=2\sigma-d$.Comment: 18 pages, 4 figures, 1 tabl