Christoffel functions and mean convergence for Lagrange interpolation for exponential weights

For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given.     

The Design of Single Mode Large Cross-section Glass-based Waveguides for Photonic Integrated Circuits

This paper presents our recent simulation results and novel designs of single mode large cross-section glass-based waveguides for photonic integrated circuits (PICs). Simulations were performed using an in-house Finite Difference (FD) based mode solver and the FD Beam propagation Method (FD-BPM). Our simulation results show that this innovative technology could provide a simplified means to couple optical energy efficiently between optical components in a single chip. This would provide the base for the future large-scale integration of optical components in PICs. The novel idea of using single mode large cross-section glass-based waveguides as an optical integration platform is an evolutionary innovative solution for the monolithic integration of optical components, in which the glass-based structures act both as waveguides and as an optical bench for integration. This allows easy and efficient optical coupling between optical components and optical fibres, removing costly and tedious alignment problems and considerably reducing optical coupling losses in PICs. We expect that the glass-based waveguide PICs technology will enable the emergence of a new generation of compact, reliable, high speed, and multifunctional devices.     

Modulation of Spin Distribution and Spin Transport by a Magnetic Field in a Quasi-One-Dimensional System with Spin--Orbit Coupling

The distributions of spin and currents modulated by magnetic field in a transverse parabolic confined two-dimensional electronic system with a Rashba spin--orbit coupling have been studied numerically. It is shown that the spin accumulation and the spin related current are generated by magnetic field if the spin--orbit coupling is presented. The distributions of charge and spin currents are antisymmetrical along the cross-section of confined system. A transversely applied electric field does not influence the characteristic behaviour of charge- and spin-dependent properties.     

Structural characterization and ferromagnetic behavior of Fe-doped TiO2 powder by high-energy ball milling

Fe-doped TiO₂ powder was prepared by high-energy ball milling, using TiO₂ Degussa P-25 and α-Fe powders as the starting materials. The structure and magnetic properties of the Fe-doped TiO₂ powder were studied by X-ray diffraction, ⁵⁷Fe Mossbauer spectroscopy and vibrating sample magnetometer. The Reitveld refinement of XRD revealed that ball milling not only triggered incorporation of Fe in TiO₂ lattice but also induced the phase transformation from anatase to rutile in TiO₂ and consequently the milled Fe-doped TiO₂ powder contained only rutile.⁵⁷Fe Mössbauer effect measure showed that Fe atoms existed in Fe²⁺ and Fe³⁺ state, which were assigned to the solid solution Fe_xTi_1−xO₂. The magnetization measurements indicated that the milled Fe-doped TiO₂ powder was ferromagnetic above room temperature. The ferromagnetism in our milled Fe-doped TiO₂ powder seemingly does not come from Fe and iron oxides particles/clusters but from the Fe-doped TiO₂ powder matrices.     

A Lower Bound for {a+b:aA, bB, and P(a,b)≠0}

Let A and B be two finite subsets of a field . In this paper, we provide a non-trivial lower bound for {a+b:aA, bB, and P(a,b)≠0} where P(x,y) [x,y].     

水雾化制备Fe74Al4Sn2P10C2B4Si4非晶合金粉末及其磁粉芯性能研究

采用水雾化方法制备Fe7Al4Sn2P10C2B4Si4合金粉末,研究发现该合金具有强的非晶形成能力和高热稳定性,在粉末粒度小于400目时可以形成非晶态合金.采用该非晶粉末制备的磁粉芯在高频下品质因数显著高于MPP粉芯,说明该磁粉芯高频损耗较低.分析表明,非晶合金磁粉芯高频下损耗低的主要原因是电阻率较高.     

Patterned uniformly orientated silicon nanocrystallite films and efficient field emission characteristics

Patterned uniformly (100)-orientated silicon nanocrystallite (SiNC) films were fabricated based on hydrogen ion implantation technique and typical electrochemical anodic etching method. The surface morphology and microstructure characteristics of the films were characterized by scanning electron microscopy, transmission electron microscopy, X-ray diffraction, and atomic force microscopy. The efficient field emission with low turn-on field of about 3.2 V/μm at current density of 0.1 μA/cm² was obtained. The emission current density from the SiNC films reached 1 mA/cm² under a bias field of about 11 V/μm. The experimental results demonstrate that the SiNC films have great potential applications for flat panel displays.     

Asymptotics for zeros of Szeg polynomials associated with trigonometric polynomial signals

The study of Wiener-Levinson digital filters leads to certain classes of polynomials orthogonal on the unit circle (Szeg polynomials). Here we present theorems that show that the unknown frequencies in a periodic discrete time signal can be determined from the limiting behavior (as N → ∞) of the zeros of fixed degree Szeg polynomials that are orthogonal with respect to a distribution defined from N successive samples of the signal. This proves an essential part of a conjecture due to Jones, Njåstad, and Saff concerning the frequency analysis problem.     

A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.