Neural Network Models for Finline Discontinuities

The radial basis network is used as the finline discontinuities electromagnetic artifical neural network(EMANN) models. EM software analysis is employed to characterize finline discontinuities. EMANN models are then trained using physical parameters and frequency as inputs and equivalent electric circuit element parameters of finline discontinuities as outputs. Once trained , the EMANN models can simulate equivalent electric circuit element parameters of finline step, notch and strip very fast and efficiently.     

Numerical experiments with several variant WENO schemes for the Euler equations

Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.     

具有电子旋转方向的旋转间断的稳定性

用一维混合粒子编码研究了具有电子旋转方向的对称和非对称旋转间断的稳定性。发现在相对窄的过渡层厚度下,具有电子旋转方向的旋转间断是不稳定的,它趋向于发展成离子旋转方向的旋转间断和一些MHD波。这个发展过程部分地受到电子温度的限制。当过渡层厚度增加到足够宽时,电子旋转方向的旋转间断变成稳定的。本文简单地讨论了导致这种旋转间断不稳定的可能原因。     

A compact high‐order HLL solver for nonlinear hyperbolic systems

We present a new finite‐volume method for calculating complex flows on non‐uniform meshes. This method is designed to be highly compact and to accurately capture all discontinuities that may arise within the solution of a nonlinear hyperbolic system. In the first step, we devise a fourth‐degree Hermite polynomial to interpolate the solution. The coefficients defining this polynomial are calculated by using a least‐square method. To introduce monotonicity conditions within the procedure, two constraints are added into the least‐square system. Those constraints are derived by locally matching the high‐order Hermite polynomial with a low‐order TVD polynomial. To emulate these constraints only in regions of discontinuities, data‐depending weights are defined; these weights are based upon normalized indicators of smoothness of the solution and are parameterized by an O(1) quantity. The reconstruction so generated is highly compact and is fifth‐order accurate when the solution is smooth; this reconstruction becomes first order in regions of discontinuities. In the second step, this reconstruction is inserted in an HLL approximate Riemann solver. This solver is designed to correctly capture all discontinuities that may arise into the solution. To this aim, we introduce the contribution of a possible contact discontinuity into the HLL Riemann solver. Thus, a spatially fifth‐order non‐oscillatory method is generated. This method evolves in time the solution and its first derivative. In a one‐dimensional context, a linear spectral analysis and extensive numerical experiments make it possible to assess the robustness and the advantages of the method in computing multi‐scale problems with embedded discontinuities. Copyright © 2008 John Wiley & Sons, Ltd.     

欧拉常数γ的几种表示

调和级数∑n=1^∞1/n是发散的，而极限lim n→∞（∑k=1^∞1/k-lnn）却是收敛的，其极限值称为欧拉常数γ，本文给出了欧拉常数γ的几个有趣的级数表示和积分表示．     

Analysis of the plane contact with discontinuous curvature

The analytical solution for the plane contact between nonconforming C¹ profiles with a curvature discontinuity is obtained and discussed. The initial gap between the undeformed profiles was represented by a double parabolic function having the curvature discontinuity within the contact region. On the basis of the analytical solution, the complete analysis of pressure distribution was obtained. A raw technique to find an approximate solution is presented and comparison to the analytic one provided. For the limit case of strong curvature ratio the asymptotic treatment is discussed in terms of consistency with hypotheses claimed.     

在无单元法里直接准确施加位移边界条件和材料不连续条件

在无单元伽辽金法(EFG)里，由于其滑动最小二乘近似位移函数不满足Kronecker条件，使得它不能准确地施加本质边界条件和材料不连续条件，从而极大地限制了EFG法的发展和进一步应用。本文在位移边界和不同材料交界面的离散结点上采用实际的结点位移值，提出了一种准确施加位移边界和材料不连续条件的方法，该方法实施简单、稳定、求解精度高，而且其推导得出的整体刚度矩阵具有正定、对称和带状分布的特点，可以和有限单元法一样，直接利用各种成熟、高效的线性方程组解法求解系统平衡方程。数值算例结果表明了文中理论和方法的正确性和可靠性。     

密立根油滴实验数据处理的一种方法

以在重力场和静电场中运动的带电油滴为研究对象,提出了一种数据处理的方法,快速、准确地求解出基本电荷的电量,验证电荷的不连续性。     

Radial Quantization in Rotating Space–Times

We examine the time discontinuity in rotating space–times for which the topology of time is S¹. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of time. Quantized radii emerge for which the associated tangential velocities are less than the speed of light. Using the de Broglie relationship, we show that quantum theory may determine the periodicity of time. A rotating Kerr–Newman black hole and a rigidly rotating disk of dust are also considered; we find that the quantized radii do not lie in the regions that possess CTCs.     

Effect of Fe substitution on the thermal expansion of the highT c superconductor Y1Ba2Cu3O y

Thermal expansion measurements have been carried out on Fe substituted superconducting compounds Y₁Ba₂(Cu_1−x Fe _x )₃O _y (0<x<4%) using a high resolution dilatometer employing the three terminal capacitance technique. The experimental set up is sensitive enough to detect changes in α of less than 10⁻⁸K⁻¹. Results show that the jump Δα in the coefficient of linear thermal expansion at the superconducting transition temperature,T _c, increases almost linearly with Fe concentration. The normal state thermal expansion coefficient α first decreases, attains a minimum value aroundx=1% and then increases for higher Fe concentrations. The oxygen content per unit formula is almost constant up tox=1% and then increases rapidly withx. It has also been observed that the anomalous behaviour of α around 260 K observed by Meingastet al [22] for Fe concentrationx=5% is due to inadequate annealing of the sample.