基于电磁拓扑的多腔体屏蔽效能快速算法

提出基于电磁拓扑理论计算开孔多腔体屏蔽效能的快速方法.首先给出双腔体等效电路和电磁拓扑信号流图,并推导孔缝节点处的散射矩阵,给出拓扑网络的散射矩阵方程和传输矩阵方程,获得双腔体的广义Baum-Liu-Tesche(BLT)方程.在此基础上研究了开孔三腔体,包括串型级联三腔体和串并型混合级联三腔体的广义BLT方程.对于串型级联三腔体,其电磁拓扑网络和广义BLT方程在双腔体基础上直接扩展即可获得.而对于串并型混合级联三腔体,通过将位于三腔体公共面上的孔缝等效为三端口网络节点,并根据三端口网络散射参数定义推导获得该节点的散射矩阵,最终得到串并型混合级联三腔体的广义BLT方程.本文方法对双腔体的计算结果与文献结果和实验结果相符合,对3组不同类型和尺寸开孔腔的屏蔽效能的计算结果与时域有限差分法计算结果符合较好.该算法不仅效率高,通过对所有计算结果和实验结果的误差统计分析,表明该算法具有较高的计算准确度.     

太赫兹波段Smith-Purcell辐射的介质加载光栅高频特性

提出了一种用于Smith-Purcell效应器件的介质加载光栅慢波结构,通过研究该结构的注-波互作用过程,推导出带电子注的色散方程,并数值求解出波的线性增长率.利用色散方程,结合电磁场传播的边界条件,推导出Smith-Purcell效应振荡器工作所需的起振电流.详细研究了高频结构长度、电子注主要参数和介质相对介电常数对起振电流的影响,并与普通金属光栅结构进行了比较.结果表明:保持其他参数不变时,高频结构长度越短,起振电流越大;保持高频结构参数不变时,起振电流随电子注厚度和注-栅距离的增大而增大,随电子注电压的增大而减小;与金属光栅相比,介质的引入提高了注-波互作用的增长率,有效减小了振荡器的起振电流.理论计算结果与软件CHIPIC的模拟结果比较符合.     

球形Dirac方程的空间格点求解及假态问题

本文在空间格点上利用虚时间步长方法求解了球形Dirac方程, 着重研究了出现的假态问题. 利用三点数值导数公式离散方程中一阶导数项, 可以证明对于量子数为 κ 和 -κ的单粒子能级能量是完全相同的, 其中一个为物理解, 另一个为假态. 通过在径向Dirac方程中引入Wilson 项, 可以解决假态问题, 得到全部物理解. 文章以 Woods-Saxon 势为例, 考虑 Wilson 项后, 得到与打靶法一致的结果.     

An investigation on surface tensions of Pb-free solder materials

Surface tensions of some Pb-free solder systems such as Ag–Bi–Sn with cross-sections Ag/Bi = 1/1, Ag/Bi = 1/2, Ag/Bi = 2/1, In–Sn–Zn with cross-sections Sn/In = 1/1, Sn/In = 1/3 and (Ag₇Cu₃)_100?x Sn_x with cross-section Ag/Cu = 7/3 are calculated from the sub-binary surface tension data using the models, such as the Muggianu, Kohler, Toop models, Butler’s equation and Chou’s General Solution Model (GSM) at 873, 923 and 1073 K, respectively. The surface tension of In–Sn–Zn increases wavily with increasing amount of Zn and it is found that the best models are the GSM for both cross-sections in question while GSM becomes the best model for (Ag₇Cu₃)_100?x Sn_x alloy in the whole experimental range. Moreover, the surface tension of (Ag₇Cu₃)_100?x Sn_x decreases slightly with increasing amount of Sn. The Muggianu, Butler and Butler models are determined as the best models for the cross-sections in the order given above for entire measurement range, respectively, and the surface tension of Ag–Bi–Sn decreases slightly with an increasing amount of Bi and Ag but increases with increasing Sn in liquid alloys.     

Some insights in superdiffusive transport

In a wide range of systems, the relaxation in response to an initial pulse has been experimentally found to follow a nonlinear relationship for the mean squared displacement, of the kind 〈x²(t)〉∝t^α$〈x^2(t)〉\propto t^{\alpha }$, where α$\alpha$ may be greater or smaller than 1. Such phenomena have been described under the generic term of anomalous diffusion. “Lévy flights” stochastic processes lead to superdiffusive behaviour (1<α<2)$(1<\alpha <2)$ and have been recently proposed to model—among the others—the subsurface contaminant spread in highly heterogeneous media under the effects of water flow. In this paper, within the continuous-time random walk (CTRW) approach to anomalous diffusion, we compare the analytical solution of the approximated fractional diffusion equation (FDE) with the Monte Carlo one, obtained by simulating the superdiffusive behaviour of an ensemble of particle in a medium. We show that the two are neatly different as the process approaches the standard diffusive behaviour. We argue that this is due to a truncation in the Fourier space expansion introduced by the FDE approach. We propose a second-order correction to this expansion and numerically solve the CTRW model under this hypothesis: the accuracy of the results thus obtained is validated through Monte Carlo simulation over all the superdiffusive range. The same kind of discrepancy is shown to occur also in the derivation of the fractional moments of the distribution: analogous corrections are proposed and validated through the Monte Carlo approach.     

Mathematical model of electromigration allowing the deviation from electroneutrality

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern–Gouy–Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.     

Exact solutions to a class of differential equation and some new mathematical properties for the universal associated-Legendre polynomials

The exact solutions to a class of differential equation are studied. Some special cases are discussed for the central potentials, single ring-shaped potential and the angular Teukolsky equation. A new expression to the associated Legendre polynomials is found. Some new properties of the universal associated-Legendre polynomials (UALPs) including the generating function, Rodrigues’ formula, parity, some special values and the recurrence relations are presented. A new different Rodrigues’ formula of associated Legendre polynomials is also obtained.     

Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one‐dimensional second‐order wave equation

In this article, we analyze a residual‐based a posteriori error estimates of the spatial errors for the semidiscrete local discontinuous Galerkin (LDG) method applied to the one‐dimensional second‐order wave equation. These error estimates are computationally simple and are obtained by solving a local steady problem with no boundary condition on each element. We apply the optimal L² error estimates and the superconvergence results of Part I of this work [Baccouch, Numer Methods Partial Differential Equations 30 (2014), 862–901] to prove that, for smooth solutions, these a posteriori LDG error estimates for the solution and its spatial derivative, at a fixed time, converge to the true spatial errors in the L²‐norm under mesh refinement. The order of convergence is proved to be , when p‐degree piecewise polynomials with are used. As a consequence, we prove that the LDG method combined with the a posteriori error estimation procedure yields both accurate error estimates and superconvergent solutions. Our computational results show higher convergence rate. We further prove that the global effectivity indices, for both the solution and its derivative, in the L²‐norm converge to unity at rate while numerically they exhibit and rates, respectively. Numerical experiments are shown to validate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1461–1491, 2015     

A macroscopic model for an intermediate state between type‐I and type‐II superconductivity

A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type‐I and type‐II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen's model. The nonlinearity is coming from the power law relation by Rhyner. The well‐posedness of the problem is discussed under low regularity assumptions and the error estimate for a semi‐implicit time‐discrete scheme based on backward Euler approximation is established. In the proofs, the monotonicity methods and the Minty–Browder argument are used. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1551–1567, 2015