Electrical capacitance of dielectric coated metallic parallelepiped and closed cylinder isolated in free space

This paper presents a method for the evaluation of the capacitance and the charge distribution of a dielectric coated metallic parallelepiped and a dielectric coated metallic hollow cylinder with the top and bottom cover plates using the method of moments (MoM) based on the pulse basis function and the point matching. Boundary conditions for the potential on the conductor surfaces and continuity of the normal component of the displacement density at the dielectric-free space interface is used to generate two integral equations. Two sets of simultaneous equations are formed from the two integral equations using the MoM. The total charge on the conductor surface is found from the solution for the set of simultaneous equations. The validity of the analysis has been justified by comparing the data on the capacitance available in the literature for metallic cube and hollow cylinder with top and bottom cover plates with the data on capacitance, computed by the present method for similar structures considering a very low dielectric constant as well as a very thin dielectric coating.     

Moment method analysis of charge distribution & capacitance for the dielectric coated tilted plates isolated in free space

This paper presents a method for the evaluation of the capacitance of the dielectric coated metallic plates forming a corner using the method of moments based on the pulse basis function and the point matching. Two integral equations are formed based on the boundary conditions for the potential on the conductor surface and continuity of the normal component of the displacement flux density at the dielectric-free space interface. A set of simultaneous equations are formed from the two integral equations using the method of moments. The total free charge on the conductor surface is found from the solution of the set of simultaneous equations. Numerical data on the capacitance and the charge distribution are presented. The validity of the analysis has been justified by comparing the data on the capacitance that is available in the literature for a metallic structure with the data on the capacitance computed with the present method for a similar structure considering a very low dielectric constant as well as a very thin dielectric coating. Further validation has been carried out by comparing the capacitance data of the specific case when the angle between two metallic plates is 180° forming a dielectric coated metallic rectangular plate for which the capacitance data are available in the literature.     

格林函数在计算部分电容中的应用

在工业上和在实验室中,我们都会遇到两个物体之间的电磁屏蔽的问题。在许多应用中,我们只须注意到两个物体之间的静电屏蔽就够了,因而它们之间的相互作用可以从计算它们之间的相互电容来定出。当干扰物体的尺寸很小因而可以认为是一个点电源时,则当它与另一个接地导体(即问题中的电磁屏蔽)共同存在时所生的效应即可由这一个接地导体的格林函数表出。关于格林函数的知识已有很丰富的积累,因而本文中所提出的方法是可以解决多种多样的问题的。文中讨论了扁椭球坐标和长椭球坐标中的格林函数,并对带虚数自变数的勒讓特函数的若干个公式作了推导,因为这些有用的公式在流行的文献中还未见到。导体表面任意形状的小孔的问题是值得讨论的,特别是有限大导体表面上的小孔问题,本文从理论上验证了文献上已经提出来的实验结果。最后我们给出如下两个物体之间的相互电容公式:其中一个是在带小孔的闭合电磁屏蔽体的另一个之内。     

Waveformation during high-speed collision between a plate and a cone

The results of experimental studies of waveformation in a contact molten layer during an axial collision of metallic plates with metallic bodies in the form of truncated right circular cones are reported. A closed regular structure of the contact layer in the form of a series (train) of long waves is formed on the external surfaces of copper and aluminum cones. The results of measurements of the wavelength as a function of the group velocity fit into the ascending branch of the dispersion curve for the wave.     

Traction-free vibration of layered elastic and piezoelectric rectangular parallelepipeds

A variational method is developed to study the traction-free vibration of layered rectangular elastic and piezoelectric parallelepipeds. The weak form of the equations of motion and the charge equation are formulated in rectangular Cartesian coordinates. Approximate solutions to these equations are sought in a form that combines piecewise linear or quadratic Lagrange basis functions through the layered dimension of the solid with continuous global polynomial or trigonometric functions in the plane. This allows for the necessary discontinuity in the shear strain and normal potential gradient across the interface between layers caused by the mismatch in material properties. Numerical results compare very well with those computed by other techniques for layered elastic and piezoelectric plates with simple support and homogeneous parallelepipeds under stress-free conditions.     

基于微陷阱结构的金属二次电子发射系数抑制研究

近年来,金属二次电子发射系数的抑制研究在加速器、大功率微波器件等领域得到了广泛关注.为评估表面形貌对抑制效果的影响,利用唯象概率模型计算方法对三角形沟槽、矩形沟槽、方孔及圆孔4种不同形状微陷阱结构的二次电子发射系数进行了研究,分析了微陷阱结构的形状、尺寸对二次电子发射系数抑制特性的影响规律.理论研究结果表明:陷阱结构的深宽比、孔隙率越大,则其二次电子发射系数抑制特性越明显;方孔形和圆孔形微陷阱结构的二次电子发射系数抑制效果优于三角形沟槽和矩形沟槽;具有大孔隙率的微陷阱结构表面的二次电子发射系数对入射角度的依赖显著弱于平滑表面.制备了具有不同表面形貌的金属样片并进行二次电子发射系数测试,所得实验规律与理论模拟规律符合较好.     

A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part III: On a staggered mesh

The consistent and conservative scheme developed on a rectangular collocated mesh [M.-J. Ni, R. Munipalli, N.B. Morley, P. Huang, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system, Journal of Computational Physics 227 (2007) 174–204] and on an arbitrary collocated mesh [M.-J. Ni, R. Munipalli, P. Huang, N.B. Morley, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh, Journal of Computational Physics 227 (2007) 205–228] has been extended and specially designed for calculation of the Lorentz force on a staggered grid system (Part III) by solving the electrical potential equation for magnetohydrodynamics (MHD) at a low magnetic Reynolds number. In a staggered mesh, pressure (p) and electrical potential (φ) are located in the cell center, while velocities and current fluxes are located on the cell faces of a main control volume. The scheme numerically meets the physical conservation laws, charge conservation law and momentum conservation law. Physically, the Lorentz force conserves the momentum when the magnetic field is constant or spatial coordinate independent. The calculation of current density fluxes on cell faces is conducted using a scheme consistent with the discretization for solution of the electrical potential Poisson equation, which can ensure the calculated current density conserves the charge. A divergence formula of the Lorentz force is used to calculate the Lorentz force at the cell center of a main control volume, which can numerically conserve the momentum at constant or spatial coordinate independent magnetic field. The calculated cell-center Lorentz forces are then interpolated to the cell faces, which are used to obtain the corresponding velocity fluxes by solving the momentum equations. The “conservative” is an important property of the scheme, which can guarantee computational accuracy of MHD flows at high Hartmann number with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers. 2D fully developed MHD flows with analytical solutions available have been conducted to validate the scheme at a staggered mesh. 3D MHD flows, with the experimental data available, at a constant magnetic field in a rectangular duct with sudden expansion and at a varying magnetic field in a rectangular duct are conducted on a staggered mesh to verify the computational accuracy of the scheme. It is expected that the scheme for the Lorentz force can be employed together with a fully conservative scheme for the convective term and the pressure term [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics 143 (1998) 90–124] for direct simulation of MHD turbulence and MHD instability with good accuracy at a staggered mesh.     

Density of states of a two-dimensional electron gas measured by high-resolution photoelectron spectroscopy

We present high energy-resolution photoemission measurements of the spectral density at the discrete quantized electronic levels of a two-dimensional (2D) electron gas. The dynamical 2D electron gas has been obtained by generating a strong accumulation layer at the (110) surface of narrow-gap III–V semiconductors. Exploitation of a number of cases generating band bending (metallic chains or clusters, atomic structure, defects) demonstrates the generality of 2D electron gas formation at charge-accumulated semiconductor surfaces. A self-consistent solution of the Poisson and Schrödinger equations gives the potential well shape, the sub-band energy level position and the accumulated charge density, in excellent agreement with the present experimental data.     

Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates

An inhomogeneous layer element method is presented to analyze the dispersion of waves and characteristic wave surfaces in plates of functionally graded piezoelectric material (FGPM). In this method, the FGPM plate is divided into a number of layered elements. The elemental elastic and electric properties are assumed as linear functions of the thickness to adopt the variety of the material property of FGPM. The Hamilton principle is applied to determine the governing equations. The phase velocity surface, phase slowness surface, phase wave surface, group velocity surface, group slowness surface, and group wave surface for FGPM plate are formulated using Rayleigh quotient and the orthogonality condition of the eigenvectors. These six surfaces are then used to illustrate the characteristics of waves in FGPM plates. Numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in FGPM plates.     

Current density and field fluctuations in a conducting medium

We study thermal fluctuations in a conducting medium which may be spatially non-uniform and anisotropic. The fluctuation spectra for charge and current density, and for the electromagnetic fields, are expressed in terms of the basic propagators of the macroscopic equations. The theory is based on an application of the generalized Nyquist theorem.     

Modal analysis and dispersion curves of a curvilinear triangular cored light guide using Goell's point matching method

This paper gives, in brief the theoretical and computational investigation of a new light guide having a curvilinear triangular core cross-section. This structure is here introduced for the first time and may be conceived as a distortion of a rectangular core cross-section. Using Goell's point matching method under weak guidance approximation, the modal characteristics equations for the lowest order mode have been derived in two cases. In one case, all the sides of the proposed light guide are bounded by dielectric material. In other case we will consider all the sides bounded by conducting materials. From these equations the modal dispersion curves are obtained and compared. It is seen that the dielectric light guide supports more modes than the metallic light guide. Thus, metallic light guide may be used as a mode filter.     

Fermi surface and anisotropic spin-orbit coupling of Sb(111) studied by angle-resolved photoemission spectroscopy

High-resolution angle-resolved photoemission spectroscopy has been performed on Sb(111) to elucidate the origin of anomalous electronic properties in group-V semimetal surfaces. The surface was found to be metallic despite the semimetallic character of bulk. We clearly observed two surface-derived Fermi surfaces which are likely spin split, demonstrating that the spin-orbit interaction plays a dominant role in characterizing the surface electronic states of group-V semimetals. The universality or dissimilarity of the electronic structure in Bi and Sb is discussed in relation to the granular superconductivity, electron-phonon coupling, and surface charge or spin density wave.     

A numerical model of streamlines in coplanar electrodes induced by non-uniform electric field

A new model for investigating the non-uniform electric field and potential distribution of fluid flow and streamlines induced by non-uniform electric field with the induced charge in the electrical double layer on the electrode surfaces is presented. Accurate computation of the non-uniform electric field is a pre-requisite for observing fluid flow and streamlines. The electric field distribution is obtained from Laplace's and Neumann's equations. Finite Element Methods is adopted for this work. The simulation results has been compared with available experimental observations of the fluid flow profile obtained by superimposing images of particle movement in a plane normal to the electrode surface. A good agreement is found between the numerical and experimental streamlines.     

Computation of the electric potential and the Lorentz force in a locally ionized magnetohydrodynamic flow in a nonuniform magnetic field for a transverse flow past a circular cylinder

An analytical solution to electrodynamic equations is obtained for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow for a transverse flow past a circular cylinder in the non-uniform magnetic field of a rectilinear conductor. Analytical formulas for computing the volume density of the Lorentz force acting on the flow in a locally ionized MHD flow are obtained for the case of the conducting and nonconducting surfaces of the cylinder. The influence of the Hall parameter and width of the MHD interaction region on the value of the Lorentz force is analyzed. It is demonstrated that the Lorentz force, which accelerates and not decelerates the flow, appears under certain conditions near the surface of the cylinder in the neighborhood of the critical point.     

On the interfacial capacitance of an electrolyte at a metallic electrode around zero surface charge

The behaviour of the capacitance of a planar double layer containing a restricted primitive model electrolyte (equi-sized rigid ions moving in a continuum dielectric) at and around zero surface charge is examined for a polarizable electrode with particular emphasis on a metallic surface. Capacitance results are reported for symmetric valency (1:1) salts encompassing a range of concentrations and temperatures covering both electrolyte solution and ionic liquid regimes. Although the modified Poisson–Boltzmann theory is principally employed, at higher concentrations the theoretical calculations have been supplemented by Monte Carlo simulations. Capacitance anomaly, that is, increase of capacitance with temperature at low temperatures, is seen to occur when the electrode is an insulator with a low dielectric constant or when it is unpolarized. No capacitance anomaly is, however, seen for a metallic electrode with an infinite dielectric constant and in this situation the capacitance increases (a) dramatically at low temperatures (strong coupling) at a given concentration, and (b) as concentration increases at a given temperature. These capacitance trends are consistent with earlier works in the presence or absence of surface polarization and, in particular, the results for a conducting electrode at ionic liquid concentrations are consistent with that recently reported by Loth et al. [Phys. Rev. E, 82, 056102 (2010)]. Overall the theoretical predictions are qualitative to semi-quantitative with the simulations.     

Effective Electrostatic Interactions Between Two Overall Neutral Surfaces with Quenched Charge Heterogeneity Over Atomic Length Scale

Using Monte Carlo results as a reference, a classical density functional theory (CDFT) is shown to reliably predict the forces between two heterogeneously charged surfaces immersed in an electrolyte solution, whereas the Poisson–Boltzmann (PB) theory is demonstrated to deteriorate obviously for the same system even if the system parameters considered fall within the validity range of the PB theory in the homogeneously charged surfaces. By applying the tested CDFT, we study the effective electrostatic potential of mean force (EPMF) between two face–face planar and hard surfaces of zero net charge on which positive and negative charges are separated and considered to present as discontinuous spots on the inside edges of the two surfaces. Main conclusions are summarized as follows: (i) strength of the EPMF in the surface charge separation case is very sensitively and positively correlated with the surface charge separation level and valency of the salt ion. Particularly, the charge separation level and the salt ion valency have a synergistic effect, which makes high limit of the EPMF strength in the surface charge separation case significantly go beyond that of the ideal homogeneously charged surface counterpart at average surface charge density similar to the average surface positive or negative charge density in the charge separation case. (ii) The surface charge distribution patterns mainly influence sign of the EPMF: symmetrical and asymmetrical patterns induce repulsive and attractive (at small distances) EPMF, respectively; but with low valency salt ions and low charge separation level the opposite may be the case. With simultaneous presence of both higher valency cation and anion, the EPMF can be repulsive at intermediate distances for asymmetrical patterns. (iii) Salt ion size has a significant impact, which makes the EPMF tend to become more and more repulsive with the ion diameter regardless of the surface charge distribution patterns and the valency of the salt ion; whereas if the 1:1 type electrolyte and the symmetrical patterns are considered, then the opposite may be the case. All of these findings can be explained self-consistently from several perspectives: an excess adsorption of the salt ions (induced by the surface charge separation) serving to raise the osmotic pressure between the plates, configuration fine-tuning in the thinner ion adsorption layer driven by the energy decrease principle, direct Coulombic interactions operating between charged objects on the two face-to-face plates involved, and net charge strength in the ion adsorption layer responsible for the net electrostatic repulsion.     

On the analysis of large amplitude vibrations of non-uniform rectangular plates

An analysis of the large amplitude vibrations of non-uniform rectangular plates is presented. The method is based on Berger's assumption of neglecting the second invariant of the middle surface strain in the expression corresponding to the total potential energy of the system, in conjunction with a Galerkin procedure.     

Numerical Analysis of Electromagnetic Fields in Multiscale Model

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments(MoM) with finite-difference time-domain(FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples.     

New solutions for charge distribution on conductor surface

In the paper, a problem of electrostatics for charge distribution on a conductor surface is analytically solved for three new particular cases of conducting surfaces with complicated shape and specified value of electrostatic potential. The exact analytical expressions for surface charge density for the bodies are obtained. All the solutions are represented in a clear view of 3D graphs. It is shown that the proposed method of electrostatic problem for conductors allows to obtain infinitely many numerical solutions for the problem but only several special cases can be solved analytically.