Classes of exact Einstein–Maxwell solutions

We find new classes of exact solutions to the Einstein–Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein–Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.     

A theoretical model for ionospheric electric fields at mid- and low-latitudes

A theoretical model for ionospheric electric fields at mid- and Iow-latitudes is developed.In the geomagnetic dipolar coordinate system, we deduce a partial differential equation of electricpotential from the ionospheric dynamo theory. The deduced equation is taken as the fundamentalequation for the present model. The principal parameters for the model input, the thermosphericneutral winds, the densities and temperatures of electrons, ions and neutral atoms and molecules,are obtained from the empirical models HWM93, IRI90 and MSISE90, respectively. In terms of therelaxation iteration method, the partial equations for electric potential are solved successfully, andthen, the ionospheric electric potential, fields, and currents are derived. Our model can reproducethe main features of the ionospheric electrodynamical processes such as the equatorial electric jet(EEJ), so it will be a useful tool for studying the upper atmosphere and ionosphere.     

Numerical solution of a modified Poisson-Boltzmann equation for 1 : 2 and 2 : 1 electrolytes in the diffuse layer

A modified Poisson-Boltzmann (MPB) equation for an unsymmetrically charged electrolyte in the diffuse part of the electric double layer at a plane charged wall is solved numerically using a quasi-linearization procedure. Computations are carried out for 1 : 2 and 2 : 1 restricted primitive model electrolytes with no imaging and for a metallic wall and the results compared with the classical Gouy-Chapman-Stern theory. Except for negligible surface charge, the system with a divalent counter ion is the most sensitive to any change in its physical parameters. In general the MPB mean electrostatic potential, in contrast to the Gouy-Chapman-Stern potential, is not a monotonic decreasing function. The asymptotic behaviour of the MPB equation implies charge oscillations above a critical electrolyte concentration (?0·23 M) while below this concentration imaging or surface charge-ion interactions can produce a charge inversion. Charge separation is found for no surface charge with a metallic wall. The point ion limit is briefly considered.     

Solution of Schrödinger and related equations for irregular and composite regions

The Schrödinger equation with a potential is mathematically equivalent to the Helmholtz equation with a spatially variable propagation constant. A new method is presented for solving certain standard problems associated with these equations. In the Schrödinger language these are the ones in which a potential ν(|r|) acts inside an irregular (aspherical) boundary, where r has its origin inside the boundary. In terms of the Helmholtz equation, these include problems in which a region of constant index of refraction, but arbitrary shape, is embedded in a second uniform region with a different index. It is shown how bound state and scattering problems for such a potential (or region) can be treated in a way that avoids the usually intractable problem of matching solutions across the irregular boundary. The method requires, in general, the truncation of an infinite set of equations for partial wave amplitudes. The special case is discussed of a potential that becomes infinite throughout a region, so the wave amplitude must vanish inside the region (and, hence, on its boundary). For a long wave length this becomes a problem with the Laplace equation, and the general technique is illustrated by a calculation of the free charge on a perfectly conducting spheroid. The theory is extended from a single potential to an ensemble of such potentials, and in particular to an ensemble of potentials with spherical boundaries. In the special case that the potentials are arranged in a periodic lattice the formulas resemble those obtained by the KKR method, but are simpler in some ways. The method is extended to an ensemble of irregular potentials, and these results are shown to be applicable to the special case of an ensemble of finite range, but overlapping, spherical potentials.     

Second order optical susceptibilities in alkali halide crystals due to FA color centers

This paper presents the first calculation of the second order optical nonlinearity of the F_A color center for second harmonic generation (SHG) in KCl:Li crystals. The real and imaginary components of the nonlinear susceptibility evaluated over a wide spectral range enclosing the resonance region of the center show interesting feature. Second harmonics generation and three wave mixing processes are nonlinear optical effects based on the second order susceptibility of materials and are very effective in providing laser radiation over a wide range of wavelengths. The density matrix formalism is employed and the equation of motion is solved by second order perturbation to evaluate the nonlinear susceptibility for SHG. It is found that the system shows large resonance-enhanced second order susceptibilities for color center concentration of 10²³ m⁻³. A scheme of phase matching in terms of anomalous dispersion of the centers is discussed.     

周期场聚焦电子束

引言 自从发现“强聚焦效应”可以应用在粒子加速器内以后,人们知道利用周期磁场能把离子束控制得更细,于是可以减少磁铁的需要量。因此近年来为了改建或新设计各种类型粒子加速器,对周期场聚焦离子束或电子束方面曾进行了很多研究工作。另一方面人们也开始研究用周期电场和磁场聚焦各种电子管内的电子束,例如行波管内电子束的聚焦等。聚焦电子束的主要特点在於必要考虑空间电荷。     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

双稳激光器的不稳定性本质研究

本文从非线性方程稳定性理论出发,给出了双稳激光器速率方程的稳定性三条件,指出了其中两个条件分别是产生双稳和自脉动的不稳定性条件,证明了双稳与光功率曲线出现负斜率的区域相对应,这时小信号分析方程有单调上升解,自脉动则与无稳定解的区域相对应,这时小信号分析方程有振荡上升解。另外两者都属于“三次”非线性现象,但是要在g达到一定的非线性时才可能产生自脉动。 关键词：     

Liquid Flow in a Porous Channel with Electrokinetic Effects

In this paper, a fully developed laminar flow in a porous channel between two paralleled flat plates in the presence of a double layer electric field is analyzed. The linear Poisson-Boltzmann equation is suggested to model the double layer electric field near the solid-liquid interface. The equation of motion is extended by including the electrical body force generating from the double layer field and then solved analytically. Different from previous models, our proposed one is continuous in the whole flow field and matches commonly-accepted models in the field of fluid mechanics.Besides, the effects of various physical parameters such as the zeta potential, the electrokinetic separation distance, and the ratio of the streaming current to conduction current on the velocity, the pressure, the apparent viscosity of the fluid,as well as the streaming potential are discussed. Physical explanations on the changing trends of those physical quantities with various parameters are given.     

Liquid Flow in a Porous Channel with Electrokinetic Effects

In this paper, a fully developed laminar flow in a porous channel between two paralleled flat plates in the presence of a double layer electric field is analyzed. The linear Poisson-Boltzmann equation is suggested to model the double layer electric field near the solid-liquid interface. The equation of motion is extended by including the electrical body force generating from the double layer field and then solved analytically. Different from previous models, our proposed one is continuous in the whole flow field and matches commonly-accepted models in the field of fluid mechanics. Besides, the effects of various physical parameters such as the zeta potential, the electrokinetic separation distance, and the ratio of the streaming current to conduction current on the velocity, the pressure, the apparent viscosity of the fluid, as well as the streaming potential are discussed. Physical explanations on the changing trends of those physical quantities with various parameters are given.     

Chargeability of ethanol–petrol biofuels

Chargeability of ethanol–petrol biofuels during refuelling has been studied in real dispenser environment in order to assess safety risks due to fuel charging at fuel filling stations. Two biofuel blends were studied: E10 containing 10 vol-% of ethanol and 90 vol-% of petrol, and E85 containing about 85 vol-% of ethanol and 15 vol-% of petrol. Charging of standard 95 Octane petrol was studied as a reference. The results show that the charging of E85 is negligible and no charge will be accumulated as long as the fuel dispenser system is properly grounded. In the case of refuelling with E10, charge is accumulated but the level of total charge is still so low that no real electrostatic ignition hazards exist due to fuel charging at filling stations as long as the system is properly grounded. Electrostatic ignition hazards due to fuel charging are real only for standard petrol fuel.     

Electromagnetically induced transparency in coupled quantum dot-ring structure under external electric field and donor impurity

The present study seeks to scrutinize the electromagnetically induced transparency of a coupled quantum dot-ring (CQDR). The effects of hydrogenic donor impurity and external electric field on real and imaginary parts of susceptibility are investigated. The Schrödinger equation with parabolic potential is solved by diagonalization method, and the real and imaginary parts of susceptibility in terms of photon energy are calculated using expanding of the density matrix operator. The results show that the susceptibility of coupled quantum dot-ring are affected by electric field, donor impurity and the depth of confinement potential.     

由接地导体限定的无限深槽内线电荷的电场

利用复数坐标系z上的施瓦茨-克利斯多菲变换和镜像法,计算由接地导体限定的无限深槽内线电荷电场中的电势分布和场强分布,给出电场线与等势线方程,并利用数学软件Matlab绘制出其电势分布三维图、电场线和等势线(面)图.     

水平层状介质并矢Green函数的递推矩阵方法

采用递推矩阵方法计算任意数目水平层状介质的并矢Green函数.根据层界面处电场和磁场的连续性条件得到3个确定Sommerfeld积分待定系数的矩阵方程组,分别对应于垂向单位电偶极子产生的TM波、水平方向单位电偶极子产生的TE波和TM波,这些方程组均可通过递推方法快速求解.只需改变3个方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的并矢Green函数.本文给出的并矢Green函数表达式形式简洁且不含指数增加项,计算时不会出现溢出现象.     

分层球形导体中任意位置直流电流元产生电位的解析解

建立了任意层球形导体头模型.从泊松方程出发，利用电磁边界条件求解了分层球形导体中由任意位置直流电流元产生电位的一般解析解，并且给出了一种以矩阵形式表示的快速求解电位表达式中相关系数的方法.以表示头皮、颅骨、脑脊液和脑的四层球导体模型为例，对解析解进行了计算.结果表明，此解在除源点外的全域内收敛，且比仅用球谐函数展开形式的电位收敛快，计算量明显降低.给出了等位线图和流线图，表明低电导率对电位分布和电流流向的影响不可忽视.还给出了球表面电位分布特征，这有利于脑电逆问题的研究以及对脑电位测量结果的解释. 关键词： 电位 电流元 分层球形导体 脑电     

Hofstadter spectrum in electric and magnetic fields

The problem of Bloch electrons in two dimensions subjected to magnetic and intense electric fields is investigated. Magnetic translations, electric evolution, and energy translation operators are used to specify the solutions of the Schrödinger equation. For rational values of the magnetic flux quanta per unit cell and commensurate orientations of the electric field relative to the original lattice, an extended superlattice can be defined and a complete set of mutually commuting space-time symmetry operators is obtained. Dynamics of the system is governed by a finite difference equation that exactly includes the effects of: an arbitrary periodic potential, an electric field orientated in a commensurable direction of the lattice, and coupling between Landau levels. A weak periodic potential broadens each Landau level in a series of minibands, separated by the corresponding minigaps. The addition of the electric field induces a series of avoided and exact crossing of the quasienergies, for sufficiently strong electric field the spectrum evolves into equally spaced discreet levels, in this “magnetic Stark ladder” the energy separation is an integer multiple of hE/aB, with a the lattice parameter.     

任意半径圆形电流在径向成层介质中产生的电磁场

采用递推矩阵方法计算径向成层介质中的二维Green函数.根据层界面处电场和磁场的连续性条件得到确定待定系数的矩阵方程组并通过递推方法快速求解.只需改变方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的二维Green函数,并进而得到具有任意半径的圆形电流在介质中产生的电磁场.本文给出的Green函数具有表达方式简洁的优点.     

Stability of two-dimensional,controlled, Bose-Einstein coherent states

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schr?dinger soliton [JETP Lett. 80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically, taking initialy a controlled soliton whose “effective mass” is several times bigger than the critical value for a weak collapse in the absence of a potential well, and allowing for reasonably large errors in the experimental realization of the trapping potential required by the theory. For repulsive and sufficiently weak attractive interactions, the controlled state is shown to remain stable inside a breathing potential well, for a time that is an order of magnitude longer than the characteristic periods of the forced and eigenoscillations of the soliton. The collapse is observed only for attractive interactions, when the nonlinear attraction exceeded the appropriate threshold. Electronic supplementary material  Supplementary Online Material     

Special Stäckel electrovac spacetimes

Classification of all electrovac specetimes permitting the separation of variables in the Hamilton-Jacobi equation for a charged test particle is carried out. This separation requires the existence of a complete set consisting of Killing’s vectors and tensors of a special kind. Every complete set defines its own type of metric and electromagnetic potential in the separable coordinate system. There exist seven types of separation of variables for electromagnetic spaces. For every type an additional classification is carried out by transformation of coordinates without any disturbance of the separation conditions, the gradient transformation of electromagnetic potential and the conformal-constant transformation of metric. The key step in solving the problem is the extraction of an autonomous subsystem which determines the metric from only the Einstein-Maxwell equations for every type of separation of variables. Representatives of all classes of metrics and electromagnetic potential are given for every type of separation of variables with the exception of the spaces found in the well-known work by Carter. The problem is solved in terms of metric formalism. The classes of electrovac spacetimes obtained are found to be related to Petrov’s classification.     

Raman自由电子激光的半经典理论

采用Ｔｈｏｍａｓ-Ｆｅｒｍｉ近似势，将多电子系统简化为单电子问题，并用微扰论求解了Ｋｌｅｉｎ-Ｇｏｒｄｏｎ方程．由电子的零级波函数求得了电荷密度和电流密度的零级表达式．通过适当简化Ｋｌｅｉｎ-Ｇｏｒｄｏｎ方程，用分离变量和ＷＫＢ近似，求得了电子波函数及相应的电荷密度与电流密度的表达式 关键词：