The Lorentz force and energy-momentum for off-shell electromagnetism

The kinematics of pre-Maxwell electrodynamics is examined and interpretations of these fields is found through an examination of the associated Lorentz force and the structure of the energy-momentum tensor.     

Boolean coverings of quantum observable structure: a setting for an abstract differential geometric mechanism

We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of quantum observables. In this manner, Boolean domain observables constitute structure sheaves of coordinatization coefficients in the attempt to probe the quantum world. Interpretational aspects of the proposed scheme are discussed with respect to a functorial formulation of information exchange, as well as, quantum logical considerations. Finally, the sheaf theoretical construction suggests an operationally intuitive method to develop differential geometric concepts in the quantum regime.     

A geometric Birkhoffian formalism for nonlinear RLC networks

The aim of this paper is to give a formulation of the dynamics of nonlinear RLC circuits as a geometric Birkhoffian system and to discuss in this context the concepts of regularity, conservativeness, dissipativeness. An RLC circuit, with no assumptions placed on its topology, will be described by a family of Birkhoffian systems, parameterized by a finite number of real constants which correspond to initial values of certain state variables of the circuit. The configuration space and a special Pfaffian form, called the Birkhoffian, are obtained from the constitutive relations of the resistors, inductors and capacitors involved and from Kirchhoff’s laws. Under certain assumptions on the voltage–current characteristic for resistors, it is shown that a Birkhoffian system associated with an RLC circuit is dissipative. For RLC networks which contain a number of pure capacitor loops or pure resistor loops the Birkhoffian associated is never regular. A procedure for reducing the original configuration space to a lower dimensional one, thereby regularizing the Birkhoffian, it is also presented. In order to illustrate the results, specific examples are discussed in detail.     

The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy

In this paper, the compatibility between the gauge transformations and the additional symmetry of the constrained discrete Kadomtsev-Petviashvili hierarchy is given, which preserves the form of the additional symmetry of the cdKP hierarchy, up to shifting of the corresponding additional flows by ordinary time flows.     

高阶微商规范不变系统的整体对称性和量子守恒律

分别从Faddeev–Popov(FP)和Faddeev–Senjanovic(FS)路径积分量子化方法对高阶微商规范不变系统导致的位形空间和相空间生成泛函出发,导出规范系统在量子水平下的守恒律,用于高阶Maxwell非AbelChern–Simons(CS)理论.得到了高阶Maxwell非AbelCS理论与标量场耦合系统的量子BRS守恒荷和量子守恒角动量,无论从位形空间或相空间的生成泛函出发,其结果是相同的.并对CS理论中的分数自旋性质给予了讨论.     

Inverse scattering method and soliton solutionfamily for the Einstein--Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.     

爱因斯坦与物理观念的突破

介绍了爱因斯坦在某些重要的物理观念的突破中所作出的伟大贡献．这些重要观念涉及时空理论、量子论、宇宙学和规范理论．     

微扰Kepler系统轨道微分方程的近似Lie对称性与近似不变量

把极角θ视为独立变量,得到Kepler系统的轨道微分方程.首先讨论Kepler系统轨道微分方程的Lie对称性和不变量,微扰Kepler系统轨道微分方程的精确Lie对称性和精确不变量,其次讨论微扰Kepler系统轨道微分方程的近似Lie对称性和近似不变量,并得到了微扰Kepler系统的9个一阶近似Lie对称性和6个一阶近似不变量,其中1个实为精确不变量,而其余5个分别等于微扰系数ε乘以Kepler系统相应的5个不变量。     

脉冲强磁场磁特性科学测量系统及其应用

作为一种极端条件下的实验技术,脉冲强磁场下的磁化测量在磁性材料等研究领域发挥着重要作用。武汉国家脉冲强磁场科学中心建成了两套先进的脉冲强磁场磁化测量系统,并已对外开放运行。文章介绍了该测量系统的组成、测量原理和系统特点,以及该系统在量子磁性材料、功能磁性材料、强关联材料等研究领域中的应用,并对未来的发展提出了展望。     

一维变系数耗散系统Lagrange函数和Hamilton函数的新构造方法

提出构造二阶微分方程的Lagrange函数和Hamilton函数的新路径. 将二阶方程写成一阶方程组并构造出对应的一阶Lagrange函数后,直接从一阶Lagrange函数导出二阶Lagrange函数和Hamilton函数. 利用上述方法得到若干耗散和类耗散系统的一阶和二阶Lagrange函数以及Hamilton函数;讨论了这种方法的优点. 举例说明所得结果的应用. 关键词： 逆问题 耗散系统 Lagrange函数 Hamilton函数     

用于开放性实验和演示实验的自制磁场测定仪

介绍作设计制作的磁场测定仪的原理、选材、制作、调试、使用方法及相关的讨论，该仪器可测狭小空间的磁场，确定磁场的性质和空间分布，该制作，既可以由教师精心制作为演示仪器，也可以作为开放性实验为大学生开设，本制作和材料均取自废旧仪器中的零散元件，成本十分低廉，如果不计较成本，对电路和元件进行精确优化，并认真定标，还可用于定量测量。     

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.     

A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions

In this paper we establish the complete multifractal formalism for equilibrium measures for Hölder continuous conformal expanding maps andexpanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal toral endomorphisms. We also construct a Hölder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.     

A Hopf-like equation and perturbation theory for differential delay equations

We extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations. Because the phase spaces of differential delay equations are infinite dimensional, phase-space densities for these systems are functionals. We derive a Hopf-like functional differential equation governing the evolution of these densities. The functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory. A necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given. Finally, we show that the evolution equation for the density functional is the Fourier transform of the infinite-dimensional version of the Kramers-Moyal expansion.     

Exact solutions of triple-order time-fractional differential equations for anomalous relaxation and diffusion I: The accelerating case

In recent years the interest around the study of anomalous relaxation and diffusion processes is increased due to their importance in several natural phenomena. Moreover, a further generalization has been developed by introducing time-fractional differentiation of distributed order which ranges between 0 and 1. We refer to accelerating processes when the driving power law has a changing-in-time exponent whose modulus tends from less than 1 to 1, and to decelerating processes when such an exponent modulus decreases in time moving away from the linear behaviour. Accelerating processes are modelled by a time-fractional derivative in the Riemann-Liouville sense, while decelerating processes by a time-fractional derivative in the Caputo sense. Here the focus is on the accelerating case while the decelerating one is considered in the companion paper. After a short reminder about the derivation of the fundamental solution for a general distribution of time-derivative orders, we consider in detail the triple-order case for both accelerating relaxation and accelerating diffusion processes and the exact results are derived in terms of an infinite series of H-functions. The method adopted is new and it makes use of certain properties of the generalized Mittag-Leffler function and the H-function, moreover it provides an elegant generalization of the method introduced by Langlands (2006) [T.A.M. Langlands, Physica A 367 (2006) 136] to study the double-order case of accelerating diffusion processes.     

电磁场递推算法及微纳光学元件中的应用

提出一种电磁场递推算法来分析微纳光学元件体内电磁场的传输.该方法基于Maxwell方程组和电磁场横向的边界条件给出了严格解.以高斯光束在亚波长矩形浮雕光栅体内的传输为例,分析了非匀幅光束在微纳光学元件体内的传输. 关键词： 递推算法 非匀幅光束 微纳光学元件     

A strategy for the development and standardisation of measurement methods for high power/cavitating ultrasonic fields: review of high power field measurement techniques

This review was compiled as part of a project to formulate a UK strategy for the development and standardisation of measurement methods for high power/cavitating ultrasonic fields. It reviews the scientific literature relating to various methods of measuring high power fields which have been developed for application in health care, sonochemistry and industrial ultrasonics, and compares these methods in terms of attributes such as spatial resolution, bandwidth and sensitivity.     

A decomposition theorem for SU(n) and its application to CP-violation through quark mass diagonalisation

It is proved that the groupG=SU(n) has a decompositionG=FCF whereF is a maximal abelian subgroup andC is an (n − 1)² parameter subset of matrices. The result is applied to the problem of absorbing the maximum possible number of phases in the mass-diagonalising matrix of the charged weak current into the quark fields; i.e., of determining the exact number of CP-violating phases for arbitrary number of generations. The inadequacies of the usual way of solving this problem are discussed. Then=3 case is worked out in detail as an example of the constructive procedure furnished by the proof of the decomposition theorem.     

A lateral differential confocal microscopy for accurate detection and localization of edge contours

Common path noise and disturbance in light source and ambient lighting affect detection accuracy of edge contours greatly in optical microscopy. In order to solve this problem, a lateral differential confocal microscopy is proposed based on principle of lateral difference and confocal microscopy. The approach proposed uses confocal dual-receiving light path arrangement and real-time heterodyne subtraction of two signals with lateral offsets by a differential detector to improve the system′s accuracy and detection sensitivity. Theoretical analyses have been presented. In addition, a simple prototype system has been built based on theoretical analyses. Related experiments have been performed under laboratory conditions. Different from former image processing methods, common path noise and additive disturbance in light source and ambient lighting are eliminated before they are recorded. Theoretical analyses and experimental results indicate a more accurate and sensitive result.