柱二维内电磁脉冲的自洽计算方法(Ⅱ)

本文是文献[1]的续篇。在麦克斯韦方程组和速率方程组及其差分格式保持不变的条件下,采用欧拉方法求解初级电子数方程组。推导了平面一维和柱二维守恒形式的初级电子方程组的差分格式,同时对柱二维作了数值计算。计算结果和[1]的结果一并放在[2]中讨论。     

Transformations between inertial and linearly accelerated frames of reference

Transformation equations between inertial and linearly accelerated frames of reference are derived and these transformation equations are shown to be compatible, where applicable, with those of special relativity. The physical nature of an accelerated frame of reference is unambiguously defined by means of an equation which relates the velocity of all points within the accelerated frame of reference to measurements made in an inertial frame of reference.     

Equations for pulse propagation in a free electron laser

The equations for pulse propagation in a free electron laser are derived. The equations are valid in a reference frame, moving with a relativistic velocity with respect to the laboratory frame, chosen in such a way that the carrier frequency of the pulse equals the pseudoradiation (wiggler) field frequency. In this reference frame the equations assume a simple non relativistic form.     

Continuity and momentum equations for moist atmospheres

The moist atmosphere with occurring precipitation is considered to be a multiphase fluid composed of dry air, water vapor and hydrometeors. These compositions move with different velocities: they take a macroscopic motion with a reference velocity and a relative motion with a velocity deviated from the reference velocity. The reference velocity can be chosen as the velocities of dry air, a gas mixture and the total air mixture. The budget equations of continuity and momentum are formulated in the three reference-velocity frames. It is shown that the resulting equations are dependent on the chosen reference velocity. The diffusive flux due to compositions moving with velocities deviated from the reference velocity and the internal sources due to the phase transitions of water substances result in additional source terms in continuity and momentum equations. A continuity equation of the total mass is conserved and free of diffusive flux divergence if the reference velocity is referred to the velocity of the total air mixture. However, continuity equations in the dry-air and gasmixture frames are not conserved due to the mass diffusive flux divergence. The diffusive flux introduces additional source terms in the momentum equation. In the dry-air frame, the diffusive flux of water substances and the phase transitions of water substances contribute to the change of the total momentum. The additional sources of total momentum in the frame of a gas mixture are associated with the diffusive flux of hydrometeors, the phase transitions of hydrometeors and the gasmixture diffusive flux. In the frame of total air mixture, the contribution to the total momentum comes from the diffusive flux of all atmospheric compositions instead of the phase transitions. The continuity and momentum equations derived here are more complicated than the traditional model equations. With increasing computing power, it becomes possible to simulate atmospheric processes with these sophisticated equations. It is helpful to the improvement of precipitation forecast.     

惯性系中直线运动的常加速度内禀刚性非惯性系

推导相对惯性系作直线运动的常加速度内禀刚性加速系的坐标变换关系式，并讨论该加速系的主要性质。     

Electrodynamics of a continuous medium in a system with specified structure

It is shown that electrodynamics can be considered not only in Minkowski space but also in Riemannian space-time. The exact solutions for the electric field within and beyond a charged plate and a sphere and the space-time geometry are found without applying the Einstein equations. The space-time geometry of a Born-rigid noninertial frame of reference (NFR) with global linear acceleration in space-time having constant curvature is obtained on the basis of the structural equations (integrability conditions). A new Lorentz-covariant condition of stationarity for possible solutions to the Maxwell equations for the particles frozen in a Born-rigid NFR is formulated. In an inertial frame of reference this condition is equivalent to zero four-curl of the field of four-accelerations of particles. This condition provides zero relativistic generalized radiation friction force. The propagation of electromagnetic waves in this NFR and the Doppler effect are described. The limitations imposed on the energy-momentum tensor in the Einstein equations are derived.     

Equations of motion of particle in circular accelerator with general field

Lagrange equations of motion are derived for a particle in a circular accelerator with arbitrarily spatially variable guiding magnetic field describing the motion of a particle by means of dimensionless deviations of the particle from a circle as the reference curve. The author also derives linearized equations of motion (so-called equations of perturbations used in stability investigations according to the Ljapunov method of the 1st approximation). The equations are given in the closed form and are thus quite exact.     

Extension of Hydrodynamic Balance Equations for Simple Fluids

A systematic approach to derivation of hydrodynamic-like balance equations for systems with a smooth continuous potential as well as hard sphere repulsion is represented. Cases of many-particle local and two-particle nonlocal hydrodynamic densities are considered. The results are applied for construction of balance equations for fluxes of momentum and energy, which form the first extension of conventional hydrodynamics. Explicit balance equations for the stress tensor and the heat flux in the local frame of reference are obtained.     

Notes on relativistic equations of spin motion

Grounds and applications of Bargmann-Michel-Telegdi equations for the precession of the polarization vector of relativistic particles are considered. A critical question in the discussion is the orientation of the rest frame reference vectors. Møller reference frames which keep constant the mutual orientation of the two infinitely close in time rest frames are shown to have a special role. The generally covariant form of the equations is discussed. The assertion that the principle of relativity is violated in the phenomenon of spin precession is proved to be untrue.     

Gravitation theory as theory of non-Lorentzian transformations of the systems of reference

According to the programme of Einstein as discussed with Abraham, gravitation can be described by the bending of the systems of inertia in special relativity. This bending means non-Lorentzian transformations of the systems of reference, depending on the point in space-time. Einstein's equations for the metric imply equations for the transformation matrix, which are also of the same structure.The non-Lorentzian transformations of the reference systems of a manifold can lead to a general map of the set of metrics into the set of vacuum metrics on the same manifold. Resulting new aspects in problems of gravitation theory are discussed.     

Reference systems for the isolated observer and the dynamics of test particles

A method of deriving the equations of motion for rotating test particles with the aid of reference systems for an isolated observer is considered. It is shown that the form of the equations depends upon the manner in which the reference system for the isolated observer are determined (calibrated). Reference systems, which in the case under consideration lead to the Papapetrou equations, were also determined. These systems were used to derive the equations of motion for particles for which the quadrupole moment of their energy-momentum tensor was taken into account.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 99–105, April, 1977.In conclusion, the authors thanks N. V. Mitskevich for useful discussion of the present work.     

一种求解逆风下火焰沿柱状燃料传播的数值方法

1引言近十几年来，国内外许多人对火焰沿薄燃料层的传播进行了研究，但很少涉及到火焰沿柱状燃料的传播。图1为所研究问题的物理模型。火焰的传播涉及到气固两相的相互作用，两相界面上存在能量和质量的交换，气相中存在着气气间的化学反应，固相中存在着裂解反应。当参考坐标系团结在火焰前锋上时，该火焰传播问题成为一准稳态问题，燃料以一固定速度供给火焰。2数学模型2．1守恒方程气相的所有守恒方程均服从下列通用方程：其中、，L和一分别表示通用变量、广义扩散系数和广义源项。固相包括：质量守恒方程：。。能量守恒方程：2．2边界…     

关于转动弦的波动方程

数学物理方法的一些学习指导书或教科书上给出了两种转动弦的波动方程,但没有考虑Coriolis力的影响,其讨论方法存在不正确(竖直转动重弦)或不全面(水平转动轻弦)之处.重新讨论了两种转动弦的波动方程及其求解问题.     

The form-invariance of wave equations without requiring a priori relations between field variables

According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.     

Application of Schiff's rotating-frame electrodynamics

The charge distribution and electromagnetic field in a rotating conductor with a net electric charge under stationary conditions are described by Schiffs equations of electrodynamics in a rotating reference frame. The existence of a spatial charge distribution in a conductor at rest in a rotating reference frame is demonstrated.     

Reformulation of electromagnetic and gravito-electromagnetic equations for Lorentz system with octonion algebra

In this paper, the real, complex octonion algebra and their properties are defined. The electromagnetic and gravito-electromagnetic equations with monopoles in terms of S and $\hbox {S}^{\prime }$ reference systems are presented in vector notations. Additionally, the duality transformations of gravito-electromagnetic situation for two reference systems are also represented. Besides, it is explained that Maxwell-like equations for gravito-electromagnetism are also invariant under Lorentz transformations. By introducing complex octonionic differential operator, a new generalized complex octonionic field term consisting of electromagnetic and gravito-electromagnetic components has been firstly suggested for Lorentz system. Afterwards, a complex octonionic source equation is obtained as in basic way, more compact and elegant notation. By defining a new complex octonionic general potential term, the field equation is attained once again. The components of complex octonionic field and wave equations are written in detailed for S and $\hbox {S}^{\prime }$ reference systems.     

大学生对麦克斯韦方程组的理解研究

本研究通过收集麦克斯韦方程组概念测试题的课堂讨论录音及书面回答,获得物理专业大学生对麦克斯韦方程组的错误理解,总结出学生常见的错误概念为不清楚方程式来源、对电场和磁场的相互关系理解有误、将电场和磁场进行不恰当类比、不能正确理解平行板间电磁场的来源、对感生电场和位移电流理解不到位等,对此提出有针对性的教学建议,为电磁学教学提供参考.     

Post-Newtonian approximation for a rotating frame of reference

The field equations of general relativity are solved to post-Newtonian order for a rotating frame of reference. A new method of approximation is used based on a 3+1 decomposition of the equations. The results are expressed explicitly in terms of the gravitational potentials. The space-time is asymptotically flat but not locally flat. The space-time metric contains gravitational terms, inertial terms, and coupled gravitational-inertial terms. The inertial terms in the equation of motion are in agreement with terms obtained by other authors using kinematic methods. The metric and equation of motion reduce to those for an inertial frame of reference under a simple coordinate transformation. The total energy of a particle is given. For the restricted three-body problem this represents the relativistic extension of Jacobi's integral to post-Newtonian order.This article received an honorable mention from the Gravity Research Foundation for the year 1984—Ed.     

Generalized relativistic dynamics in a non-inertial reference frame

Generalized relativistic field equations have been derived for dynamics in a non-inertial reference frame interpreted as a Finsler space where events are specified by both spacetime coordinates and corresponding velocities (tangent vectors). The field equations follow in two alternative forms from exact general conservation laws derived through application of Cartan covariant differentiation within the framework of Finsler geometry. Velocity-dependent (curvature) terms in the field equations can account for the anisotropy of the gravitational field, together with the associated acceleration and expansion of the universe.     

A dynamical model for the increasing absorption optical bistability

By phenomenological analysis with reference to Miller et al. [2a], a specific Hamiltonian for increasing absorption optically bistable systems is proposed and the corresponding coupled dynamical equations are derived.