Earnshaw (1805–1888) and Passive Magnetic Levitation

S. Earnshaw, a mathematical physicist born in England two centuries ago, was the author of studies on the transmission of sound and light. His theory on the transmission of light by “detached particles” has also influenced some studies on the stability of bodies in potential fields, particularly studies on the levitation of permanent magnets, i.e. on passive magnetic levitation. This theorem was so well known that even Maxwell mentioned it, and is today cited almost as an axiom in the ambit of passive magnetization. However, what is less well known is that the theory actually only relates to magnetostatics. In this paper, the mathematic model of the theory that refers to stability is outlined, along with some works that refer to it, in particular those on passive magnetic levitation. It is then pointed out that spaces of low instability exist in magnetostatics, and that stability may exist in the magneto-stationary and in magneto-dynamic ambit.     

Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh diffraction integral formula and without using the far-field approximation, a solution of the wave equation beyond the paraxial approximation is found, which represents vectorial non-paraxial elliptical Gaussian beams in free space. The far-field expressions for non-paraxial Gaussian beams and elliptical Gaussian beams can be regarded as special cases treated in this paper. Some basic propagation properties of vectorial non-paraxial elliptical Gaussian beams, including the irradiance distribution, phase term, beam widths and divergence angles are studied. Numerical results are given and illustrated.     

Higher-order implicit strong numerical schemes for stochastic differential equations

Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined.     

第二类Fredholm积分方程的泰勒展开解法

本进一步发展了用Taylor公式求解第二类Fredholm积分方程的方法，并给出了近似解的误差精度分析．     

ICF研究中的Rayleigh-Taylor不稳定性实验用靶

 概述了当前研究Rayleigh-Taylor不稳定性增长实验所用的靶型情况。从实验用靶来看，调制靶的设计正从平面向立体发展，出现了球形和柱形等新靶形，制备手段包括精密机械微加工、激光束、电子束和离子束加工、半导体工艺和微米纳米技术加工等。根据对国外新靶型的研究，结合国内工艺条件和实验需求，对国内可能采用的靶型进行了研究探索。     

Gauge Dependence of the Effective Gravitational Field

We analyze the gauge ambiguity problem for the effective gravitational field from the standpoint of the measurement process. The motion of a test point particle playing the role of a measuring device is investigated in the field of a point gravitating mass in the one-loop approximation. We show that the gravitational field value determined from the effective equations of motion of the device explicitly depends on the Feynman gauge parameter. This dependence is essential in the sense that a gauge variation cannot be interpreted as a deformation of the reference frame, which leads to a gauge ambiguity in the values of observed quantities. In particular, this result disproves the hypothesis that gauge dependence is canceled in the effective equations of motion of a classical point particle.     

Simulation of the instability of an accelerating gaseous envelope

The development of perturbations of the parameters of a dense gaseous envelope traveling with an acceleration driven by a difference in the pressures on either side is investigated numerically. Plane and axisymmetric time-dependent flows of a compressible medium are considered. The effect of both the density of the envelope and the form of the initial perturbations of its shape and motion on the mass cumulation in the compactions formed is studied. The evolutions of the perturbations of a layer and the surface of a contact discontinuity accelerated by an impinging plane shock wave are compared.     

A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

调制不稳定性对级联放大光纤传输系统信噪比的影响

在考虑光纤损耗和级联放大器的情况下，推导了调制不稳定性的产生条件和增益的普适解析表达式，分析了调制不稳定性对信噪比的影响，给出了一个新的计算信噪比的表达式。     

Modeling film flows down inclined planes

A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations. Received: 16 April 1998 / Revised: 29 June 1998 / Accepted: 2 July 1998