球面折射物象公式的几种推导方法

分别从光线方程，程函方程，折射定射的矢量表示，哈密顿混合特征函数和球面折射矩阵出发导出近轴光线条件下球折射的物象公式。     

On the theory of small-amplitude vibrations of curved-surface diaphragms

An equation is derived describing small-amplitude vibrations of an arbitrary curved diaphragm, whose surface is considered as a two-dimensional Riemannian space. The derivation is based on the variational principle, from which the motion equation and conservation law follow in a form invariant with respect to arbitrary transformations of coordinates on the diaphragm surface. It has been shown that the wave equation, along with the two-dimensional Laplace-Beltrami operator, includes an additional term proportional to the scalar curvature of the diaphragm surface. As an example, the equations are considered for a spherical diaphragm and a catenoid-shaped diaphragm with a minimal surface of revolution.     

微粗糙面上方球形粒子的光散射及其散射截面的计算

基于互易定理研究了光波入射时微粗糙面与其上方球形粒子复合模型的光散射。根据粗糙表面电流积分方程并利用表面微扰展开，得到了微粗糙面表面极化电流的迭代解，给出了耦合电场的计算方法。结合散射耦合场散射矩阵和已有的微粗糙面及球形粒子的散射矩阵，给出了复合模型散射截面的计算公式，数值计算了复合模型的后向散射截面并进行了详细讨论。     

Surface plasmon dispersion for very small metallic spheres: A quantum mechanical formulation

We have derived a pair of matrix equations describing the surface plasmon dispersion for a very small spherical metal particle, using the quantum mechanical random-phase approximation (RPA). The surface of the sphere is represented by an infinite spherical potential well for the conduction electrons and the positive ions are assumed to be uniformly distributed into a “jellium”. The dispersion relation is obtained as the condition that a solution of the RPA integral equation for charge fluctuation would exist for the particle.     

Diffuse mode genesis

An exact condition for parasitic oscillation in laser elements with isotropic scattering surfaces is given in the form of an integral equation for the surface brightness. Analytic solutions valid for large gain are derived, with spherical, cylindrical and rectangular symmetry.     

On the far field in the Lorenz-Mie theory and T-matrix formulation

The far field within the context of the Lorenz-Mie theory and the T-matrix formulation is usually expressed on the basis of the asymptotic properties of vector spherical waves. The radiation condition is taken into account by employing proper vector spherical functions as the expansion basis of the scattered field. The asymptotic behavior of the Hankel function is obtained from differential equations. The asymptotic far field can also be obtained from the Kirchhoff surface integral equation, in which the radiation condition has been implemented when it is derived from the Maxwell equations. This note is to present an explicit establishment of the relationship between the asymptotic far field and the near field in the Lorenz-Mie theory and the T-matrix formulation through the Kirchhoff surface integral.     

Diffraction of sound by an elastic cylinder near the surface of an elastic halfspace

Diffraction of an acoustic wave by an elastic cylinder near the surface of an elastic halfspace is considered. The solution relies on a Helmholtz-type integral equation and uses the Green function of an elastic halfspace. The latter function is represented in the form of an integral over the Sommerfeld contour on the plane of a complex variable that has the meaning of the angle of the wave incidence on the halfspace boundary. An integral equation for the sound pressure distribution over the cylinder surface is derived. This equation is reduced to an infinite system of equations for the Fourier-series expansion coefficients of this distribution. The results obtained are valid for the diffraction of a cylindrical wave and a plane wave. They also describe the diffraction of a spherical wave when the transmitter and receiver are far from the cylinder and lie in one plane that is orthogonal to the cylinder axis.     

球面旋涂光刻胶膜厚分布的数学模型

提出了球面旋涂微米级厚度光刻胶膜层薄化率公式及径向位置演变公式,并得到了膜厚分布的演变公式。与平面涂胶相比,球面涂胶离心力及重力分量是在不断的变化。根据平面旋涂运动方程及球面面形特征,给出了球面旋涂运动方程;结合流体层流的表面条件及不可压缩流体的质量连续方程,推导出了膜厚h及径向位置r对时间t的演变公式,并得到了在径向位置r处初始厚度为h0的膜厚演变的数学模型。通过对模型参数的分析可知,球面旋涂光刻胶应采用主从轴偏心旋涂,旋涂时工件的开口应朝向侧面(旋转轴水平)。     

On the thermodynamics of surfaces

Isotropic macroscopic thermodynamics is used to treat a classical model of surfaces. An equation of the Gibbs-Duhem type is derived from which the relation between surface stress and specific surface free energy follows. This derivation specifically considers the pressure dependence on size of a spherical particle bounded by an isotropic surface and hence is not restricted to the usual constant pressure assumptions. It follows from the conditions of thermodynamic equilibrium and the above Gibbs-Duhem relation that surface stress is the fundamental parameter controlling the internal hydrostatic pressure of isotropic particles as well as equilibrium vapor pressure and other phenomena dependent on internal pressure.     

折射等光程面与傍轴成像球面之间的关系

利用费马原理得到了两个齐明点之间折射等光程面的曲面方程,然后得到了折射等光程面顶点(即齐明点连线与折射面的交点)处的曲率半径表达式,它与球面傍轴成像公式具有完全相同的形式.这说明,傍轴成像中的球面与折射等光程面之间存在联系.分析发现,傍轴成像球面实际上就是对顶点处曲率半径等于该球面半径,并在顶点处与该球面相切的一系列折射等光程面的近似.     

关于球面波波动方程及其通解

本文从普遍的波动方程出发,推导出球面波的波动方程并求得其通解     

水中浮升气泡的半径和速度变化

根据牛顿运动定律推导了小气泡在水中浮升过程中的速度和位置坐标的表达式;基于理想气体物态方程和球形液面的压强差公式推导了小气泡在水中浮升过程中的半径变化率;考虑小气泡在水中浮升过程的气泡半径和速度的变化,用计算机模拟了不同初始条件下的气泡群在浮升过程中半径和位置随时间的变化规律.     

Coupled ripplon-plasmon modes in a multielectron bubble

In multielectron bubbles, the electrons form an effectively two-dimensional layer at the inner surface of the bubble in helium. The modes of oscillation of the bubble surface (the ripplons) are influenced by the charge redistribution of the electrons along the surface. The dispersion relation for these charge redistribution modes (‘longitudinal plasmons’) is derived and the coupling of these modes to the ripplons is analysed. We find that the ripplon-plasmon coupling in a multielectron bubble differs markedly from that of electrons on a flat helium surface. An equation is presented relating the spherical harmonic components of the charge redistribution to those of the shape deformation of the bubble.     

Derivation of governing equation for predicting thermal conductivity of composites with spherical inclusions and its applications

A governing differential equation for predicting the effective thermal conductivity of composites with spherical inclusions is shown to be simply derived by using the result of the generalized self-consistent model. By applying the equation to composites including spherical inclusions such as graded spherical inclusions, microballoons, mutiply-coated spheres, and spherical inclusions with an interphase, their effective thermal conductivities are easily predicted. The results are compared with those in the literatures to be consistent. It can be stated from the investigations that the effective thermal conductivity of composites with spherical inclusions can be estimated as long as their conductivities are expressed as a function of their radius.     

Exchange pressure and the Wigner-Seitz approximation

Working formulas are derived for numerically calculating the exchange part of the pressure in a metal in the spherical Wigner-Seitz cell approximation. The derivation is based on an equation obtained by Dmitriev in the Hartree-Fock approximation. An ARRIEP research report, 1964. Prepared for printing by M.F. Sarry.     

强电场下气泡形变对液体绝缘的影响

 基于液体气泡击穿的椭球模型,推导了气泡形变的流体动力学方程;利用软件Comsol模拟了气泡受力后的形变;根据模拟结果,结合气体击穿的帕邢定律,讨论了气泡形变对液体绝缘的影响。结果表明:气泡在静电引力和表面张力的作用下,沿电场线方向拉伸成椭球,椭球长短轴之比与外加电场强度和气泡初始半径成正比;形变导致电场方向气体通道延长,气泡更容易击穿,外加气压是避免气泡击穿的有效途径之一,外加气压的大小与电场强度和气泡初始半径成正比。     

偏心和倾斜光学系统初级象差理论的研究

在共轴光学系统波象差的基础上,推导出了光学元件的偏心和倾斜分别对主要象差的影响.得出了除了球差外,每一种象差由于偏心和倾斜都引入了它同种类的象差;小量的偏心和倾斜并不改变系统的球差的结论;如果球差并不为零,将会产生与象高无关的彗差,即轴向彗差等等.     

Derivative Form of Off-axis Aberration Correction Surface and Its Application in Solar Energy Concentration

By using the derivative method, we obtained the same result with that of the previous work of Chen et al. in 2006. Different from the integral form, the derivative form of the surface expression published in this paper is derived from differential equation and based on the theory of non-imaging focusing heliostat proposed by Chen et al. in 2001. The comparison of the derivative form of fixed aberration correction surface has been made with that of integral form surface as well as that of spherical surface in concentrating the solar ray.     

Dispersion Properties of High-and Low-Frequency Electrostatic Oscillations of Plasma Spheres:Application to the Metallic Nanoparticles

The dispersion properties of high-and low-frequency electrostatic oscillations of a spherical metallic plasma consisting of hot electrons and cold ions are investigated.The main interest and the key first applications of this system are the spherical metal nanoparticles.General expressions of dispersion relations are obtained for the so-called surface and bulk plasmon waves,and surface and bulk ion-acoustic waves in spherical geometry,using hydrodynamic equations and Poisson equation with appropriate boundary conditions.Numerical results show that dispersion effects become large for metallic particles of small radii,particularly in the range of few nanometers.     

Analytical solutions of the simplified spherical harmonics equations

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared to solutions of the diffusion equation, especially for large absorption coefficients, short time values, and small distances from the source.