A radiating Kerr-Newman solution

A non-static exact solution of Einstein’s equations corresponding to a field of flowing null radiation plus an electromagnetic field is presented. The geometry of the solution is described by the Kerr-Schild metric. The solution admits a shear-free, geodetic null congruence. It has the symmetry of the Kerr-Newman solution and when a certain parameter is put equal to zero the solution becomes static and reduces to the Kerr-Newman solution.     

A note on reflection of spherical waves

In 1909 Sommerfeld gave an exact solution for the reflection of a spherical wave from a plane surface in terms of an oscillatory integral and also presented an asymptotic solution for the case where both source and receiver are at the boundary. Weyl (1919) presented an alternative solution and also an asymptotic solution for the case where the source is at the boundary. It is known that the general case is solved if a general solution for the case where the source is at the boundary is known. Here it is demonstrated that it is sufficient to have the general solution for the case where both source and receiver are at the boundary. This is mainly of theoretical interest, but may have practical applications. As an example it is demonstrated that Sommerfeld's approximate solution gives Ingard's (1951) approximate solution which is valid for arbitrary source and receiver heights.     

一类非线性方程类孤波的近似解法

采用了一个简单而有效的技巧,研究了一类扰动发展方程.首先引入求解一个相应典型方程的类孤波近似解,然后利用泛函映射方法得到了原扰动发展方程的近似解,指出了近似解级数的收敛性,并用解析方法,讨论了近似解的精度.     

基于光子晶体的物质的量浓度测量研究

利用平面波展开法对二维光子晶体在H极化下的光子带隙进行数值计算。考虑了溶液温度和物质的量浓度对光子带隙的影响。结果表明,以半乳糖和木糖的水溶液作为空气孔中介质材料,当溶液物质的量浓度一定时,光子带隙随溶液温度的变化而改变;而当溶液温度一定时,光子带隙随溶液物质的量浓度发生变化。较高物质的量浓度和较高温度的溶液更容易形成光子带隙。在某些情况下,木糖的光子带隙大于半乳糖的光子带隙。     

会聚光在柱状模拟生物组织中的实验研究

在中空的柱状有机玻璃中充入Intralipid-10%溶液构成单层圆柱模拟样品.在会聚单色光入射Intralipid-10%溶液的情况下,利用特制的光纤探头、锁相放大器、斩波器和微动平台等组成测试装置,测量了柱状Intralipid-10%溶液内后向散射光、能流率的空间分布情况,并对测量结果进行分析.对参量不同的溶液中的光分布进行了比较,得出了柱状溶液中光分布的初步规律.     

一类Landau-Ginzburg-Higgs扰动方程孤子的近似解

利用解析方法研究了一类Landau-Ginzburg-Higgs方程. 由广义变分迭代理论得到了相应方程的解,从而得到了对应方程孤子的近似解. 关键词： 孤子 扰动 变分迭代     

An elastodynamic solution of finite long orthotropic hollow cylinder under torsion impact

The paper presents an analytical method to solve the elastodynamic problem of a finite-length orthotropic hollow cylinder subjected to a torsion impact often occurring in engineering fields. The elastodynamic solution is composed of a quasi-static solution of homogeneous equation satisfied with the non-homogeneous boundary condition and a dynamic solution of non-homogeneous equation satisfied with homogeneous boundary condition. The quasi-static solution can be obtained by directly solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of a non-homogeneous dynamic equation is obtained by means of a finite Hankel transform to a radial variable r, Laplace transform to a time variable t and finite Fourier transform to an axial variable z. Thus, the elastodynamic solution of the finite length of an orthotropic hollow cylinder subjected to a torsion impact is obtained. On the other hand, a dynamic finite element for the same problem is also carried out by applying the ANSYS finite-element analysis system. Comparing the theoretical solution with finite-element solution, it can be found that two kinds of results obtained by making use of two different solving methods are suitably approached. Therefore, it is further concluded that the methods and computing processes of the theoretical solution are effective and accurate.     

Generating solutions of Einstein's field equations by typing mistakes

A solution to Einstein's field equations is presented that represents a Petrov type II electromagnetic null field with one Killing vector. This solution generalizes a vacuum solution previously discovered by Hoenselaers. The solution was found by the peculiar method of generalizing a member of this class inadvertently discovered by making a typing error when checking the vacuum solution with the computer algebra system SHEEP.     

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic(MHD) steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.     

An analysis of Bonnor's dipole solution

Some years ago Bonnor presented a solution of the Einstein-Maxwell equations describing the field of a massive source carrying a magnetic dipole. In this paper I present an analysis of this solution. Bonnor's solution is interesting because of its close connection to the Kerr solution and also because it is not a member of the Weyl electromagnetic class.     

温度和雷诺数对表面活性剂溶液传热的影响

对不同温度和雷诺数下阳性离子表面活性剂十六烷基三甲基氯化铵(CTAC)溶液在循环回路中的传热特性进行了实验研究。在水中加入表面活性剂后溶液的传热特性明显降低,在不同的温度工况下均存在一个临界雷诺数,随着溶液温度的改变而发生变化。在不同的实验浓度条件下均存在一个临界温度,在临界温度以下时,临界雷诺数随温度升高而增加;在临界温度以上时,临界雷诺数随温度升高而急剧下降。分析该表面活性剂溶液阻力减小和传热性能降低之间的关系,提出了通过对溶液温度的控制来改变减阻流体传热特性的方法。     

Reference-wave solutions for the high-frequency fields in inhomogeneous-background random media

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is therefore desirable to have a solution for the high-frequency field propagating along an isolated ray trajectory. A new reference wave is applied to obtain an analytic solution of the parabolic wave equation that describes propagation along the ray trajectory of the deterministic-background medium. The methodology is based on defining a paired-field measure as a product of an unknown field propagating in a disturbed medium and the complex-conjugate component propagating in a medium without random fluctuations. When a solution of the equation for the paired-field measure is obtained, the solution of the deterministic component can be extracted from the paired solution to determine the solution of the unknown field in an explicit form.     

On the global geometry of the stephani universe

A preliminary investigation of global properties of the Stephani solution of the Einstein field equations is presented. This solution generalizes those of Friedman-Robertson-Walker (FRW) in such a way that the spatial curvature indexk (a constant in the FRW models) is a function of the time coordinate. The de Sitter solution, which is also a special case of the Stephani solution, is analyzed in the Stephani coordinates to gain insight into the global structure of the manifold and its foliation. The general metric is found to have several properties in common with this example. It has singularities which can be avoided either by matching the solution to an (as yet unknown) empty-space solution or confining the curvature index to be positive at all times.     

Travelling Wave Solution of Korteweg-de Vries-Burger's Equation

An attempt has been made to obtain exact analytical travelling wave solution of Korteweg-de Vries-Burger's (KdVB) equation by the so-called tanh-method. This equation can be derived for dust ion acoustic shocks by using reduction perturbation method. It is found that an exact solution of the KdVB equation is obtained by tanh-method, provided the parameters involved satisfy a constraint relation. However a special exact analytical solution can be obtained where no such restriction is necessary. This solution has the structure of a shock wave. Numerical solution is also obtained for travelling wave with or without the assumption of the constraint relation. We have also found a singular solution in terms of cosech and coth functions.     

Modal theory for the two-frequency mutual coherence function in random media: point source

The recently introduced modal expansion representation for the two-frequency mutual coherence function is applied here to the solution of a point-source field in a random medium. This approach reduces the solution for any structure function to an eigenvalue problem for an ordinary differential equation. For the initial point source it is shown here that the modal expansion yields a result similar to that for the initial plane wave, modified by a spherical free-space phase which contains a weighted coordinate that does not interact with the medium. Having established these general characteristics, special attention is paid to power-law media and, in particular, to a quadratic medium, for which a new exact solution is derived. Via a collective summation of this new modal solution, we rederive the alternative exact solution which exists in the literature. We also discuss the new parameterization implied by the new modal solution.     

Applications of Extended Hyperbolic Function Method for Quintic Discrete Nonlinear Schr(o)dinger Equation

By using the extended hyperbolic function method,we have studied a quintic discrete nonlinear Schr(o)dinger equation and obtained new exact localized solutions,including the discrete bright soliton solution,dark soliton solution,bright and dark soliton solution,alternating phase bright soliton solution,alternating phase dark soliton solution,and alternating phase bright and dark soliton solution,if a special relation is bound on the coefficients of the equation.     

Detection of free radicals produced by a pulsed electrohydraulic discharge using electron spin resonance

The detection of free radicals such as hydroxyl radical and hydrogen radical for plasma in solution induced by a pulsed electrohydraulic discharge are successfully performed using electron spin resonance measurement. The plasma reactor is a barrier-type and consists of a stainless needle high-voltage (+35 to 65 kV) electrode partially immersed in the solution and a Pyrex glass solution container around which an aluminum film grounded electrode is wrapped. Streamers are induced in the solution. After adding iron (II) sulfate or radical trapping agent before the plasma application, the spectrum for radicals is clearly detected. A reactive dye solution is dramatically decolorized.     

Bifurcations and traveling waves in a delayed partial differential equation

Here cell population dynamics in which there is simultaneous proliferation and maturation is considered. The resulting mathematical model is a nonlinear first-order partial differential equation for the cell density u(t,x) in which there is retardation in both temporal (t) and maturation variables (x), and contains three parameters. The solution behavior depends on the initial function varphi(x) and a three component parameter vector P=(delta,lambda,r). For strictly positive initial functions, varphi(0) greater, similar 0, there are three homogeneous solutions of biological (i.e., non-negative) importance: a trivial solution u(t) identical with 0, a positive stationary solution u(st), and a time periodic solution u(p)(t). For varphi(0)=0 there are a number of different solution types depending on P: the trivial solution u(t), a spatially inhomogeneous stationary solution u(nh)(x), a spatially homogeneous singular solution u(s), a traveling wave solution u(tw)(t,x), slow traveling waves u(stw)(t,x), and slow traveling chaotic waves u(scw)(t,x). The regions of parameter space in which these solutions exist and are locally stable are delineated and studied.     

Skin formation and bubble growth during drying process of polymer solution

When a polymer solution with volatile solvent is dried, skins are often formed at the surface of the solution. It has been observed that after the skin is formed, bubbles often appear in the solution. We conducted experiments to clarify the relation between the skin formation and the bubble formation. We measured the time dependence of the thickness of the skin layer, the size of the bubbles, and the pressure in the solution. From our experiments, we concluded that i) the gas in the bubble is a mixture of solvent vapor and air dissolved in the solution, ii) the bubble nucleation is assisted by the pressure decrease in the solution covered by the skin layer, and iii) the growth of the bubbles is diffusion limited, mainly limited by the diffusion of air molecules dissolved in the solution.     

An asymptotic solving method for the periodic solution of a class of disturbed nonlinear evolution equation

<正>A class of disturbed evolution equation is considered using a simple and valid technique.We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation.Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method.We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis.