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.     

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。     

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.     

Effect of ultrasound “Preinsonification” of solutions on the structuring of dried microdrop trails

The effect of ultrasound preinsonification of a solution on the kinetics and end result of the drying (evaporation) of a microdrop of this solution on a substrate was examined. The results of experiments with salt solution (NaCl) of albumin drops and of an alkaline (NaOH) solution drops are presented. It is shown that the morphology of the dried microdrop residual trail of a preinsonified solution differs noticeably compared to the microdrop trail of a solution that has not been insonified. The main reasons for the revealed effects are analyzed.     

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.     

高分子梯度溶液吸声机理的研究

制备了高分子均匀溶液和梯度溶液,并在声管中测试其声衰减性能.实验结果表明,高分子梯度溶液的声衰减效果明显优于(即大于)相应的均匀溶液的声衰减.根据连续分层介质中声波传播理论建立了计算高分子梯度溶液声衰减的数学模型.计算结果与实验结果一致.由实验和理论分析结果得出了高分子梯度溶液的梯度吸声机理,即多次反射、多次吸收,最终将声能转化为热能.     

超声波在不同浓度NaCl溶液中传播速度的研究

利用超声波声速测定仪测定出超声波在不同浓度NaCl溶液中的传播速度.实验给出,超声波在NaCl溶液中的传播速度与溶液浓度呈线性关系.溶液温度对超声波波速也有影响,并从理论作了分析研究,给出了合理的解释.     

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。     

Time dependent compressible flow about a spherically symmetric polymer in solution

We obtain the general solution of the linear Navier-Stokes equation for time dependent compressible viscous flow about a spherically symmetric polymer molecule. The solution is presented in a covariant form valid in a general cartesian coordinate frame. In the course of deriving the solution we obtain a general decomposition of the unperturbed flow in the absence of the polymer. Our solution generalizes the earlier solution derived by Schmitz and Felderhof for the case of creeping flow.     

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.     

经典单色短峰水波理论的三阶完备解

针对经典的有限水深三阶单色短峰波,考虑环境均匀流效应,赋予一新的解析解,从而与原经典解析解构成完备的解析解.这就在第二阶解、第三阶解结构上显示出多种相互作用机制.     

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.     

Colliding Plane Waves in Einstein–Maxwell Theory

Recently, a simple solution of the vacuum Einstein–Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein–Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose–Khan solution and a solution obtained by Griffiths as separate limiting cases.     

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.     

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.     

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.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

New series of asymptotically flat axisymmetric and stationary gravitational solutions

The equations for the pseudopotential of Harrison's Bäcklund transformations with seed solution an asymptotically flat solution of the Ernst equation are solved. A new series of asymptotically flat solutions of the equations of general relativity is obtained from the determinants of matrices, whose elements are known. The first solution of the series is calculated as a ratio of two sums of monomials. This solution has five arbitrary real constants. For a particular choice of the constants it becomes Kerr's solution.     

Perfect-Fluid Sources for the Levi-Civita Metric II

A regular static interior solution of Einstein’s field equations representing a perfect fluid cylinder of finite radius is presented. The solution is matched to the Levi-Civita vacuum solution at a boundary where the pressure vanishes. The density and pressure are finite and positive inside the cylinder for a specific range of the mass parameter. The solution could thus represent a reasonable source for the Levi-Civita metric.     

The Convergence Estimation of the Parallel Algorithm of the Linear Cauchy Problem Solution for Large Systems of First-Order Ordinary Differential Equations Using the Solution as Expansion over Orthogonal Polynomials

This paper is devoted to the algorithm of the linear Cauchy problem solution for large systems of first-order ordinary differential equations using parallel calculations. The proof of the convergence of the iteration process using the solution as expansion over orthogonal polynomials for the interval [0,1] is presented. The features of this algorithm are its simplicity, the opportunity to get a solution by parallel calculations, and also the possibility to get a solution for nonlinear problems by changing the operator using the solution from the iteration process.