Boltzmann方程的奇异扰动解法(Ⅱ)——初始层解

求解小Knudsen数的Boltzmann方程时,本文改进了Grad展开,得到了没有久期项的初始层解,这个解反映出气体中可能存在高阶矩的声波。 关键词：     

Boltzmann方程的奇异扰动解法(Ⅰ)——正规解

本文用奇异扰动方法讨论了具有小Knudsen数的Boltzmann方程的正规解,证明把Hil-bert展开和Enskog展开加以改进可以消除久期项。 关键词：     

α系数和A(ALPhAS)系数族的相互关联和转换及消去项的选择问题

历来各文献求算α系数和A系数(为了区别,凡不消去项的校正系数用α表示,有消去项的校正系数用A表示)都是先求出α系数,再消去一项转换成A系数。由此可见各种基体影响系数尽管名称和形式不同,其本质都是一致的,都来源于α系数。为此,本文从α系数入手,依照B-B方程的形式,采用所谓“加入法”,依次推出在元素体系中,在氧化物混合体系中,在稀释熔融体系中的方程式,从而给出基本α系数、混合α系数、修正α系数表达式及其相互转换关系,然后消去一项,分别推出在上述三种体系中的L-T方程式,从而给出基本A系数、混合A系数、修正A系数表达式及其相互转换关系,进而推出相应的α系数和A系数的相互转换关系,还可以推出不同消去项的A系数的转换关系。在上述推导基础上,结合文献几个分析实例,探讨一下消去项的选择问题,指出消去LOI(或LOF)项,分析元素i项,主元素各有其优点,应根据不同的试样分别选择上述三个消去项,为此而提出一种改进的熔融制片方法。     

在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

两自由度带电耦合振子系统的守恒量与近似解

由于两自由度带电耦合振子系统的Lagrange函数中存在耦合项,从而导致其运动微分方程是非线性耦合的.先通过坐标变换消去Lagrange函数中的耦合项,用直接积分法求得系统的守恒量,用Adomian分解法求得系统的近似解,再通过坐标反变换求得系统在原坐标下的守恒量与近似解,并对近似解作了讨论.     

异核偶极相互作用非久期项对交叉极化弛豫速率的影响

本文通过计入异核偶极相互作用的非久期项对交叉极化弛豫速率的影响而推广交叉极化理论。自旋系统内部的快运动可以使得异核偶极相互作用的非久期项对交叉弛豫的贡献变得可观。本文给出了交叉弛豫速率的一般公式,并讨论了本理论在交叉极化实验中的应用。     

关于Brueckner-Goldstone相连项展开公式

本文的目的是指明,倘满壳层外只有一个粒子或只含一个空穴,即使情态存有退化,我们仍可以求得消去了所有含有粒子自能图的项、而且在形式上和满壳层情况完全一样的相连项展开公式。     

氢原子斯塔克效应的能级分裂规律

根据简并情况下的微扰理论和n=1,2,3,4能级对应的久期方程的规律,推出任意状态下氢原子斯塔克效应中的久期方程行列式中各矩阵元的分布规律,并找出了氢原子一级斯塔克效应在电场中的能级分裂规律.     

激光脉冲作用下囚禁离子的规则与混沌运动

研究驻波型激光脉冲作用下，失谐量足够大时，囚禁于Paul阱中的单离子系统的久期运动.通过分析和数值计算相结合的方法，导出系统的精确解及其描述的时间演化性质，得到系统的规则和混沌运动轨道以及阱频很小时系统进入整体混沌的临界条件,并提出了控制系统共振失稳的方法. 关键词： 激光脉冲 囚禁离子 规则与混沌运动 精确解 稳定性     

随机对流扩散方程的数值仿真

本文针对对流一扩散随机过程在随机输入（即随机输运和源项）,作用下进行数值仿真。我们先将对流扩散随机微分方程中的随机函数采用有限项截断的多项式浑沌展开（Polynomial Chaos Expansion）展开,再由Galerkin映射法得到求解浑沌展开系数的确定性方程组。这是一个在物理空间包含多尺度解的大方程组。为此我...     

Boltzmann方程的奇异扰动解法(Ⅲ)——边界层解

用奇异扰动方法讨论了具有小Knudsen数的Boltzmann方程的边界层解,并把它归结为求解联立代数方程的问题。对于Maxwell边界条件,还得到了温度间断系数对于边界上的调节系数的依赖关系。 关键词：     

Scalar field exact solutions for non-flat FLRW cosmology: a technique from non-linear Schrödinger-type formulation

We report a method of solving for canonical scalar field exact solution in a non-flat FLRW universe with barotropic fluid using non-linear Schrödinger (NLS)-type formulation in comparison to the method in the standard Friedmann framework. We consider phantom and non-phantom scalar field cases with exponential and power-law accelerating expansion. Analysis on effective equation of state to both cases of expansion is also performed. We speculate and comment on some advantage and disadvantage of using the NLS formulation in solving for the exact solution.     

Modeling the characteristics of the waves scattering by a group of scatterers

The pattern equations method is extended to solving the diffraction problem on a group of bodies. The problem is reduced to solving an algebraic system of equations with respect to the expansion coefficients of the scattering patterns by using a series expansion of the scattering patterns in angular spherical harmonics. The explicit (asymptotic) solution of the problem is obtained in a case when the scattering bodies are far enough from each other.     

Instanton-like self-dual solution to lattice Euclidean Gravity: Difference from Eguchi–Hanson solution to continuous gravity

An analytical solution has been obtained for the spherical isothermal expansion of the outer layer of a ball whose mass increases at a constant areal density of the heated layer, which is equal to the product of the initial values of the depth of heating and the density of the layer for the entire time of expansion into vacuum. This solution differs from the known solution for the isothermal spherical expansion of a given mass of a material in a slower decrease in the density and, as a result, in the pressure of the expanding material with the time. In particular, it describes the expansion of the boundary layer of the ball heated by a flow of fast electrons in application to the problem of the ignition of an inertial confinement fusion target by a shock wave induced because of the heating of the target by the flow of laser-accelerated fast electrons (shock ignition).     

电解精炼制备太阳级硅杂质行为研究

在氟化物电解质体系下,把Cu与冶金级多晶硅熔配成合金作为阳极,利用杂质与硅析出电位的差别,通过控制电解工艺条件和参数,对冶金硅进行了电解精炼提纯研究.结果表明,阳极铜硅合金对硅中的杂质有滞留作用,且在大电流密度下Cu不会随着合金中硅的减少而溶解到电解质中;预电解对电解质净化效果明显,XRF分析表明P含量从10降为1ppmw;阴极电沉积的硅呈颗粒状,并与电解质混杂,随着电解时间的延长,分散的硅的颗粒聚集成1—2cm直径的大尺寸硅球.ICP-AES分析表明,最后得到的产物硅与冶金级硅相比,硼含量由12·7降低到2·2ppmw,磷含量由98·6减少到4·1ppmw,说明电解精炼除杂进行多晶硅的提纯是有效和可行的.     

The kinetic energy partition method applied to a confined quantum harmonic oscillator in a one-dimensional box

A new, physically motivated, basis set expansion method for solving quantum eigenvalue problems with competing interaction potentials is presented. In contrast to the usual dissection of the potential energy into unperturbed and perturbing terms, we divide the kinetic energy into partial terms by modifying the mass factor. The partition scheme results in partial kinetic energies with their effective mass factors. By distributing each partial kinetic energy to a respective potential energy to form a subsystem, the total Hamiltonian is written as the sum of subsystem Hamiltonians. Using a linear combination of the subsystem wave-functions to represent the system wave-function we obtain a set of coupled equations for the expansion coefficients, by solving these energies and wave-functions can be obtained. We demonstrate the solution scheme with a standard model system: a confined harmonic oscillator in a one-dimensional box. With only a few (less than ten) basis functions from each subsystem, we can reproduce the exact solutions very accurately, thus showing the applicability of this method.     

Light scattering by multilayer axially symmetric particles

An exact solution to the problem of light scattering by multilayer axially symmetric particles is derived and some aspects of its computer-aided implementation are discussed. The main specific features of the solution are (i) separation of the incident, scattered, and internal fields into two parts and special selection of the scalar potentials for each of them; (ii) expansion of the potentials in terms of spherical wave functions; (iii) formulation of the problem in the form of surface integral equations; and (iv) solution of the reduced systems of the linear algebraic equations for the coefficients of the potential expansions. Mathematical justification of the solution is discussed, which is formulated in the recursive and nonrecursive form (for the T-matrix). The developed computer program has shown that the proposed approach makes it possible to consider axially symmetric particles with essentially different internal structures (i.e., with a spherical core, oblate spheroidal shell, or prolate spheroidal intermediate layer). The results of calculations of the optical properties of the multilayer nonspherical particles are presented and discussed.     

截断展开方法和广义变系数KdV方程新的精确类孤子解

利用特殊的截断展开方法求出了广义变系数KdV方程新的类孤子解.这种方法的基本思想是假定形式解具有截断展开形式,以致可把广义变系数KdV方程转化为一组待定函数的代数方程组,进而给出待定函数容易积分的常微分方程.利用例子证明了这种方法是十分有效的. 关键词： 截断展开法 变系数 KdV方程 孤波解     

ELECTROSTATIC POTENTIAL OF STRONGLY NONLINEAR COMPOSITES: HOMOTOPY CONTINUATION APPROACH

The homotopy continuation method is used to solve the electrostatic boundary-value problems of strongly nonlinear composite media, which obey a current-field relation of J=σ E+χ|E|²E. With the mode expansion, the approximate analytical solutions of electric potential in host and inclusion regions are obtained by solving a set of nonlinear ordinary different equations, which are derived from the original equations with homotopy method. As an example in dimension two, we apply the method to deal with a nonlinear cylindrical inclusion embedded in a host. Comparing the approximate analytical solution of the potential obtained by homotopy method with that of numerical method, we can obverse that the homotopy method is valid for solving boundary-value problems of weakly and strongly nonlinear media.