位势流动和非均匀介质中声波方程的36种形式

声波方程是对大多数声学问题进行数学描述的出发点. 那些得到 广泛应用的经典波动方程及对流波动方程都存在苛刻的适用条件, 即仅适用于描述处于静态或匀速运动状态的定常 均匀介质中的线性无耗散声波. 然而, 很多实际场合并不满足这些严格的适用条件. 本文对经典声波方程和对流声波 方程进行推广, 导出了编号为W1$\sim$W36的36种不同形式的声波方程, 涵盖了处于静止、势流或旋涡流状态下的非均匀 和/或非定常介质中的声波传播问题. 所考虑的声波传播情形包括: (1) 线性波, 即具有小梯度(小振幅)性质; (2)非线性波, 即具有陡峭梯度性质, 包括``波纹'(小振幅大梯度)或者大振幅波. 本文仅考虑非耗散声波, 即排除了由剪切、体积黏度及热传导所引起的耗散. 对具有匀熵或等熵(熵沿流线守恒)性质的均匀介质和非均匀介质中的声传播进行了研究但非等熵(即耗散)情况除外; 另外, 对非定常介质中的 声波问题也进行了分析. 所涉及的介质可以处于静止、匀速运动状态, 或者是非匀速的和/或非定常的平均流动, 包括: (1)低Mach数的势平均流(即不可压缩的平均态), 或高速势平均流(即非均匀可压缩的平均流); ② 变截面管 道中的准一维传播, 包括无平均流的号管和具有低或高Mach数平均流的喷管; 或③平面的、空间的、或轴对称的单 向剪切平均流. 本文没有探讨其他类型的旋涡平均流(将与耗散及其他情形一起留待下一步研究), 例如, 可能与剪切效应相结合的轴对称旋转平均流. 通过对流体力学的一般方程进行消元处理或根据声学变分原理, 导出了36种波动方程, 对一些波动方程还采用这两种方法进行相互校验. 尽管声波方程的36种形式没有涵盖非线性、非均匀与非定常及非匀速运动介质 这3个效应的所有可能的组合情形, 但它们的确包括了孤立状态下的各种效应, 并包括了多种多重效应组合的 情形. 虽然经典波动方程和对流波动方程仅适用于处于静止(或匀速运动)的均匀定常介质中的线性无耗散声波, 但它们在 相关文献中已被广泛采用; 本文给出的36种声波方程提供了它们多种有用的推广形式. 在许多实际应用中, 经典波动方 程和对流波动方程仅是粗略的近似, 声波方程的更一般形式可提供更令人满意的理论模型. 本文每节末尾给出了这些应用 的众多范例. 在这篇评论文章中引用了240篇参考文献.     

Propagation of nonlinear waves in an inhomogeneous gas-liquid medium. Derivation of wave equations in the Korteweg-de Vries approximation

Equations describing the propagation of waves of small but finite amplitude in a liquid with gas bubbles are derived. The bubble distribution density is a continuous function of bubble size and spatial coordinates. It is found that, for a uniform bubble distribution, the obtained equations become the Korteweg-de Vries, Kadomtsev-Petviashvili and Khokhlov-Zabolotskaya equations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 188–197, March–April, 2009.     

Entanglement in a two-qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriya couplings and an inhomogeneous magnetic field

Ground state entanglement and thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of the different Dzyaloshinski-Moriya interaction and inhomogeneous magnetic field are investigated.By the concept of concurrence, we find that the inhomogeneity of the magnetic field may make entanglement last for a long time and the critical temperature is dependent on Jz and b. The entanglement can be increased by increasing the temperature in some cases. We also find that the x-component parameter Dx has a higher critical temperature and more entanglement for a certain condition than the z-component parameter Dz.     

Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam

In this paper based on the equivalence principle and the reciprocity theorem, the scattered field up to second-order by two parallel 2D targets arbitrarily located in a Gaussian beam is considered. The first-order solution can easily be obtained by calculating the scattered field from isolated targets when illuminated by a Gaussian beam. However, because of the difficulty in formulating the couple scattering field, it is almost impossible to find an analytical solution for the second-order scattered field if the shapes of 2D targets are not canonical geometries. In order to overcome this problem, in this paper, the second-order solution is derived by using the technique based on the reciprocity theorem and the equivalence principle. Meanwhile, the relation between the secondary scattered field from target #1 and target {\#}2 is obtained. Specifically, the bi- and mono-static scattering of Gaussian beam by two parallel adjacent inhomogeneous plasma-coated conducting circular cylinders is calculated and the dependence of attenuation of the scattering width on the thickness of the coated layer, electron number density, collision frequency and radar frequency is discussed in detail.     

Hamilton体系辛半解析法及在非均匀电磁波导中的应用

力学中的Hamilton体系需用对偶变量来描述,而电磁场正好有电场和磁场这一对对偶变量．尝试将力学中的Hamilton体系理论应用于电磁波导的分析,以横向电场和磁场作为对偶变量,将电磁波导的基本方程导向辛几何的形式．基于Hamilton变分原理, 导出横向离散的半解析系统方程, 保持体系的辛结构．以非均匀波导为例, 求解了方程的辛本征值问题, 计算结果与解析解相当吻合．     

Analytical Solitary Wave Solutions to a (3+1)-Dimensional Gross-Pitaevskii Equation with Variable Coefficients

A (3+1)-dimensional Gross-Pitaevskii (GP) equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrödinger (NLS) equation. Exact solutions of the (3+1)D GP equation are constructed via those of the NLS equation. By applying specific time-modulated nonlinearities, dispersions, and potentials, the dynamics of the solutions can be controlled. Solitary and periodic wave solutions with snaking and breathing behavior are reported.     

On the Nonlocal Electron Kinetics in s and p Striations of DC Glow Discharge Plasmas: II. Electron Properties in Periodic States

The spatial relaxation behavior of the electron gas acted upon by stronglymodulated striation-like electric fields, typically occurring in s and pstriations of dc neon plasmas, has been investigated on a kinetic basis inpart I of this paper. These studies have clearly shown that the electronrelaxation in the striationlike field leads to the establishment of anunambiguous spatially periodic state, which is characterized by largemodulation depths and phase delays of the microscopic and macroscopicquantities with respect to the striationlike field. The present part givesa detailed analysis of these quantities in the established striationlikestates. These investigations clearly reveal the distinctly nonlocal electronproperties, which are especially pronounced in the s-type of striations. Inaddition, the kinetic studies are completed by analyzing the impact of thefield modulation degree and the sensitive destruction of the resonancebehavior of the electron gas when imposing slightly nonresonant electric fields.     

Kinetics of the Electrons in Striations of Spherical Glow Discharges

Recent observations of spherical striations in large-volume nitrogen dcdischarges with a central anode have stimulated investigations of thenonlocal electron kinetics in these striations by solving the spatiallyinhomogeneous Boltzmann equation adapted to spherical geometry. Becausethe radial course of the electric potential is largely unknown in thisdischarge, different models concerning its radial course have been developedand used. These models are based on the measured radii of the striationsand the assumption that the potential drop between successive striationsdoes not change. As a consequence, with decreasing distance between thestriations the electric field strongly increases toward the centralanode. It has been found that spherical striations are only obtained ifthe electric field is strongly modulated. In this case, a highly nonlocalbehavior of the velocity distribution function and strongly modulatedradial courses of the macroscopic quantities have been obtained.     

Kinematics of finite-strain elastic-inelastic deformation

Polar decomposition tensors are constructed for slightly disturbed kinematic elastic, inelastic, and thermal strain tensors. Provided that the inelastic and thermal site gradients are pure deformations without rotations, relations are obtained between inelastic small strains and small rotations and between thermal small strains and small rotations which transform an intermediate configuration to a close current configuration. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 165–172, January–February, 2008.     

HeH2+分子多通道谐波发射的理论研究

利用非波恩奥本海默近似模型,理论研究了强激光场下HeH2+分子发射高次谐波的特点。计算结果表明,HeH2+分子的谐波截止能量要大于经典预言值。理论分析表明,延伸的谐波截止能量是由于激发态激光诱导电子跃迁所产生的多通道电子电离-回碰过程所导致的。随后利用双色空间非均匀激光场机制,谐波截止能量进一步延伸,形成了1个由单一量子路径贡献而成的482eV的超长平台区。该辐射能量相当于单色激光场场强被增强了3倍的结果。并且高振动激发态会产生强度更高的谐波光谱。最后,通过适当的叠加谐波平台上的谐波, 可获得一系列脉宽在30as的超短X射线光源。