New exact travelling wave solutions for the Ostrovsky equation

In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation.     

Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type.     

Determining junction temperature based on material properties and geometric structures of LEDs

Based on the material properties and geometric structures of LEDs, this paper proposes an analytical model for predicting the junction temperature. The parameters relevant to the junction temperature are calculated using the material properties and geometric structures of LEDs. The junction temperature of AlGaInP LED predicted from this work agrees with the available experimental data. Effects of LED working parameters and material properties on the junction temperatures are discussed in this study.     

Numerical method based on the lattice Boltzmann model for the Fisher equation

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.     

PSP—SA模拟金团簇的几何结构与基态能量

采用基于模拟退火的粒子群智能算法(PSO-SA)和紧束缚二阶动量矩势函数(TB-SMA)对金团簇Aun(n≤10)的基态能量、结构及其随团簇尺寸变化的规律进行了研究.结果表明n为偶数的金团簇的结构比邻近为奇数的金团簇稳定,具有"奇-偶"振荡效应;由金团簇基态能量的二阶差分可以看出Au4、Au6、Au8结构比较稳定,具有"幻数"效应.     

A geometric insight into the Fokker-Planck equation

The introduction of an extended evolution space allows to give an intrinsic formulation of the Fokker-Planck equation and makes clear its structural invariance under the chronoprojective geometry. Symmetry algebras and solutions in time dependent parabolic external fields are deduced.     

On the geometric structure underlying the eikonal equation

Given the eikonal equation _i=1 ³ (/x ⁱ ) ² =n ², we investigate the geometric structure that underlies the law of propagation of the wavefronts (x ¹,x ²,x ³) —ct=0. It turns out that Huygens' principle for the propagation of wavefronts is given in terms of a contact structure. Wavefronts are carried into wavefronts by contact transformations. As regards the wave-particle duality principle that arises in quantum mechanics, there is a natural geometric structure, a symplectic manifold (M ²ⁿ , ), which unifies Fermat's principle and the eikonal equation (Huygens' principle).On leave of absence from Institut für Angewandte Mathematik, Fachbereich Mathematik der Universität Mainz, Mainz, German Federal Republic.     

The geometric equation of dislocation dynamics

Recent advances in the continuum theory of dislocations have been achieved mainly in two directions: (1) the differential geometric (non-linear) theory of stationary dislocations, and (2) the formal linear dislocation dynamics. These two are unified here to form a differential geometric dynamical theory of continuous distributions of dislocations. To begin with, the basic concepts of the geometric theory are briefly summed up. The fundamental geometric equation of time-dependent distortions is derived first in a physically instructive elementary way and afterwards by means of exact differential geometry. A symmetrized form of the equation is given in terms of deformations or the metric tensor. The physical meaning of a previously introduced dislocation current tensor is discussed. A general form of the continuity equation for the dislocation current is then given. Thereafter the forces acting on dislocations are dealt with in connection with energy dissipation during plastic deformation and Ohm's law for dislocations, which has been introduced recently. The dislocation conductivity in simple cubic crystals is discussed. Finally, an invariant partition of the torsion (or dislocation) tensor is introduced. The semi-symmetrical part of this tensor corresponds to volume deformations, while the remainder is associated with shape deformations only. The main unsolved problems are enumerated, and some concluding remarks, concerned with the correspondence between dislocation theory on the one hand and general relativity and differential geometry on the other, are added.

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Numerical analysis of Ytterbium-doped double-clad fiber lasers based on the temperature-dependent rate equation

The effects of temperature on the output power and optimal conditions of Ytterbium-doped double-cladding fiber lasers (YDDFLs) are discussed. Temperature-dependent rate equations for YDDFLs based on Boltzmann distribution are built in two-end pump model. The results show that the output power and the slope efficiency decrease with the increase of temperature. The increase of pump power results in that the effect of the temperature on the output performance increases, and the fiber length is a factor that the effect of the temperature depends on really. Moreover we combine the heat distribution formula with the rate equations and compare the numerical results considering with that not considering the temperature-dependence inside laser cavity, the effect of temperature can be ignored only when the pump power is lower, and the optimal fiber length becomes longer when considering the temperature-dependence.     

基于Burton-Miller方程的轴对称结构声学边界元方法

提出了一种求取轴对称结构任意边界条件下声辐射特性的边界元方法。采用Burton和Miller改进型公式将高阶奇异项转化为弱奇异项之和,保证声辐射参数的唯一性,且计算简单精确。将结构表面声压与振速按照旋转轴角度进行Fourier级数展开,利用级数的正交性建立各项待定系数的求解公式;然后转化格林函数的法向偏导为切向偏导,方便直接计算各项积分,并将面积分公式表示为沿结构边界的线积分和沿旋转角度的积分;进一步采用二次等参单元离散结构边界线,建立声压与振速的关系矩阵,从而确定结构声辐射参数。以脉动球源和横向振动球源为例计算,与解析解和传统边界元法结果作对比,说明该方法的有效精确性。     

数值求解三维含时Schrodinger方程及其应用

发展了一套高精度、高效率的伪谱方法,以非微扰的方式求解真实原子三维含时Schrodinger方程.该方法选用二阶劈裂算符作为时间演化算子,分别选择能谱表象和坐标表象作为含时波函数演化的两个表象.在坐标表象下波函数的径向部分使用库仑波函数离散变量表象来离散;角向波函数展开在两维的Gauss-Legendre-Fourier格点上.以H原子的光激发和光电离过程为例,进行了数值计算并和解析解进行了比对.结果表明二者符合很好.该方法很好地处理了库仑奇点问题.还计算了强激光辐照H原子的多光子电离过程,并和其他的数值方案进行了比较.结果表明,在计算收敛的前提下本方法计算效率更高.

Abstract：

We present an accurate and effective pseudospectral method for solving the three-dimensional time-dependent Schrodinger equation involving the Coulomb potential. In this method, the Hamiltonian is evaluated by exploiting the two representations of the wave function. One is a grid representation, in which the angular dependence of the wave function is expanded in a two-dimensional Gauss-Legendre-Fourier grid in the coordinate space of polar and azimuthal angles. The radial coordinate is discretized using a discrete variable representation constructed from the Coulomb wave function (CWDVR) . The other is a spectral representation, in which the wave function is expanded in a set of square integrable functions chosen as the eigenfunctions of a zero-order Hamiltonian. The time of propagation of the wave function is calculated using the well-known second-order split-operator method implemented through the transform between the grid and spectral representations. Calculations on the photo-absorption strength of hydrogen atom are presented to demonstrate the accuracy of present method in low energy limit by the time-dependent wave-packet propagation method. As another example, the present method is applied to multiphoton ionization of H atom. For a wide range of field parameters, ionization rates calculated using the present method are in excellent agreement with those from other accurate numerical calculations. The new algorithm will be found more efficient than the close coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.     

On the geometric properties of the dispersionless Toda equation

The problem of constructing exact solutions, Noether symmetries, and conservation laws for the (2 + 1)-dimensional dispersionless Toda equation u _xy = exp(?u _zz ) is considered.     

SiC多型体几何结构与电子结构研究

采用平面波超软赝势法和范数不变赝势法对几种SiC多型体的几何结构、能带结构等进行了系统的研究.结果表明:6HSiC导带最低点在ML线上U点,用平面波超软赝势法计算时U点在(0000,0500,0176)点附近;而用范数不变赝势法计算时在导带最低点附近能带呈现不连续点,不连续点出现在(0000,0500,0178)点附近.两种赝势法计算结果相比,用平面波超软赝势法得到的导带最低点位置更靠近布里渊区M(0,05,0)点.在平面波超软赝势下,随着六角度的增加,cp,cpa增大的趋势较为明显,能隙和价带宽度变宽的趋势也较为明显.在计算极限内,绝对零度下4HSiC系统能量最低、最稳定,而Ewald能量显示3CSiC最稳定. 关键词： 密度泛函理论 电子结构 SiC     

基于FW-H方程的Hartmann哨辐射声场数值研究*

该文基于声类比法,通过求解FW-H方程,对不同喷口与谐振腔位置关系的Hartmann哨的声场分布进行了分析,计算了不同位置关系的Hartmann哨的声指向性。得到了以下结论:喷口与谐振腔位置关系对Hartmann哨的发声基频几乎不产生影响。对称位置关系的Hartmann哨的声场呈对称趋势,且在垂直于喷流方向上达到最大;非对称位置关系的Hartmann哨不再呈现对称趋势。Hartmann哨的最大声压级随着偏离对称位置的距离的增加有小幅增加,最大声压级出现的方向向着谐振腔方向移动。     

非完整系统Boltzmann-Hamel方程的Birkhoff化及其广义辛算法

针对非完整系统的Boltzmann-Hamel方程,当其满足一定条件时,可以进行广义Birkhoff化.构造生成函数,利用当前比较优越的非自治Birkhoff广义辛算法对其进行数值仿真.仿真结果和传统的Runge-Kutta算法结果相比较,非自治Birkhoff广义辛算法在长期跟踪后更加准确.     

密度泛函理论计算内掺氢分子富勒烯H2@C60及其二聚体的几何结构和电子结构

采用密度泛函理论中的广义梯度近似(generalized gradient approximation, 简称GGA),对内掺氢分子富勒烯H2@C60及其二聚体的几何结构和电子结构进行了计算研究.发现无论是在H2@C60单体,还是在其二聚体中,氢倾向以分子形式存在于碳笼中心处,且在室温下氢分子可以做自由旋转.电子结构分析表明,氢分子掺入到C60和C120中,仅对距离费米能级以下-8eV至-5eV能级处有一定的贡献,其他能级的分布和能隙几乎没有变化.     

Abundant multisoliton structures of the Konopelchenko-Dubrovsky equation

Using the homogenous balance method, the nonlinear transformations of the (2+1)-dimensional integrable Konopelchenko-Dubrovsky equation are given, and then some new special types of single solitary wave solution and the multisoliton solutions are constructed. The project is supported by the Natural Science Foundation of Shandong Province in China and the Natural Science Foundation of Liaocheng University.     

Numerical integration of the fluctuating hydrodynamic equations

An approach to numerically integrate the Landau-Lifshitz fluctuating hydrodynamic equations is outlined. The method is applied to one-dimensional systems obeying the nonlinear Fourier equation and the full hydrodynamic equations for a dilute gas. Static spatial correlation functions are obtained from computer-generated sample trajectories (time series). They are found to show the emergence of long-range behavior whenever a temperature gradient is applied. The results are in very good agreement with those obtained from solving the correlation equations directly.