含速率平方阻力项的一维相对论谐振子的Lagrange函数与守恒量

用Taylor级数展开的方法得到含速率平方阻力项的一维相对论谐振子的运动微分方程.从守恒量的性质及运动微分方程出发得到了系统的Lagrange函数和守恒量的表达式. 关键词： 相对论谐振子 Lagrange函数 守恒量     

Bifurcation of travelling wave solutions in a nonlinear variant of the RLW equation

By using the method of planar dynamical systems to a nonlinear variant of the regularized long-wave equation (RLW equation in short), the existence of smooth and non-smooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed. We notice that some results in [Wazwaz AM. Analytic study on nonlinear variants of the RLW and the PHI-four equations. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2005.03.001] are incorrect.     

Well‐conditioned boundary integral formulations for high‐frequency elastic scattering problems in three dimensions

We construct and analyze a family of well‐conditioned boundary integral equations for the Krylov iterative solution of three‐dimensional elastic scattering problems by a bounded rigid obstacle. We develop a new potential theory using a rewriting of the Somigliana integral representation formula. From these results, we generalize to linear elasticity the well‐known Brakhage–Werner and combined field integral equation formulations. We use a suitable approximation of the Dirichlet‐to‐Neumann map as a regularizing operator in the proposed boundary integral equations. The construction of the approximate Dirichlet‐to‐Neumann map is inspired by the on‐surface radiation conditions method. We prove that the associated integral equations are uniquely solvable and possess very interesting spectral properties. Promising analytical and numerical investigations, in terms of spherical harmonics, with the elastic sphere are provided. Copyright © 2014 John Wiley & Sons, Ltd.     

Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates

We consider the Shigesada-Kawasaki-Teramoto cross-diffusion model for two competing species. If both species have the same random diffusion coefficients and the space dimension is less than or equal to three, we establish the global existence and uniform boundedness of smooth solutions to the model in convex domains. This extends some previous works of Kim [12 Kim, J.U. (1984). Smooth solutions to a quasilinear system of diffusion equations for a certain population model. Nonlinear Anal. 8:1121–1144.[Crossref], [Web of Science ®] , [Google Scholar]] and Shim [21 Shim, S.-A. (2002). Uniform boundedness and convergence of solutions to cross-diffusion systems. J. Diff. Eqs. 185:281–305.[Crossref], [Web of Science ®] , [Google Scholar]] in one dimensional space.     

Approximate homotopy symmetry method: Homotopy series solutions to the sixth-order Boussinesq equation

An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation,which arises from fluid dynamics.We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders,educing the related homotopy series solutions.Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation.Higher order similarity solutions can be obtained by solving...     

光子晶体光纤接续损耗的理论分析

基于超格子构造法,采用全矢量模型计算了光子晶体光纤的模场半径,由此出发理论分析了光子晶体光纤与普通单模光纤之间接续损耗分别受横向偏移、轴向倾斜以及模场不匹配的影响,给出了光子晶体光纤在部分常用结构参量区域{Λ,d/Λ}内与SMF-28接续损耗的理论值,讨论了光子晶体光纤各结构参量与接续损耗之间的关系。并简要分析了不同结构光子晶体光纤之间的接续损耗。结果表明,接续损耗对横向偏移和轴向倾斜都非常敏感;孔距是决定接续损耗大小最主要的因素;与普通单模光纤接续,当光子晶体光纤的孔距比该单模光纤纤芯半径大一些时,接续损耗比较小;两种不同结构光子晶体光纤之间的接续损耗大小最主要取决于它们孔距的差异。     

掺铒玻璃波导放大器中抽运光信号光重叠因子分析

通过分析掺铒(Er3 )玻璃波导放大器(EDWA)的放大增益机理,提出抽运光与信号光光模场分布之间的归一化重叠积分因子(Γ),并引入到掺铒波导放大器增益模拟计算中,使理论模型更切合实际。以Ag -Na 二次离子交换工艺制作的具有埋入型渐变折射率分布的掺铒波导放大器为例,采用数值方法模拟了条形波导截面上的二维折射率分布及抽运光、信号光的光模场分布。计算了不同工艺参量设置下的Γ大小,讨论Γ对放大器增益的影响。结果显示,在二次离子交换制作过程中设置适当工艺参量优化折射率分布,能有效改善波导中抽运光与信号光光模场分布之间的重叠因子,提高掺铒波导放大器的增益。计算结果显示,在一定条件下,Γ从0.5增至0.8,每厘米长度掺铒波导放大器的放大增益可提高近1.5 dB。     

Suppressing effect of the laser extraction on heat generation in Nd:YAG

The suppressing effect of the laser extraction on heat generation in Nd:YAG was investigated. The extraction efficiency could be deduced from the slope efficiency, and heat generation in Nd:YAG could be obtained with the heat model developed, which was verified by the previous experiment. The essential reasons were given to explain the change trend of heat generation under the condition of laser extraction.     

激光器内腔频差对双折射外腔激光回馈系统输出影响的理论及实验研究

玻璃材料的内应力关系及所在系统的稳定性、安全性和可靠性,是精密加工领域的重要问题.基于双折射外腔激光回馈效应的应力测量技术以其先进新颖的测量原理受到普遍关注.传统理论普遍认为双折射回馈系统中激光器的输出相位仅由外腔相位延迟决定,而将测量误差归因于外腔镜的非线性运动.本文结合正交偏振激光原理和三镜腔等效模型,测量了激光器的内腔双折射引起的频差大小,进行了频率调谐回馈实验,并根据结论计算了内腔频差对外腔相位延迟测量结果的影响,发现激光器的输出相位由外腔相位延迟、内腔频差、外腔长度共同决定.本文总结了内腔和外腔各向异性共同作用下激光器正交偏振态的相位特性,补充了激光回馈的物理内容,对于应力-双折射、位移、距离等重要参量的精确测量,都具有重要指导意义.     

Approximating the ideal free distribution via reaction-diffusion-advection equations

We consider reaction-diffusion-advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness, where fitness is defined as a logistic local population growth rate. We show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics. The modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution. The analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability. The models are quasilinear parabolic equations with nonlinear boundary conditions.