Analytic Propagation for Nonlinear Weakly Hyperbolic Systems

The propagation of analyticity for sufficiently smooth solutions to either strictly hyperbolic, or smoothly symmetrizable nonlinear systems, dates back to Lax [14 Lax , P.D. ( 1953 ). Nonlinear hyperbolic equations . Comm. Pure Appl. Math. 6 : 231 – 258 . [Google Scholar]] and Alinhac and Métivier [2 Alinhac , S. , Métivier G. ( 1984 ). Propagation de l'analyticité des solutions de systèmes hyperboliques nonlinéaires [Propagation of analyticity for solutions of nonlinear hyperbolic systems]. Invent. Math. 75, 189–204 . [Google Scholar]]. Here we consider the general case of a system with real, possibly multiple, characteristics, and we ask which regularity should be a priori required of a given solution in order that it enjoys the propagation of analyticity. By using the technique of the quasi-symmetrizer of a hyperbolic matrix, we prove, in the one-dimensional case, the propagation of analyticity for those solutions which are Gevrey functions of order s for some s < m/(m ? 1), m being the maximum multiplicity of the characteristics.     

Numerical investigation of gain characteristics of Er3+/Yb3+ co-doped fiber amplifiers

In this work, a model for analyzing the gain characteristics of heavily Er³⁺/Yb³⁺ co-doped compact fiber amplifier is presented. Four-level rate equations and finite-difference beam propagation method are applied to simulate the optical field evolution along the active fiber. Based on this model, the influences of ion concentration, fiber length and pump power on the gain characteristics of Er³⁺/Yb³⁺ co-doped phosphate glass fiber amplifiers are theoretically investigated. Numerical results show that for a fiber length of 3.6 cm the internal gain can reach 27.2 dB with N _Er = 2.6 × 10²⁶ ions/m³ and N _Yb = 1.2 × 10²⁷ ions/m³ when pumped with 224 mW at 980 nm. The gain per centimeter is 7.56 dB/cm. The results can provide useful information to optimize the gain performance of these compact fiber amplifiers.     

夫琅禾费衍射场的相位弯曲及其对光传输和成像过程的影响

在普通物理的框架内对不同情况下夫琅禾费衍射光场的相位弯曲因子的形成进行了推导,并对其物理意义给出直观的说明;指出并讨论了该因子对光波传输过程的重要影响;从而纠正了光学教材中的一个常见误式,它将对成像过程导致悖论。     

一种裂纹扩展的有限元仿真分析方法及其实现

为分析含多裂纹体在任意载荷下的断裂过程问题,给出了一种基于有限元的仿真方法及程序.基于商业有限元软件的应力分析结果和合适的断裂力学准则,判断裂纹的扩展以及扩展角;通过对每一个裂纹尖端扩展影响区域进行单元重划分,实现了多裂纹任意扩展的几何描述有限元模型更新.由于只对裂纹扩展区局部进行有限单元更新,网格划分和前期网格结果到新网格的映射的工作量相对较小,典型的裂纹扩展分析实例表明本文方法和程序的有效性.     

Time-resolved Monte Carlo Simulation of Propagation of Photons Through Layered Tissues

The propagation of photons through layered tissues is discussed using time resolved Monte Carlo method. The effects of the absorption coefficient, scattering coefficient and anisotropy coefficient on the shape of time resolved transmission are investigated. The energy attenuation of light in layered tissues is also achieved for the infinitesimal-width light and infinite-width light, respectively.     

保偏光纤中在不同频率区域拉曼效应和参量放大增益谱

根据考虑拉曼效应后的双折射光纤所满足的非线性相干耦合薛定谔方程, 推导出了当沿两个偏振轴入射两束不同波长的激光脉冲时所产生的增益表达式. 通过与入射相同频率的光脉冲所产生增益的对比, 在考虑拉曼效应的情况下, 讨论了入射不同频率光脉冲对增益谱的影响. 结果表明, 在正常色散区和反常色散区, 当输入两束激光脉冲频率不同时, 增益谱较输入相同频率激光脉冲时产生了明显的变化, 其外侧的斯托克斯部分和反斯托克斯部分增益峰, 随着群速度失配的增加强度明显加强、偏离中心频率, 可以用于提取太赫兹脉冲.当两偏振模处于不同色散区时, 增益谱与不考虑拉曼效应时也存在明显的不同, 增益谱的对称性遭到破坏, 斯托克斯部分的增益峰强度要明显高于反斯托克斯部分. 关键词： 不同频率区域 保偏光纤 拉曼效应 参量放大     

切槽孔爆破动态力学特征的动焦散线实验

应用爆炸加载的透射式动焦散线测试系统,分析了有机玻璃切槽孔爆破模型的裂纹动态特征变化规律。比较了不同切槽角度、切槽深度的定向断裂裂纹尖端的扩展长度、扩展速度和动态应力强度因子。初步探讨了切槽爆破的动态效应,研究表明切槽孔爆破早期裂纹破坏模式为爆炸拉应力波作用下的I型快速扩展裂纹,裂纹尖端拉应力集中积聚的较大应变能维持了爆炸裂纹进一步扩展,裂纹尖端扩展后期表现为P波、S波共同作用下的复合型扩展特征。切槽角为60时获得的定向断裂效果最好,合理切槽深度为炮孔半径的1/4～1/2。     

固体中短波传播单位分解有限元法的解析积分

针对固体中短波传播数值模拟的单位分解有限元法中单元矩阵积分的被积函数的强烈振荡特性,应用直角坐标系下标准有限元形函数和单元内的波动方向知识提出了一种单元矩阵的解析积分方案。它对于平面三,六,四,八和九节点的直边单位分解有限单元是完全解析的,对于与这些单元相应的曲边单元则是半解析的。数值结果显示所提出的积分方案在计算效率上比高斯-勒让德积分有大幅度提高。     

Parameterized Post-Post-Newtonian Light Propagation in the Field of One Spherically-Symmetric Body

We derive a more generally parameterized post-post-Newtonian solution for the light propagation in the gravitational field of one spherically-symmetric body.Based on the solution for the light velocity,we give the formula of the light deflection when both the emitter and receiver are located in the regions far away from the body,which is the most important scenario in the real applications.Our results can be applied to more metric theories of gravitation.