Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler--Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.     

Lie symmetries and conserved quantities for a two-dimentional nonlinear diffusion equation of concentration

The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.     

Noether symmetries of discrete mechanico-electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.     

双调制深度大线性动态范围自适应PDH稳频方法

针对Pound-Drever-Hall(PDH)技术存在的线性动态范围窄、抗干扰能力弱的问题,提出一种基于双调制深度+双误差信号的PDH稳频方法。首先采用数字正交解调技术精确提取干涉信号相位以实现本振信号相位和干涉信号相位的自动匹配;然后利用透射功率信号P_tran和传统误差信号S_PDH构建一个新误差信号S_pre,以扩大PDH稳频系统的线性动态范围;接着,采用大调制深度对应的新误差信号S_pre实现快速捕获和预锁定;最后,采用小调制深度对应的误差信号S_PDH实现精确锁定。锁定后,可根据P_tran幅值变化自动切换调制深度和误差信号,实现大线性动态范围和高灵敏度的PDH稳频。研制了基于现场可编辑逻辑门阵列(FPGA)的稳频控制系统,对法布里-珀罗腔进行了锁定测试。实验结果表明,双调制深度+双误差信号的自适应锁定机制可极大地提高锁定系统的抗干扰能力,且锁定精度高,3小时腔长相对稳定度达5.72×10^-9,所提方法可以广泛应用于激光频率/谐振腔锁...     

非线性动态特性的逆推演方法及其在干涉术中的应用

提出了研究对象非线性动态特性的逆推演新方法,它的特点是从已知对象的非微分方程解析解导出该对象可能的微分方程,从而开拓它的解域或解空间,或者说恢复丢失的解。同时讨论了当对象为法布里－珀罗干涉（F－P）或迈克耳孙干涉时该方法的应用过程,并且对法布里－珀罗定义新的不透过系数（u＝1／τ）,从而给出更简洁和易分析的对象动态特性微分议程,以及由此导出测量法布里－珀罗干涉相位的过程,值得注意的是由新方法导出的微分议程揭示对象更一般的时空演化特征。而且在现有的经验和知识基础上可以进一步唯象地拓展至其他可能的非线性形式,从而使对象的表达方式更接近它的实际情况。     

Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.     

银纳米粒子与氧化物纳米异质结构制备及应用

总结了近期银纳米粒子与氧化物纳米异质结构制备及应用研究进展情况,特别是银纳米粒子修饰的氧化钼纳米纤维异质结构、银纳米粒子修饰的钛酸盐纳米纤维异质结构、银纳米粒子@二氧化硅@银纳米粒子三明治异质结构的制备方法与性能表征.介绍了以上三种异质纳米复合结构的催化性能和银纳米粒子修饰的二氧化物纳米纤维异质结构的气体传感性能.