Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems

This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results.     

基于PolySim电子级多晶硅还原炉三维数值模拟

利用PolySim软件建立了国内电子级多晶硅9对棒现役还原炉的三维模型,对还原炉内部的流动、传热进行了数值模拟,得到还原炉内部流场、温场以及硅棒表面温度的分布情况,指出硅棒桥接附近气体流速较小、气体温度及硅棒表面温度过高是该区域沉积不均匀的主要原因.和实际生产结果对比表明,模拟计算数据的误差不超过5;.     

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.     

基于数值模拟电子级多晶硅还原 炉流动结构改进研究

针对现役电子级多晶硅还原炉炉内气体循环不强、硅棒桥接处沉积质量较差的问题,提出了调整喷嘴直径的优化方案,并利用建模工具建立了原有设计和优化设计的物理模型,对炉体内部的混合气体流动、硅芯电阻加热、辐射传热等进行了数值模拟计算,计算结果收敛,经后处理得到不同设计下炉体内部流速、温度及硅棒表面温度分布云图.实验表明,在其他工艺条件不变的情况下,优化设计可以提供比原有设计更高的沉积速率和致密料比例.     

Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system

In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified.