A multisymplectic integrator for the periodic nonlinear Schrödinger equation

A multisymplectic integrator for the periodic nonlinear Schrödinger equation is presented in this paper. Its accuracy is proved. By introducing a norm, we investigate its nonlinear stability. We also discuss the relationship between this multisymplectic integrator and two variational integrators which are derived by using the discrete multisymplectic field theory and the finite element method.     

基于小波网络的高超音速飞行器鲁棒自适应积分反步控制

针对高超音速飞行器非线性模型具有不确定性的问题,提出一种基于小波网络的鲁棒自适应积分反步控制方法。该方法运用反步法设计非线性控制律,并引入积分项以减小系统跟踪误差;用小波网络在线逼近系统不确定项,提高系统鲁棒性;设计鲁棒项消除小波网络逼近误差。通过Lyapunov稳定性分析,该方法能够保证闭环系统跟踪误差最终收敛。通过与常规反步、积分反步、自适应反步进行仿真对比,结果表明：所设计的控制律可以有效抑制系统不确定性的影响,设计方法可行。     

几何精确梁的Hamel场变分积分子

利用场论下的Hamel形式,对几何精确梁提出一种保结构的变分积分子,并通过数值仿真说明该算法保持能量、动量和几何结构的特性。     

基于SOGI的MMC环流抑制方法

基于模块化多电平换流器的柔性直流输电(high voltage direct current based on modular multilevel convert-er,MMC-HVDC)系统在电力领域已经占据重要地位,但MMC系统存在环流,会增加开关器件和其他元件的额定容量以及系统损耗,严重影响了MMC的工作特性....     

辛普森公式的推广形式及应用

鉴于当前常用数值积分方法的不足,以及直角坐标系下辛普森公式的局限性,研究并提出了辛普森公式在三维柱坐标系和球坐标系下的推广形式,并将其应用于地球物理测井中自然伽马射线强度函数数值积分运算。     

Extensive Numerical Tests of Leapfrog Integrator in Middle Thermostat Scheme in Molecular Simulations

Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics (MD) simulations. Despite the massive use of the conventional leapfrog (LF) integrator in modern computational tools within the framework of MD propagation, further development for better performance is still possible. The alternative version of LF in the middle thermostat scheme (LF-middle) achieves a higher order of accuracy and efficiency and maintains stable dynamics even with the integration time stepsize extended by several folds. In this work, we perform a benchmark test of the two integrators (LF and LF-middle) in extensive conventional and enhanced sampling simulations, aiming at quantifying the time-stepsize-induced variations of global properties (e.g., detailed potential energy terms) as well as of local observables (e.g., free energy changes or bond-lengths) in practical simulations of complex systems. The test set is composed of six chemically and biologically relevant systems, including the conformational change of dihedral flipping in the N-methylacetamide and an AT (Adenine-Thymine) tract, the intra-molecular proton transfer inside malonaldehyde, the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A, the hydroxyl bond variations in ethaline deep eutectic solvent, and the potential energy of the blue-light using flavin photoreceptor. It is observed that the time-step-induced error is smaller for the LF-middle scheme. The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables. Overall, the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.     

关于高阶不确定非线性系统的鲁棒适应干扰衰减问题

研究一类高阶不确定非线性系统的鲁棒适应H∞干扰衰减问题。本质改进了加幂积分器技巧及backstepping算法,并设计出一个光滑鲁棒适应动态反馈控制律,使得闭环系统既具有内稳定性,又使系统达到干扰衰减．所得结果改进了相关文献中的结论．     

Multisymplectic Geometry,Local Conservation Laws and a Multisymplectic Integrator for the Zakharov–Kuznetsov Equation

The multisymplectic geometry for the Zakharov–Kuznetsov equation is presented in this Letter. The multisymplectic form and the local energy and momentum conservation laws are derived directly from the variational principle. Based on the multisymplectic Hamiltonian formulation, we derive a 36-point multisymplectic integrator.     

1990年以来苏州市句法空间集成核演变

依托空间句法分析技术,构建了1995年和2004年2个时期苏州城市空间集成核.通过SPSS对不同时期集成核轴线进行了定量分析,总结集成核形态、结构与增长中心等变化特征,分析集成核变化所隐含的城市空间中心性变化,从而为城市演变提供了空间系统的内在解释.建议新一轮空间规划遵循空间系统内在的句法法则,构建不同职能的主副多中心结构,充分利用环路与干道交接地带的集成效应,加强主集成核沿线地下空间开发与地铁建设等.     

Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules

Shadow hybrid Monte Carlo (SHMC) is a new method for sampling the phase space of large molecules, particularly biological molecules. It improves sampling of hybrid Monte Carlo (HMC) by allowing larger time steps and system sizes in the molecular dynamics (MD) step. The acceptance rate of HMC decreases exponentially with increasing system size N or time step δt. This is due to discretization errors introduced by the numerical integrator. SHMC achieves an asymptotic O(N^1/4) speedup over HMC by sampling from all of phase space using high order approximations to a shadow or modified Hamiltonian exactly integrated by a symplectic MD integrator. SHMC satisfies microscopic reversibility and is a rigorous sampling method. SHMC requires extra storage, modest computational overhead, and a reweighting step to obtain averages from the canonical ensemble. This is validated by numerical experiments that compute observables for different molecules, ranging from a small n-alkane butane with four united atoms to a larger solvated protein with 14,281 atoms. In these experiments, SHMC achieves an order magnitude speedup in sampling efficiency for medium sized proteins. Sampling efficiency is measured by monitoring the rate at which different conformations of the molecules' dihedral angles are visited, and by computing ergodic measures of some observables.