A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components

Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

二维非线性Schr?dinger方程的两类局部守恒算法

本文针对二维非线性Schr?dinger方程,提出两类局部守恒算法.不需要考虑边界条件,即可保持任意时空区域上相应的局部能量守恒律和局部动量守恒律.在合适的边界条件下,它们能自然地保持电荷、全局能量或全局动量守恒律.本文同时对算法进行了守恒分析和误差分析.在数值实验部分,本文构造了类似的多辛Preissman算法进行比较,数值结果验证了其长时间计算的优势.     

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

Considering the coupled nonlinear Schrodinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

教学目标阐明——物理教学设计系列讲座之三

教学目标阐明，是指根据教学设计的前期分析，将期望学习者达到的结果性或过程性目标加以明确化和具体化的过程．教学目标不仅是编制评价试题的依据，而且也是教学过程设计、教学设计形成性评价实施的依据．     

新型含螺噁嗪聚甲基丙烯酸甲酯微球的制备与光致变色性能

以甲基丙烯酸甲酯（MMA）为原料,螺噁嗪（SPO）为光致变色染料,经悬浮聚合法制备了光致变色微球（PMMA SPO）,其结构经红外光谱、扫描电镜和差热分析表征。研究了SPO浓度对微球转化率和环境温度对光致变色开环体热稳定性的影响。结果表明：在SPO的空间位阻效影响下,微球的玻璃化转变温度由82.4 ℃升高至85.3 ℃,随着SPO浓度下降,微球转化率由89%降低至15%,光致变色开环体的热稳定性随环境温度增大而增强,微球在淡粉色和黄绿色之间可逆转化20次以上未见明显的疲劳现象。     

教学设计形成性评价与修改——物理教学设计系列讲座之五

教学设计方案是课堂教学过程设计中各要素分析和设计的终结性成果．对教学设计方案进行评价是教学设计的基本内容之一；教学设计的涵义本身就包括了对解决问题的预想方案进行评价的要求．通过评价，可以获取关于教学设计方案有效性、完整性、规范性、可实施性、创新性等方面的基本信息，     

教学设计前期分析——物理教学设计系列讲座之二

前期分析（Front—End　Analysis）是美国学者哈里斯（J．Harless）于1968年提出的一项技术，旨在教学设计过程的开端就分析清教学中存在的问题，以避免后续工作无的放矢，浪费人力物力．在不同的教学设计过程模式中，前期分析的内容不尽相同，但一般应包括学习需要分析、学习任务分析、学习者分析和学习背景分析．     

教学过程设计——物理教学设计系列讲座之四

教学过程是为实现教学任务和达成教学目标，通过对话、沟通和合作，以动态生成的方式推进教学活动的进程；其基本环节和内在逻辑结构都是动态的．教学过程设计形成的是一个“弹性化”方案，但一般应对教学顺序、教学组织形式、学习方式、教学模式、教学方法、学习环境及课堂管理等方面进行分析和设计．     

带乘性噪声的空间分数阶随机非线性Schrödinger方程的广义多辛算法

带乘性噪声的空间分数阶随机非线性Schrödinger方程是一类重要的方程,可应用于描述开放非局部量子系统的演化过程.该方程为一个无穷维分数阶随机Hamilton系统,且具有广义多辛结构和质量守恒的性质.针对该方程的广义多辛形式,在空间上采用拟谱方法离散分数阶微分算子,在时间上则采用隐式中点格式,构造出一类保持全局质量的广义多辛格式.对行波解和平面波解等进行数值模拟,结果验证了所构造格式的有效性和保结构性质,时间均方收敛阶约在0.5到1之间.     

Multi-symplectic wavelet splitting method for the strongly coupled Schrodinger system

<正>We propose a multi-symplectic wavelet splitting method to solve the strongly coupled nonlinear Schrodinger equations.Based on its multi-symplectic formulation,the strongly coupled nonlinear Schr(o|¨)dinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem.For the linear subsystem,the multi-symplectic wavelet collocation method and the symplectic Buler method are employed in spatial and temporal discretization,respectively.For the nonlinear subsystem,the mid-point symplectic scheme is used.Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.