Linearization of Systems of Nonlinear Diffusion Equations

We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.     

二维线性色散方程的色散量子化现象

研究了定义在平面有界矩形区域的二维线性KdV方程和二维线性Schr?dinger方程的色散量子化现象.证明了在有理时刻,方程周期初边值问题的解是初值条件的线性组合,而在无理时刻,解呈现类分形,连续不可微的状态.     

初一物理活动课的探讨

本文以“ 高空独轮车表演”的演示实验为引入, 让学生认识到物体重心的位置会影响物体的稳定性. 中 国古人已经发现这一规律并利用这项规律制作出计量的器具 — — — 欹器. 接下来在教师的指导下进行实验, 让学生 逐步了解欹器的工作原理. 实验中, 学生会经历实验失败、 寻找原因、 再次实验、 实验成功等完整的物理探究过程, 这 种教学方式有效地培养了学生发现问题、 解决问题的能力. 在本课的教学中, 学生不仅能了解中国古人的智慧, 同时 还能让学生体会到满则覆、 谦受益的人生启示     

Dynamical energy equipartition of the Toda model with additional on-site potentials

We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time teq depending on the energy density εand the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find teq∝(1/ε)~a(1/α)~b, where b ≈ 2 a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes.     

Symmetry groups and Gauss kernels of Schrödinger equations

The relationship between symmetries and Gauss kernels for the Schrödinger equation iu_t=u_xx+f(x)u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schrödinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.     

Distinct edge states and optical conductivities in the zigzag and armchair silicene nanoribbons under exchange and electric fields

Based on the tight binding model, we investigate the low energy bandstructures, edge states, and optical absorptions for the silicene nanoribbons(SiNRs) with different terminations under an in-plane exchange field and/or a perpendicular electric field. We find that the zigzag SiNRs are gapped by the exchange field, but they could reenter the metallic state after the application of the electric field. Contrarily, a certain kind of armchair SiNRs remain gapless even if a weak exchange field is present. Furthermore, the combination of the exchange and electric fields could effectively modulate the penetration length and the components of the edge states in the SiNRs. The corresponding optical conductivities for the SiNRs are also calculated, which show remarkable dependence on the edge types of the SiNRs and the two external fields.     

再生水补给河流的水质模糊风险评价

采用再生水进行河流补给,对河流生态系统健康产生直接或潜在的危害.探讨河流水环境系统的不确定性,基于忽略弥散的一维河流水质模型,建立了再生水补给影响下的河流水质模型,选用三角模糊数来描述和处理水环境风险评价.应用结果表明,所建模型对于河流水质模拟与风险评价具有很好的适用性和稳定性.     

基于“最近发展区”视角下的初中生几何直观素养的培养

通过精选教材典例,进行一题多变,深度的加工设计,旨在培养学生对数学问题也能守正创新的意识,减负提质,更好地发展学生几何直观,空间观念等核心素养.     

Symmetry groups and Gauss kernels of Schrdinger equations

The relationship between symmetries and Gauss kernels for the Schrdinger equation iu_t=u_xx+f（x）u is established.It is shown that if the Lie point symmetries of the equation are nontrivial,a classical integral transformations of the Gauss kernels can be obtained.Then the Gauss kernels of Schrdinger equations are derived by inverting the integral transformations.Furthermore,the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.