基于欠阻尼振动的液体黏度测量装置

本文设计了一种用于测量液体黏度的阻尼振动装置.该装置以一个做欠阻尼振动的弹簧振子为核心,利用光电接近开关收集数据,并在数字示波器上显示图像,再将该图像数据传递到计算机上进行分析.该方法的适用范围广,便于收集与分析实验数据,避免了实验中的多种干扰因素,消除了传统落球法实验的弊端,提高了实验测量的准确度.     

Double Wronskian Solutions for a Generalized Nonautonomous Nonlinear Equation in a Nonlinear Inhomogeneous Fiber

A generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber, is investigated. N-soliton solutions for such an equation are constructed and verified with the Wronskian technique. Collisions among the three solitons are discussed and illustrated, and effects of the coefficientsσ1(x, t),σ2(x, t),σ3(x, t) and v(x, t) on the collisions are graphically analyzed, whereσ1(x, t),σ2(x, t),σ3(x, t) and v(x, t) are the first-, second-, third-order dispersion parameters and an inhomogeneous parameter related to the phase modulation and gain(loss), respectively. The head-on collisions among the three solitons are observed, where the collisions are elastc. Whenσ1(x, t) is chosen as the function of x, amplitudes of the solitons do not alter, but the speed of one of the solitons changes.σ2(x, t) is found to affect the amplitudes and speeds of the two of the solitons. It reveals that the collision features of the solitons alter withσ3(x, t)=-1.8x. Additionally, traveling directions of the three solitons are observed to be parallel when we change the value of v(x, t).     

Systematic analysis of DJ(2580), DJ(2650), DJ(2740), DJ(2760), DJ(3000) and DJ(3000) in the D meson family

In this work, we tentatively assign the charmed mesons D_J(2580), D_J^*(2650), D_J(2740), D_J^*(2760), D_J(3000) and D_J^*(3000) observed by the LHCb collaboration according to their spin, parity and masses, then systematically study their strong decays to ground state charmed mesons plus pseudoscalar mesons with the ³P₀ decay model. Based on these studies, we assign the D_J^*(2760) as the 1D(5/2)3^- state, the D_J^*(3000) as the 1F(5/2)2⁺ or 1F(7/2)4⁺ state, the D_J(3000) as the 1F(7/2)3⁺ or 2P(1/2)1⁺ state in the D meson family. As a byproduct, we also study the strong decays of the states 2P(1/2)0⁺, 2P(3/2)2⁺, 3S(1/2)1^-, 3S(1/2)0^- etc, which will be valuable in searching for the partners of these D mesons.     

周期场时间导数Ornstein-Uhlenbeck噪声Fokker-Planck方程的小参数展开求解

通过引入变量,周期场中内部时间导数Ornstein-Uhlenbeck噪声驱动的布朗运动可用高维Fokker-Planck方程来描述. 上述系统不能直接应用通常的小参数展开和势谷中心展开近似求解. 用一种变通的小参数展开方法近似求解了系统的Fokker-Planck方程,结果适用于小势垒高度、中等关联时间和较大的相空间区域,近似解析解可获得系统的改进. 关键词： Fokker-Planck方程 周期势 时间导数Ornstein-Uhlenbeck噪声 小参数展开     

Bell Polynomial Approach and N-Soliton Solutions for a Coupled KdV-mKdV System

In fluid dynamics, plasma physics and nonlinear optics, Korteweg-de Vries (KdV)-type equations are used to describe certain phenomena. In this paper, a coupled KdV-modified KdV system is investigated. Based on the Bell polynomials and symbolic computation, the bilinear form of such system is derived, and its analytic N-soliton solutions are constructed through the Hirota method. Two types of multi-soliton interactions are found, one with the reverse of solitonic shapes, and the other, without. Both the two types can be considered elastic. For a pair of solutions to such system, u and v, with the number of solitons N even, the soliton shapes of u stay unvaried while those of v reverse after the interaction; with N odd, the soliton shapes of both u and v keep unchanged after the interaction.     

直流圆形线圈径向磁感应强度研究

基于毕奥-萨伐尔定律，分别考虑及不考虑直流通电圆形线圈的径向宽度和纵向厚度，推导出两种情况下该线圈沿径向方向的磁感应强度分布公式.然后，利用Matlab软件对获得的分布公式进行数值积分，得到理论上的磁感应强度分布数据.为了考察理论值的正确性，通过设计自制圆形线圈，进行实际测量.结果表明，考虑径向宽度和纵向厚度的影响时，磁感应强度实际测量值与理论值的相对误差较小.通过理论计算与实验研究相结合考察直流通电圆形线圈沿径向方向的磁感应强度分布，既能消除电磁感应法测交变磁场实验中磁场分布的系统误差，还可加强学生对电磁理论的理解与认识，提高电磁学课程的教学效果.