共形场论和相变

本文讨论了共形对称性,量子共形对称理论以及相变现象。讨论了二维共形场论中最基本的自由玻色场和费米场,也介绍了玻色化、高斯泛函、ＳＧ模型及其简单应用     

关于“莱顿瓶电震实验”的两点质疑

在人教版高中《物理.选修1-1》第一章第四节"电容器"中,为了引入电容器这个电器元件,教材首先讲述了1748年在巴黎圣母院前由物理学家诺莱特(A.J.A.Nollrt,1700～1770)表演的一个"魔术".教材表述如下:"魔术师"诺莱特调来700个修道士,让他们手拉手站成一排,全长约300m,     

BIFURCATIONS OF DEGENERATE SINGULAR POINT OF A PREDATOR-PREY SYSTEM WITH HOLLING-IV FUNCTIONAL RESPONSE

A predator-prey system with Holling-IV functional response is investigated. It is shown that the system has a positive equilibrium, which is a cusp of co-dimension 2 under certain conditions. When the parameters vary in a small neighborhood of the values of parameters, the model undergoes the Bogdanov-Takens bifurcation. Dif- ferent kinds of bifurcation phenomena are exhibited, which include the saddle-node bifurcation, the Hopf bifurcation and the homo-clinic bifurcation. Some computer simulations are presented to illustrate the conclusions.     

数形结合解复合函数的零点个数的常见解法

本文通过利用函数图像的方法研究复合函数y=g（f（x））的零点问题,即复合函数方程g（f（x））=0的根,令u=f（x）（内层方程）,这样g（f（x））=0就转化成g（u）=0.当外层方程g（u）=0容易求解时,可以先解方程g（u）=0,再解内层方程u=f（x）,这样方程的总个数即为复合函数y=g（f（x））的零点个数.     

随机哈密尔顿系统的周期变差解和近不变环面解

本文研究具有随机扰动的哈密顿系统的重现现象,尤其是轨道随机周期变差解和近不变环面解.具体来说,对线性薛定谔方程,我们完整阐述了随机周期变差解何时存在;对随机扰动的近可积哈密顿系统,我们证明了近不变环面的存在性与驱动噪声对应的哈密顿函数的对合性相关.     

Transition for Optimal Paths in Bimodal Directed Polymers

The problem for optimal paths in bimodal directed polymers is studied. It is shown that the distribution of the thermal average position of the endpoints of the optimal paths is discontinuous below the threshold p〈pc. The origin is that there is a finite possibility that only one endpoint takes the global minimum energy for p 〈 pc. Our results suggest that the percolation threshold for directed percolation is also the critical point of the transition for the possibility that the optimal paths converge to one endpoint.     

从弹簧滑块到地震预测:BK模型今昔谈

Burridge-Knopoff弹簧－滑块模型作为一个概念性的地震模型，自1967年提出以来一直为地震学家和物理学家所关注，对BK模型的研究成为物理学与地震学之间的一个活跃的交叉领域，BK模型的一些性质，例如确定性浑沌，自组织，孤立波，等等，能够为理解地震的性质和解决地震预测问题提供有用的线索，BK模型与目前的一些悬而未决的复杂性物理问题的联系，使它不仅对地震研究，而且对更普遍的多体系统问题的研究，都有重要的影响。     

Intermittency Growth in Fluid Turbulence

Measurement and phenomenological analyses of intermittency growth in an experimental turbulent pipe flow and numerical turbulence are performed, for which working definitions such as degree, increment, and growth rate of intermittency are introduced with the help of quasiscaling theory. The logarithmic-normal inertial scaling model is extended to quasiscaling as the second-order truncation of the Taylor expansion and is used for studying the intermittency growth problem. The extended self-similarity properties are shown to be not consistent with the monotonicity of the third order local quasiscaling exponent and the nonmonotonic behaviour of the intermittency growth rate as a result of bottleneck. Digestions of the results with scale-dependent multifractals are provided.     

风筝实验·雷电现象·避雷针

 一、放电现象--类比猜测1743年～1744年间,美国物理学家富兰克林在费城和波士顿看到了来自苏格兰的斯宾塞(A.Spence)博士利用玻璃管和莱顿瓶所做的简单的电学实验时,心里激起了强烈的探求欲望。他买下了全部展品,开始研究电学问题,一位他在伦敦英国皇家学会结识的朋友柯林森(PeterCollinson)得知此事后,给富兰克林寄来了一批电学著作、莱顿瓶和一些摩擦起电的设备,并在信中介绍了使用方法。     

三圆盘扭振系统主共振的理论与实验研究

本文应用非线性振动的平均法，分析了一个具有立方非线性并受简谐激励作用的三圆盘扭振系统的第二阶主共振，求得了稳态响应的分岔方程，并进行了奇异性分析，理论结果与实验结果相符·