Control and Nash Games with Mean Field Effect

Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007, of Gueant-Lasry-Lions in 2011, of Huang-Caines-Malham in 2007 and many others). There are a lot of applications. In general, the applications concern approximating an infinite number of players with common behavior by a representative agent. This agent has to solve a control problem perturbed by a field equation, representing in some way the behavior of the average infinite number of agents. This approach does not lead easily to the problems of Nash equilibrium for a finite number of players, perturbed by field equations, unless one considers averaging within different groups, which has not been done in the literature, and seems quite challenging. In this paper, the authors approach similar problems with a different motivation which makes sense for control and also for differential games. Thus the systems of nonlinear partial differential equations with mean field terms, which have not been addressed in the literature so far, are considered here.     

Order Parameter Hysteresis on the Complex Network

Collective synchronization is investigated on the small-world network （NW model）. The order parameter is introduced to measure the synchronization of phase. It is found that there are differences between the processes of synchronization and desynchronization. The dependence of order parameter on the coupling strength is shown like a hysteresis loop. The size of the loop demonstrates the non-monotonicity with the change of adding probability, and is relevant to the construction of the network. The area may be maximum, as the adding probability is equal to 0.4. This phenomenon indicates that the clusters in the network play an important role in the processes of synchronization and desynchronization.     

一款教育类移动应用程序“爱猜元素”的开发

北京大学化学国家级实验教学示范中心开发了一款名为"爱猜元素"的教育类移动应用程序。它是以元素周期表为框架,"猜谜游戏"为逻辑主线,围绕元素知识及相关原理而设计的科普资源平台。本文主要介绍了该化学教育类app的设计理念、产品特点及其应用场景。     

疏水作用对光化学和光物理过程的影响 Ⅻ.2-羟基-4-烷氧基二苯甲酮在不良溶剂中的簇集

测定了2-羟基-4-甲氧基二苯甲酮(HMDB)和2-羟基-4-辛氧基二苯甲酮(HODB)在良溶剂和不良溶剂中的吸收光谱。在不良溶剂(乙二醇-水的混合溶剂)中,带长链的HODB发生簇集。由于簇集体内极性较小,HODB的吸收光谱与其在环己烷中相似。HMDB不发生簇集。     

1,3－取代方酸衍生物的光谱研究及二聚体、簇集体的形成

本文合成了1,3-取代方酸衍生物:1,3-双[4-二甲胺苯基]-2,4二羟基环丁二烯氢氧双内盐(DMCS),1,3-双[4-双十六烷胺苯基]-2,4二羟基环丁二烯氢氧双内盐(DHCS).研究了DMCS和DHCS在不同溶剂中的光物理行为,估算了DMCS、DHCS的基态与激发态之间偶极矩差值。在CTAB胶束中,除DMCS单体分子外,DMCS形成了二聚体。在二氧六环-水体系中,研究了DHCS的簇集行为,并测定了DHCS的临界簇集组成(C_ψ)及临界簇集浓度(C_A)。     

原子核集体运动的新模式

 由Z个质子和N个中子(统称核于)构成的原子核,在一些场合下表现出独立粒子运动的特征,在另一些场合下表现出A个核子(A=Z+N)集体运动的特征,这两种运动形态又常常相互影响,相互耦合.本文着重介绍原于核集体运动的若干新模式.首先介绍集体振动的新模式.     

构造一种与置换群成反同构的群

通过对中国古代一种游戏的讨论,建立了数学模型,从而构造了一种与置换群成反同构的互换群,得到一些有趣的结果     

24Mg集体态的三体非对角玻色相互作用修正

引入三体非对角玻色相互作用计算了²⁴Mg的能谱,克服了以往理论谱中0过低的困难,改进了理论和实验的符合程度.说明在某些情形下三体非对角玻色相互作用有可能是重要的.     

多极形变系统的集体运动

给出了一个描写多极形变系统集体运动的普遍公式,在那里,动能被拆分成三部分:体坐标框架下的振动,体坐标系围绕实验室系的转动以及振动与转动的耦合.定义了18种不同的八极形变内禀系,按其度规矩阵的行列式分为9个不同的类.其中以参数a₃₀,a₃₁,a₃₂,b₃₁和a₃₀,a₃₁,b₃₁,b₃₂定义的八极形变内禀系,度规矩阵的行列式(分别为9a232和9b232)是最简单的.     

振动合成在气垫导轨上的验证

晶格中原子的集体振动——声子与晶格的热力学性质密切相关。它是凝聚态物理中的重要内容并具有广泛的应用。由于介绍量子化的声子需要较多的基础知识,目前很少在本科教学中展示该内容。本文从经典物理的角度出发,通过气垫导轨实验来演示滑块的集体振荡,验证了任一种振动均是由基振动线性叠加而成,这一实验在本科教学中可帮助学生理解"合成、叠加、耦合"等现代物理学概念。