Quantitative universality for a class of nonlinear transformations

A large class of recursion relationsx _{n + 1} = f(x_n) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum . With sufficiently small),z > 1, the universal details depend only uponz. In particular, the local structure of high-order stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio ( = 2.5029078750957... forz = 2). This structure is determined by a universal functiong ^*(x), where the 2ⁿth iterate off,f ⁽ⁿ⁾, converges locally to ^–n g ^*( ⁿ x) for largen. For the class off's considered, there exists a _n such that a 2ⁿ-point stable limit cycle including exists; – _n R~ ^–n ( = 4.669201609103... forz = 2). The numbers and have been computationally determined for a range ofz through their definitions, for a variety off's for eachz. We present a recursive mechanism that explains these results by determiningg ^* as the fixed-point (function) of a transformation on the class off's. At present our treatment is heuristic. In a sequel, an exact theory is formulated and specific problems of rigor isolated.Research performed under the auspices of the U.S. Energy Research and Development Administration.  

LiH，LiO和LiOH的分析势能函数与分子反应动力学

基于相对论有效原子实势（RECP）和密度泛函（B3LYP/SDD）方法，优化得到了LiH，LiO和LiOH的分子结构；研究得到了LiH和LiO的Murrell-Sorbie分析势能函数以及LiOH的多体项展式分析势能函数，由势能函数导出了LiH，LiO和LiOH的离解能，分别为2.722eV，3.592eV和9.085eV，与实验值基本一致.在分析势能函数基础上，用准经典分子散射理论方法，研究了LiH与O的分子反应动力学.结果表明，碰撞反应是一个无阈能反应，即较低的初始平动能更有利于反应产物的形成，主要生  

球对称动态黑洞Dirac场的统计熵

利用改进的brick-wall模型，计算最一般球对称动态黑洞Dirac场的统计熵.结果表明，任一时刻黑洞熵都与黑洞事件视界面积成正比.特别是给出了动比例系数的计算公式，通过计算动比例系数，可直接得出各种球对称动态黑洞Dirac场的统计熵.  

Economic small-world behavior in weighted networks

The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation is valid only for topological networks. In this paper we propose a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of economic small worlds, that formalizes the idea of networks that are “cheap” to build, and nevertheless efficient in propagating information, both at global and local scale. In this way we provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are studied, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems. Received 6 November 2002 / Received in final form 24 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: latora@ct.infn.it  

Epidemic outbreaks in complex heterogeneous networks

We present a detailed analytical and numerical study for the spreading of infections with acquired immunity in complex population networks. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations in the limit of a very large number of nodes, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures. Received 20 September 2001 and Received in final form 4 February 2002  

人造量子系统的理论研究与代数动力学

从控制与利用微观系统的量子工程的观点，讨论了人造量子系统的基本物理问题。针对人造量子系统中的一大类———非自治量子系统的求解问题，提出了代数动力学理论方法。运用代数动力学，对人造量子系统进行了理论研究；对可积的非自治系统，详细介绍了线性系统和非线性可积系统的求解问题；对不可积系统，用代数动力学观点研究了量子规则运动和无规运动的特征，它们之间的过渡，以及它们对时间有关外场的不同响应。  

芳香族氨基酸的太赫兹光谱研究

利用太赫兹时域光谱研究了三种芳香族氨基酸，即酪氨酸、色氨酸和苯丙氨酸，在02—1 6THz波段的光学特性，得到了对应的吸收谱.对比各自的吸收谱发现，酪氨酸和色氨酸分 别在0976THz和1465THz有明显的吸收峰，而苯丙氨酸则没有明显的吸收峰.利用密度泛 函(DFT)理论初步计算表明，氨基酸在THz波段的吸收是由分子转动或扭动造成的，氨基酸的 不同结构造成了它们在THz波段不同的吸收峰位.另外，还得到了三种氨基酸在该波段的折射 率谱并首次定量给出了三种氨基酸在02—16THz波段的平均折射率.酪氨酸、色氨酸和苯 丙氨酸的平均折射率分别为1507，1526和1686.这项研究不仅为研究生物分子结构和 动力学提供了新的理论和实验方法，而且对进一步利用THz时域光谱研究其他生物大分子具 有借鉴意义.  

线阵CCD用于实时动态测量技术研究

本文研究的是在连续光条件下线阵ＣＣＤ实时动态测量技术，除了考虑ＣＣＤ像元响应非均匀性、非线性等影响因素外，还应认真考虑采样频率、测量精度、动态范围、快速电路等问题。本文还详细讨论了测量精度和动态范围问题，推导了测量精度公式与动态范围公式。为了减小测量误差和提高被测信号的频率，必须相应减小积分时间。精度公式是进行线阵ＣＣＤ电路设计的基本依据公式。动态范围与频率无关，只与结构参数有关，为了充分利用ＣＣＤ的动态范围，激光功率要可调。  

尾流中气泡对光传播的影响

从几何光学的角度出发,针对气泡直径与光束直径之间的大小关系,分两种情况,推得了单个气泡的散射光强变化情况,以及气泡速度与散射光强之间的关系.得出散射光强的变化频率与气泡半径和速度存在一定的关系,光束的直径与气泡直径的大小关系决定光强变化的强弱.在此理论基础上,模拟了光强的变化,并与实验所得曲线相比较,验证了实际与理论的相符性.同时用短曝光、连续拍摄的数码相机对气泡进行拍摄,进一步验证了理论推导的正确性.  

线阵CCD图像处理算法研究

研究了线阵CCD在动态测量中的整体图像处理方法 ,包括杂散点剔除、图像平滑、边缘识别等方法。提出的整体图像的样条插值方法使得边缘识别精度比较高 ,实现起来较容易 ,该方法特别对复杂环境下的动态CCD图像处理有效