平板边界层中湍流的发生与混沌动力学之间的联系

通过对平板边界层流动中的测量数据的仔细分析,证实了在平板边界层的湍流发生的过程中存在着奇怪吸引子.将这一结论与先前的转捩动力学分析结果相比较,证明了湍流的发生本身具有着混沌动力学本质,从而在平板边界层中的湍流发生与混沌之间建立了联系 关键词： 边界层 转捩 湍流的发生 混沌 奇怪吸引子     

工科物理中介绍“混沌与分形”的认识与实践

介绍一种用普通物理风格讲授混沌与分形的教学方案，实践证明该方案可使学生较容易地掌握复杂现象的物理本质     

混沌动力学方法在等离子体尾迹流场研究中的应用

用混沌动力学方法对多道扫描静电探针的离子饱和电流信号进行分析,研究了等离子体尾迹流场.通过对相关维、Renyi熵和最大Lyapunov指数的分析,得到了近尾流场的分层结构.利用最大Lyapunov指数,观测到了在x>10D以后的远尾流场与自由流场相似.结合探针信号的自相关函数,研究流场湍流结构,发现近尾可能存在大涡拟序结构,而在远尾则没有湍流.观察到了流场具有一定的间歇特征,认为这种间歇性与湍流有关.结果还表明,混沌动力学的分析方法对信号中非周期成分十分敏感,在研究等离子体尾迹流场这一类非线性系统时,它具有明显的优越性 关键词： 混沌动力学 尾迹 等离子体湍流 静电探针     

双参数动力学系统中混沌的控制

研究了双参数动力学系统中混沌行为的控制问题,提出了控制混沌的参数微调方法,给出了参数变化方程,然后应用到两个例子:Henon映射和强迫布鲁塞耳振子,得到了很好的控制结果,并且与单参数的Ott,Grebogi和Yorke(OGY)方法进行了比较,最后对有关问题进行了讨论. 关键词：     

工科物理中介绍“混沌中分形”的认识与实践

介绍一种用普遍物理风格讲授混沌与分形的教学方案，实践证明该中使学生 掌握复杂现象的物理本质。     

一个新的混沌系统的动力学分析及混沌控制

提出了一个新的混沌系统,研究了其基本动力学特性.设计了实现该系统的混沌电路,电路实验结果验证了系统的混沌行为.根据Lyapunov稳定性理论,采用自适应backstepping控制方法,把系统控制到一个有界点.数值仿真证明了该方法的有效性和可行性.     

湍流边界层中下扫流与“反发卡涡”

用氢气泡法观测湍流边界层的下扫流和有关的流动结构.实验中发现一种新型涡结构，它的特征与典型的发卡涡正好相反.发卡涡的头部指向下游，而它的头部指向上游； 发卡涡的两腿之间，由于涡的诱导产生上升流，而它则在其两腿之间，由于涡的诱导产生下扫流. 关键词： 湍流边界层 流动显示 流动结构 发卡涡     

平板湍流边界层瞬时摩擦阻力的光学测量和统计分析

采用近壁粒子图像测速（particle image velocimetry,PIV）技术实现了中低Reynolds数光滑平板湍流边界层瞬时摩擦阻力的测量.发展了单行互相关算法和迭代拟合技术估算瞬时摩擦阻力,其法向空间分辨率可达到2~4 pixel.作为对比,同时分析了相似Reynolds数范围的直接数值模拟数据.统计结果表明:摩擦阻力的脉动强度随Reynolds数升高呈现对数增长趋势,证实了外区大/超大尺度结构对壁面的影响.谱分析结果表明近壁区的低速条带结构主导着摩擦阻力的多尺度脉动特性,外区大/超大尺度结构对摩擦阻力的印迹作用较小,其主要通过调制作用实现对摩擦阻力的影响,这一结论可以从瞬时摩擦阻力的偏度以及概率密度函数曲线具有Reynolds数不变性得到进一步证实.      

连续混沌调频信号的动力学设计与分析

提出了基于连续混沌时间尺度变换的连续混沌调频信号动力学设计理论,并以Colpitts电路为例给出了具体的实现模型.通过吸引子重构和Lyapunov指数分析,阐述了连续混沌调频信号的动力学特性.结果显示连续混沌调频信号的最大Lyapunov指数与混沌信号的最大Lyapunov指数相同;连续混沌调频信号的动力学设计实现方式简单且系统参数易于控制,同时信号形式与数学意义上的连续混沌调频信号保持一致.     

一种识别混沌时间序列动力学异同性的方法

定义了两个新的统计量，分别记为Q和R，Q称为动力学自相关因子指数，R称为动力学互相关 因子指数.用Q和R对不同时间序列的动力学“距离”或同一时间序列中不同区段（窗口）的 动力学“距离”进行估算，可以鉴别这些时间序列的动力学属性或它们内在的动力学结构层 次以及复杂性.一些典型实例检验表明，这种方法是有效的. 关键词： 混沌时间序列 动力学自相关因子指数 动力学互相关因子指数     

Intermittency at critical transitions and aging dynamics at the onset of chaos

We recall that at both the intermittency transitions and the Feigenbaum attractor, in unimodal maps of non-linearity of order ζ > 1, the dynamics rigorously obeys the Tsallis statistics. We account for theq-indices and the generalized Lyapunov coefficients λ^q that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the onset of chaos with the appearance of a special value for the entropic indexq. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.     

Tsallis non-extensive statistics,intermittent turbulence,SOC and chaos in the solar plasma. Part two: Solar flares dynamics

In this study which is the continuation of the first part (Pavlos et al. 2012) [1], the nonlinear analysis of the solar flares index is embedded in the non-extensive statistical theory of Tsallis (1988) [3]. The q$q$-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the singular value decomposition (SVD) components of the solar flares timeseries. Also the multifractal scaling exponent spectrum f(a)$f\left(a\right)$, the generalized Renyi dimension spectrum D(q)$D\left(q\right)$ and the spectrum J(p)$J\left(p\right)$ of the structure function exponents were estimated experimentally and theoretically by using theq$q$-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000) [25]. Our analysis showed clearly the following: (a) a phase transition process in the solar flare dynamics from a high dimensional non-Gaussian self-organized critical (SOC) state to a low dimensional also non-Gaussian chaotic state, (b) strong intermittent solar corona turbulence and an anomalous (multifractal) diffusion solar corona process, which is strengthened as the solar corona dynamics makes a phase transition to low dimensional chaos, (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of the functions: (i) non-Gaussian probability distribution function P(x)$P\left(x\right)$, (ii) f(a)$f\left(a\right)$ and D(q)$D\left(q\right)$, and (iii) J(p)$J\left(p\right)$ for the solar flares timeseries and its underlying non-equilibrium solar dynamics, and (d) the solar flare dynamical profile is revealed similar to the dynamical profile of the solar corona zone as far as the phase transition process from self-organized criticality (SOC) to chaos state. However the solar low corona (solar flare) dynamical characteristics can be clearly discriminated from the dynamical characteristics of the solar convection zone.     

Accuracy of semiclassical dynamics in the presence of chaos

We review some of the issues facing semiclassical methods in classically chaotic systems, then demonstrate the long-time accuracy of semiclassical propagation of a nonstationary wave packet using the quantum baker's map of Balazs and Voros. We show why some of the standard arguments against the efficacy of semiclassical dynamics for long-time chaotic motion are incorrect.     

Tsallis non-extensive statistics,intermittent turbulence,SOC and chaos in the solar plasma,Part one: Sunspot dynamics

In this study, the non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988, 2004, 2009) ,  and . The q$q$-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum f(a)$f\left(a\right)$, the generalized Renyi dimension spectrum D(q)$D\left(q\right)$ and the spectrum J(p)$J\left(p\right)$ of the structure function exponents were estimated experimentally and theoretically by using the q$q$-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2001, 2000)  and . Our analysis showed clearly the following: (a) a phase transition process in the solar dynamics from high dimensional non-Gaussian SOC state to a low dimensional non-Gaussian chaotic state, (b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov’s studies (Zelenyi and Milovanov (1991) [21]); Milovanov and Zelenyi (1993) [22]; Ruzmakin et al. (1996) [26]) (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of (i) non-Gaussian probability distribution function P(x)$P\left(x\right)$, (ii) multifractal scaling exponent spectrum f(a)$f\left(a\right)$ and generalized Renyi dimension spectrum _Dq$D_q$, (iii) exponent spectrum J(p)$J\left(p\right)$ of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.     

Effects of barrier fluctuation on the tunneling dynamics in the presence of classical chaos in a mixed quantum-classical system

We present a numerical investigation of the tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier which is coupled to a non-integrable classical system and study the interplay between classical chaos and barrier fluctuation in the tunneling dynamics. We found that the coupling of the quantum system with the classical subsystem decreases the tunneling rate irrespective of whether the classical subsystem is regular or chaotic and also irrespective of the fact that whether the barrier fluctuates or not. Presence of classical chaos always enhances the tunneling rate constant. The effect of barrier fluctuation on the tunneling rate in a mixed quantum-classical system is to suppress the tunneling rate. In contrast to the case of regular subsystem, the suppression arising due to barrier fluctuation is more visible when the subsystem is chaotic.      

湍流级串和动力学过程之间的关系

利用在边界层转捩中逐渐建立起来的主要动力学过程，对湍流级串概念做了进一步的分析.对边界层转捩的测量结果进行定量分析，从所得能谱中可以清楚看到湍流级串与转捩的动力学过程的对应关系，进而丰富了对湍流级串的理解. 关键词： 级串 动力学 转捩     

Minimum description of the onset of pipe turbulence

To demonstrate essentials of the mechanism for the onset of turbulence in a pipe at Re=2000, 48 degrees of freedom are enough. The derivation from the Navier-Stokes equation uses a novel type of modes which guarantee linear stability. For the reduction of the nonlinear interactions, the modes are grouped in 3 blocks. Facilitated by these simplifications the interdependence between linear and nonlinear processes is analysed, however, just for a special example. A phenomenon resembling backflow is identified. Received 20 October 1997