一个二维分段光滑映象中的边界激变

解析地讨论一个冲击振子模型中的边界激变特征,证明了这类分段光滑二维映象中激变的生 存时间标度律为τ-ε^-γ,而γ=ln|β₂|ln|β₁β2|(β₁,β₂分别是混沌吸引子吸引域边界上鞍点的不稳 定和稳定本征值),这与处处光滑二维映象中相应的规律完全不同. 关键词： 激变 分段光滑映象 生存时间标度律     

一个不连续不可逆映象中的新型激发

报道了既不连续又不可逆一维映象中出现的一种具有新特征的激发(crisis)模式。这一新型激发产生于不连续性与不可逆性相互作用所导致的“映孔”与混沌吸引子的碰撞。映孔的出现可使迭代过程逃逸原来吸引子所占据的相空间区域,从而发生吸引子的突然扩张。数值计算结果表明,激发的特征时间<τ>与外控参量距其临界值距离的依赖关系为<τ>∝exp(U_0—U_(0c))~(-1/2),τ的不变分布P(τ)随τ增长呈现指数衰减关系。这种产生机制及主要特征与三种常见的激发相比均有新的特点。 关键词：     

动力学不连续性引起的新型激变

在描述张弛振子的一维不连续映象中，可以观察到由于混沌吸引子与动力学不连续点集碰撞而引起的具有新特征的激变．参量空间中的表征不同特征激变的四个临界曲面有可能会聚于一个公共“尖点”．在此尖点附近，参量的扰动会导致混沌吸引子的突然膨胀或收缩 关键词：     

一类新的边界激变现象:混沌的边界激变

混沌吸引子的激变是一类普遍现象.借助于广义胞映射图论(generalized cell mapping digraph)方法发现了嵌入在分形吸引域边界内的混沌鞍,这个混沌鞍由于碰撞混沌吸引子导致混沌吸引子完全突然消失,是一类新的边界激变现象,称为混沌的边界激变.可以证明混沌的边界激变是由于混沌吸引子与分形吸引域边界上的混沌鞍相碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混沌吸引子连同它的吸引域突然消失,同时这个混沌鞍也突然增大 关键词： 广义胞映射 有向图 激变 混沌鞍     

一类含非黏滞阻尼的Duffing单边碰撞系统的激变研究

以一类含非黏滞阻尼的Duffing单边碰撞系统为研究对象, 运用复合胞坐标系方法, 分析了该系统的全局分岔特性. 对于非黏滞阻尼模型而言, 它与物体运动速度的时间历程相关, 能更真实地反映出结构材料的能量耗散现象. 研究发现, 随着阻尼系数、松弛参数及恢复系数的变化, 系统发生两类激变现象: 一种是混沌吸引子与其吸引域内的混沌鞍发生碰撞而产生的内部激变, 另一种是混沌吸引子与吸引域边界上的周期鞍(混沌鞍)发生碰撞而产生的常规边界激变(混沌边界激变), 这两类激变都使得混沌吸引子的形状发生突然改变. 关键词： 非黏滞阻尼 Duffing碰撞振动系统 激变 复合胞坐标系方法     

一个强、弱耗散功能可分隔系统中的特征激变

报道一个由保守映象和耗散映象不连续、不可逆地分段描述的系统，以及在其中发生的一例特征激变.激变的独特之处在于逃逸孔洞.由映象的不连续、不可逆性而导致相平面中出现一个胖分形迭代禁区网，它使得一个混沌吸引子突然失稳而发生激变后出现的两个周期吸引子的吸引域边界成为点滴状.仅仅在每个周期点邻近存在这样的一个作为逃逸孔洞的、受到强耗散性支配和禁区边界限制的规则边界吸引域. 关键词： 激变 保守映象 耗散映象 逃逸孔洞     

常微分方程系统中内部激变现象的研究

应用广义胞映射图论方法研究常微分方程系统的激变.揭示了边界激变是由于混沌吸引子与 在其吸引域边界上的周期鞍碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混 沌吸引子连同它的吸引域突然消失,在相空间原混沌吸引子的位置上留下了一个混沌鞍.研 究混沌吸引子大小(尺寸和形状)的突然变化,即内部激变.发现这种混沌吸引子大小的突然 变化是由于混沌吸引子与在其吸引域内部的混沌鞍碰撞产生的,这个混沌鞍是相空间非吸引 的不变集,代表内部激变后混沌吸引子新增的一部分.同时研究了这个混沌鞍的形成与演化. 给出了对永久自循环胞集和瞬态自循环胞集进行局部细化的方法. 关键词： 广义胞映射 有向图 激变 混沌鞍     

一种“类耗散系统”中的“类Ⅴ型阵发”

一类不连续不可逆保面积映象可以展示类似耗散的行为,因此可称其为“类耗散系统”.在一种类耗散系统中观察到了椭圆周期轨道及其周围的椭圆岛与映象不连续边界碰撞而消失的现象.周期轨道消失后,经过一系列过渡椭圆周期轨道之后,系统的行为由一个混沌类吸引子主导.在混沌类吸引子刚刚出现时,混沌时间序列呈现层流相与湍流相的无规交替.这一切都与不连续耗散系统中发生的Ⅴ型阵发的相应性质十分相似,因此可称为“类Ⅴ型阵发”.然而,当混沌类吸引子刚刚出现时,仅可以找到最后一个过渡椭圆岛的“遗迹”,并不存在它的“鬼魂”,因此类Ⅴ型阵发不遵从Ⅴ型阵发的特征标度规律.反之,混沌类吸引子的鬼魂却存在于最后一个过渡椭圆周期轨道的类瞬态过程中,因此在类Ⅴ型阵发导致混沌运动的临界点之前,由此“类瞬态混沌奇异集”中逃逸的规律就成为标志这一种临界现象的标度律.这与Ⅴ型阵发又根本不同. 关键词： 类耗散性 类混沌吸引子 类Ⅴ型阵发     

Duffing单边碰撞系统的混沌鞍合并激变

以典型的Duffing单边碰撞系统为研究对象,对系统中的混沌鞍进行了细致的分析.研究表明,系统的混沌鞍同样存在合并激变,合并激变是由连接两个混沌鞍的周期鞍的稳定流形与不稳定流形相切所诱发,相切使得边界上的混沌鞍与内部的混沌鞍发生碰撞而突然合并为一个较大的边界混沌鞍.混沌鞍的合并激变行为最终会诱导混沌吸引子的合并激变发生. 关键词： Duffing碰撞系统 混沌鞍 周期鞍 稳定与不稳定流形     

不可微不可逆映象中的V型阵发

一个既不可微(或不连续)又不可逆的一维映象可以展示一种新型的阵发。它的机制是稳定不动点与映象不可微或不连续点碰撞而消失。这种阵发可以在该不动点附近的线性化映象本征值绝对值在阵发前为小于1的任何值的情况发生,因而可能突然出现在倍周期分岔序列中途任一部分,使序列中断进入混沌。在稳定不动点消失后映象产生的阵发时间序列中,层流相长度呈现与外控参数距临界值距离的对数依赖关系。这种新型标度规律不依赖于映象的细节。作者认为这种阵发应广泛存在于许多实际系统之中。 关键词：     

Finite-temperature perturbation theory for the random directed polymer problem

We study the random directed polymer problem—the short-scale behavior of an elastic string (or polymer) in one transverse dimension subject to a disorder potential and finite temperature fluctuations. We are interested in the polymer short-scale wandering expressed through the displacement correlator 〈[δu(X)]²〉, with δu(X) being the difference in the displacements at two points separated by a distance X. While this object can be calculated at short scales using the perturbation theory in higher dimensions d > 2, this approach becomes ill-defined and the problem turns out to be nonperturbative in the lower dimensions and for an infinite-length polymer. In order to make progress, we redefine the task and analyze the wandering of a string of a finite length L. At zero temperature, we find that the displacement fluctuations 〈[δu(X)]²〉 ∝ LX ² depend on L and scale with the square of the segment length X, which differs from a straightforward Larkin-type scaling. The result is best understood in terms of a typical squared angle 〈α²〉 ∝ L, where α = ? _x u, from which the displacement scaling for the segment X follows naturally, 〈[δu(X)]²〉 ∝ 〈α²〉 X ². At high temperatures, thermal fluctuations smear the disorder potential and the lowest-order results for disorder-induced fluctuations in both the displacement field and the angle vanish in the thermodynamic limit L → ∞. The calculation up to the second order allows us to identify the regime of validity of the perturbative approach and provides a finite expression for the displacement correlator, albeit depending on the boundary conditions and the location relative to the boundaries.     

Why are chaotic attractors rare in multistable systems?

We show that chaotic attractors are rarely found in multistable dissipative systems close to the conservative limit. As we approach this limit, the parameter intervals for the existence of chaotic attractors as well as the volume of their basins of attraction in a bounded region of the state space shrink very rapidly. An important role in the disappearance of these attractors is played by particular points in parameter space, namely, the double crises accompanied by a basin boundary metamorphosis. Scaling relations between successive double crises are presented. Furthermore, along this path of double crises, we obtain scaling laws for the disappearance of chaotic attractors and their basins of attraction.     

Optical Tomography for Single- and Two-Mode Squeezed Chaotic Fields

Different from the previous methods of obtaining optical tomography of quantum states, in this paper we use the Radon transform between the single- (two-)mode Wigner operator and the pure-state density operator |q〉 _{f,g f,g} 〈q| (|η,τ ₁,τ ₂〉〈η,τ ₁,τ ₂|) to analytically obtain optical tomograms for single- (two-)mode squeezed chaotic fields, where the states |q〉 _f,g (|η,τ ₁,τ ₂〉) refer to the newly introduced intermediate coordinate-momentum (entangled) states. More interestingly, we find that the tomograms of squeezed chaotic fields and those of coherent states are related by a integration. Thus, we establish a new convenient approach of obtaining tomograms for quantum states.     

On the transition to hyperchaos and the structure of hyperchaotic attractors

Using a recently proposed algorithmic scheme for correlation dimension analysis of hyperchaotic attractors, we study two well-known hyperchaotic flows and two standard time delayed hyperchaotic systems in detail numerically. We show that at the transition to hyperchaos, the nature of the scaling region changes suddenly and the attractor displays two scaling regions for embedding dimension M ≥ 4. We argue that it is an indication of a strong clustering tendency of the underlying attractor in the hyperchaotic phase. Because of this sudden qualitative change in the scaling region, the transition to hyperchaos can be easily identified using the discontinuous changes in the dimension (D ₂) at the transition point. We show this explicitely for the two time delayed systems. Further support for our results is provided by computing the spectrum of Lyapunov Exponents (LE) of the hyperchaotic attractor in all cases. Our numerical results imply that the structure of a hyperchaotic attractor is topologically different from that of a chaotic attractor with inherent dual scales, at least for the two general classes of hyperchaotic systems we have analysed here.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_?)^?1 with the dwell time τ_D through the cavity and the dephasing rate τ _? ^?1 , we find an exponential suppression of weak localization by a factor of ∝ exp[? $\tilde \tau $ /τ_?], where $\tilde \tau $ is the system-dependent parameter. In the dephasing probe model, $\tilde \tau $ coincides with the Ehrenfest time, $\tilde \tau $ ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, $\tilde \tau $ ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F.     

耦合映射混沌同步系统在加性噪声中的筛形域性态

由于实际系统中噪声不可避免，噪声使得同步混沌吸引子A变成具有一定生存时间<τ>的准稳态吸引子A′.以加性噪声作用下的二维耦合映射混沌同步系统为例，给定系统实验时间长 度T，解析发现：仅当<τ>>2T时准稳态同步混沌吸引子的筛形吸引域才可被定性观察到；而 当<τ><2T时则不复存在，此时，根据原无噪声时的筛形吸引域特征的不同，筛形域不仅可 以转变成时变筛形结构，还可以转变成分形结构.同时利用数值模拟作了进一步验证.该结果 对于二维耦合映射混沌同步系统具有普遍意义. 关键词： 混沌同步 筛形吸引域 瞬态混沌 耦合映射 加性噪声     

Intermittency in the atmospheric surface layer: Unresolved or slowly varying?

We present streamwise velocity structure functions 〈δv_L(τ)〉=〈|v(t+τ)−v(t)|^p〉 (with p=1:5) obtained in the near neutral atmospheric surface layer at the Utah SLTEST site at the highest terrestrial Reynolds number Re_τ=O(10⁶). We show that the occurrence of very large scale coherent oscillations in the streamwise velocity throughout the wall region, interpreted as genuine structural features of the canonical turbulent boundary layer, affects the scaling exponents of the p>3 order structure functions. This results in a slight alteration of the intermittent behavior of the velocity field. It was found that for positive (fast) large scale oscillation of the low-pass filtered velocity signal, deviations from the Kolmogorov K41 prediction (absence of multiscaling) are more marked, as compared to negative (slow) excursion. The results are discussed in terms of convergence of statistics from atmospheric boundary layer measurements.     

An Analytical APproach to the Turbulence—Relaxed State in Tokamak Plasmas

Starting from the continuity, temperature, and motion equations of the trapped electron fluid in general tokamak magnetic field with positive or reversed shear and the definition of Lagrangian invariant, dL/dt≡(\partial_t+ u•▽)L=0, where u is convective velocity, the trapped electron dynamics is considered in the following two assumptions: (i) the turbulence is low frequency electrostatic, and (ii) L is a functional only of the density n, temperature T, and magnetic field B, and the effect of perturbation potential φ is included in the convective velocity u, i.e., u is a functional of n, T, B, and φ. The Lagrangian invariant hidden in the trapped electron dynamics is strictly found: L=ln[(n/B)^c₁(T/B^2/3)^c₂], where c₁ and c₂ are dimensionless changeable parameters and c₁∝c₂. From this Lagrangian invariant the turbulent particle and electron thermal transport scaling laws are derived: 〈n>_ψq(ψ)=const. and 〈T^3/2>_ψq(ψ)=const., which, in the limit of large aspect ratio, reduce to n(r)q(r)=const. and T^3/2(r)q(r)=const., respectively. The latter two scaling laws are compared with existent experimental results, being in good agreement.     

Charged hadron production ine + e − annihilation in the Υ and Υ′ region

Charged hadron production ine ⁺ e ^? annihilation is studied in the 7 to 10 GeV CM energy region and at the Υ (9.46) and Υ′ (10.01) resonances with the LENA detector at DORIS. The statistical moments of the charged multiplicities are studied. The data show KNO scaling behaviour and suggest the presence of long range correlations. An average charged multiplicityrise of Δn(Υ)=0.55±0.19 and Δn(Υ′)=1.26±0.29 over the continuum is observed for the Υ and Υ′ direct decays. The jet structure of the Υ and Υ′ direct decays is investigated using the charged particles. The polar angular distributions of the jet axis behave like 1+α(T) cos²θ with 〈α(T)〉_Υ=0.7±0.3 and 〈α(T)〉_Υ′=0.6±0.4. The 〈α(T)〉_Υ value is in agreement with the QCD vector gluon assignment and excludes scalar gluons by more than four standard deviations.