大气湍流的混沌吸引子特征

采用时间延迟技术,利用高性能的超声风温仪和红外湿度脉动仪所测得的大气湍流脉动资料,重构相空间中的湍流吸引子,估算了其相关维D2和最大Lyapunov指数λ1。结果表明,在不同地点、不同时间以及不同大气稳定度条件下,大气湍流的最大Lyapunov指数λ1均大于零,说明大气湍流的确具有混沌特征,且存在低维奇怪吸引子,其维数在3～7之间,视变量的不同(动力变量还是非动力变量)而不同,且受大气稳定度影响。首次使用了湍流动能来重建湍流吸引子。     

Metallogenic Districts of Yangtze Cratonic Rim at the Edge of Chaos

Ｔｈｒｅｅｆｕｎｄａｍｅｎｔａｌｔｈｅｏｒｉｅｓａｒｅｒａｉｓｅｄｆｏｒ“ｃｏｍｐｌｅｘｉｔｙａｎｄｓｅｌｆ－ｏｒｇａｎｉｚｅｄｃｒｉｔｉｃａｌｉｔｙ（ＳＯＣ）ｏｆｍｅｔａｌｏｇｅｎｉｃｄｙｎａｍｉｃｓｙｓｔｅｍｓ”（Ｙｕ,１９９８）：（１）Ｎｏｎｌ...     

大气海洋环境数值模拟中的若干计算问题

为了适应发展气候数值模拟和环境数值模拟的需要,综合介绍了与此密切有关的若干计算问题。首先,指出这类问题易于出现计算紊乱、非物理解和非线性计算不稳定,同时,简要介绍造成这些问题出现的三种机理：虚假频散、能量关系破坏和能谱的非线性转移。然后,把这类问题归结为一种“发展方程”,给出了与此有关的几个定理,阐述了计算稳定性、能量守恒性和算子非负性之间的密切关系。接着,分别介绍了多种完全平方守恒的差分格式的构造方法,其中包括隐式的和显式的完全平方守恒的差分格式,高时间精度和高阶紧致的完全平方守恒的差分格式,同时也给出若干具体算例说明这些格式的计算效果。最后,对全文作了小结,并指出今后应进一步研究的若干重要问题。     

Chaos in three-body dynamics: Kolmogorov–Sinai entropy

An ensemble of Newtonian three-body models with close initial separations is investigated by following the evolution of a 'drop' in the homology map. The onset of chaos is revealed by the motion and the complex temporal deformation of the drop. In the state of advanced chaos, the drop spreads over almost the whole homology map, quite independently of its initial position on the map. A general quantitative measure of this process is the mean exponential rate of spreading, which bears resemblance to Kolmogorov–Sinai entropy; this is introduced and estimated in terms of the homology mapping. In a similar manner we also estimate the mean exponential rate of divergence of initially close-by trajectories. This is a close analogue to the Lyapunov exponent. These parameters measure two complementary aspects of dynamical instability, which is the basic mechanism of the onset of chaos.     

Symplectic Tangent map for Planetary Motions

Equations are presented for the computation of tangent maps for use in nearly Keplerian motion, approximated by use of a symplectic leapfrog map. The resulting algorithms constitute more accurate and efficient methods to obtain the Liapunov exponents and the state transition matrix, and can be used to study chaos in planetary motions, as well as in orbit determination procedures from observations. Applications include planetary systems, satellite motions and hierarchical, nearly Keplerian systems in general. This revised version was published online in July 2006 with corrections to the Cover Date.     

Asteroid 522 Helga is chaotic and stable

Celestial Mechanics and Dynamical Astronomy -     

Tame and chaotic behavior in the planar isosceles 3-body problem

We show that every planar isosceles solution of the three-body problem encounters a collision of the symmetric particles, either forwards or backwards in time. Regularizing analytically this collision, the solution has at least a syzygy configuration and/or leads to a total collapse. Some further simple results support the intuitive image on the tame local behavior of the motion as long as it does not lead to a triple collision. As a main result we prove that total collapse singularities, can be regularized in aC ¹-fashion with respect to time, for all values of the masses. Using symbolic dynamics, the chaotic character of theC ¹-regularized solutions is pointed out.     

The Trojan asteroid belt: Proper elements,stability, chaos and families

I have computed proper elements for 174 asteroids in the 1 : 1 resonance with Jupiter, that is for all the reliable orbits available (numbered and multi-opposition). The procedure requires numerical integration, under the perturbations by the four major planets, for 1,000,000 years; the output is digitally filtered and compressed into a synthetic theory (as defined within theLONGSTOP project). The proper modes of oscillation of the variables related to eccentricity, perihelion, inclination and node define proper elements. A third proper element is defined as the amplitude of the oscillation of the semimajor axis associated with the libration period; because of the strong nonlinearity of the problem, this component cannot be determined by a simple Fourier transform to the frequency domain. I therefore give another definition, which results in very good stability with time. For 87% of the computed orbits, the stability of the proper elements-at least over 1M yr-is within the following bounds: 0.001AU in semimajor axis, 0.0025 in eccentricity and sine of inclination. Half of the cases with degraded stability of the proper elements are found to be chaotic, with e-folding times between 16,000 and 660,000yr; in some other cases, chaotic behaviour does not result in a significantly decreased stability of the proper elements (stable chaos). The accuracy and stability of these proper elements is good enough to allow a search for asteroid families; however, the dynamical structure of the Trojan belt is very different from the one of the main belt, and collisional events among Trojans can result in a distribution of fragments difficult to identify. The occurrence of couples of Trojans with very close proper elements is proven not to be statistically significant in almost all cases. As the only exception, the couple 1583 Antilochus — 3801 Thrasimedes is significant; however, it is not easy to account for it by a conventional collisional theory. The Menelaus group is confirmed as a strong candidate collisional family; Teucer and Sarpedon could be considered as significant clusters. A number of other clumps are detected (by the same automated clustering method used for the main belt by Zappalà et al., 1990, 1992), but the total number of Trojans with reliable orbits is not large enough to detect many significant candidate families.     

Fractal and chaotic phenomena of seismic dissipated energy in an energy system of engineering structures

Fractal and chaotic phenomena in engineering structure are discussed in this paper, it means that the characters of fractal and chaos on dynamic system of seismic dissipated energy activity intensity E _d and activity intensity of seismic dissipated energy moment I _e are analyzed carefully. Based on the conceptions of the energy system of engineering structures Θ, seismic dissipated energy activity intensity E _d and activity intensity of seismic dissipated energy moment I _e, the chaotic phenomena of dynamic systems E _d and I _e are discovered by theoretic derivation, then the fractal characters of them are also discovered from theoretical inferring and numerical computation. Attractor of relative dimension d ₂, Renyi entropy of the second order k ₂, mean predictable time scale 1/k ₂ and other parameters of the dynamic system which were constructed in light of a large number of actual measuring seismic data have been achieved in the end. These parameters are exactly what the fractal and chaotic phenomena have represented in practical dynamic system, which may be valuable for earthquake-resistant theory and analytical method in practical engineering structures.     

Complexity and Self-Organized Criticality of Solid Earth System(Ⅰ)

ＰＯＳＩＮＧＴＨＥＰＲＯＢＬＥＭ“ＣｏｍｐｌｅｘｉｔｙａｎｄＳｅｌｆ－ＯｒｇａｎｉｚｅｄＣｒｉｔｉｃａｌｉｔｙｏｆＳｏｌｉｄＥａｒｔｈＳｙｓｔｅｍ”ｉｓａｎｅｗｐｒｏｂｌｅｍａｓｗｅｌａｓａｎｅｗｐｒｏｐｏｓｉｔｉｏｎ．Ｔｈｅａｕｔｈｏｒｐｕｔｓｆｏ...