Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.     

Lagrangian and Eulerian velocity intermittency

Usual turbulence experiments, based on the Taylor hypothesis, differ from true Eulerian measurements. This is the origin of the apparent discrepancy between a recent two point correlation analysis and the multiplicative cascade picture. Indeed, both Eulerian and Lagrangian observations perfectly agree with this picture. Received 19 June 2002 / Received in final form 29 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: bcastain@ens-lyon.fr     

非Kolmogorov大气湍流温度谱标度指数的测量与分析

 阐述了非Kolmogorov湍流谱理论以及湍流谱标度指数的测量与计算方法。在近地面多个地点对大气湍流温度起伏进行了多次的实验观测，结果表明：实际大气湍流温度谱标度指数多数不等于-5/3，并且通常在-2到-1之间变化。分析了湍流温度谱标度指数与湍流发展程度的相关性，利用小波分析方法展现了不同湍流强度下湍流温度脉动能量在各尺度之间的分配状态，发现湍流温度谱标度指数的绝对值在一定程度上随湍流强度的增加而增大。     

不同地区大气光学湍流内外尺度测量

 用光学湍流参数自动测量系统对内陆地区和沿海地区光学湍流内外尺度进行了大量的实验观测。分析了湍流尺度的日变化规律，给出了其频数分布。结果表明：两地内尺度的均值为十几mm，外尺度的均值约为2 m；内陆地区内尺度日变化趋势较为复杂，而外尺度的日变化趋势与湍流强度十分相似；沿海地区内外尺度与湍流强度均无明显关系。大气湍流尺度的大小和分布状态是随时间和空间变化的，因此，在估算实际大气湍流对光学系统的影响时，需要实测湍流尺度以便得到准确的结果。     

Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added. Supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151) and the Innovative Team Program of Liaoning Educational Committee     

Infinite Prandtl Number Convection

We prove an inequality of the type NCR ^1/3(1+log₊ R)^2/3 for the Nusselt number N in terms of the Rayleigh number R for the equations describing three-dimensional Rayleigh–Bénard convection in the limit of infinite Prandtl number.     

Multi-separation, centrifugality and centripetality imply chaos

Let be an interval. need not be compact or bounded. Let be a continuous map, and be a trajectory of with or . Then there is a point such that . A point is called a centripetal point of relative to if or , and is centrifugal if or . In this paper we prove that if there exist centripetal points of in , then has periodic points of some odd () period . In addition, we also prove that if ) is multi-separated by Fix(), or there exists a centrifugal point of in , then is turbulent and hence has periodic points of all periods.

     

On parallel asynchronous high-order solutions of parabolic PDEs

In achieving significant speed-up on parallel machines, a major obstacle is the overhead associated with synchronizing the concurrent processes. This paper presents high-orderparallel asynchronous schemes, which are schemes that are specifically designed to minimize the associated synchronization overhead of a parallel machine in solving parabolic PDEs. They are asynchronous in the sense that each processor is allowed to advance at its own speed. Thus, these schemes are suitable for single (or multi) user shared memory or (message passing) MIMD multiprocessors. Our approach is demonstrated for the solution of the multidimensional heat equation, of which we present a spatial second-order Parametric Asynchronous Finite-Difference (PAFD) scheme. The well-known synchronous schemes are obtained as its special cases. This is a generalization and expansion of the results in [5] and [7]. The consistency, stability and convergence of this scheme are investigated in detail. Numerical tests show that although PAFD provides the desired order of accuracy, its efficiency is inadequate when performed on each grid point.In an alternative approach that uses domain decomposition, the problem domain is divided among the processors. Each processor computes its subdomain mostly independently, while the PAFD scheme provides the solutions at the subdomains' boundaries. We use high-order finite-difference implicit scheme within each subdomain and determine the values at subdomains' boundaries by the PAFD scheme. Moreover, in order to allow larger time-step, we use remote neighbors' values rather than those of the immediate neighbors. Numerical tests show that this approach provides high efficiency and in the case which uses remote neighbors' values an almost linear speedup is achieved. Schemes similar to the PAFD can be developed for other types of equations [3].This research was supported by the fund for promotion of research at the Technion.     

Experimental artefacts in 2D-MAS exchange experiments: non-uniform mixing time within a single 2D run

The practical realization of rotor-synchronized mixing-times in 2D-MAS exchange experiments without the need for a special hardware is reviewed; its consequence for the ‘true mixing time' of the experiment is discussed. We demonstrate influences on experimental rate constants derived from such experiments as well as on the appearance of the 2D-MAS spectra, taken at short mixing times.     

Finite element formulation of thermal boundary layers

In this article we discuss the finite element discretization of the two-dimensional, incompressible, and turbulent boundary layers. The formulation of the momentum equation is essentially due to Baker and Soliman [1] with some modifications.The versatility and the accuracy of the method is established by considering several test cases. The predictions are satisfactory and compare favorably with alternative numerical techniques.