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多标度分形理论及进展 被引量:33

THE CURRENT STATUS OF MULTIFRACTAL APPROACH
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摘要 一个分形体的几何特征通常需要用一个多标度分形谱来描述。多标度分形理论建立了分形体的局域标度特性与分形体总体特性的关系。它的物理思想与热力学是类似的。如果已知一个分形体的多标度分形谱,还可以反过来推断其动力学特性。这方面的进展使我们加深了对扩散限制的凝聚过程、完全发达的湍流现象、通向浑纯的若干途径、无序系统等等问题的认识。本文是对上述问题的一篇较为简要的综述。 The geometrical features of a fractal object can mostly be characterized by multifractal approach. Multifractal approach relates the local scaling properties of a fractal to its global geometrical properties, and reveals the particular characters in a dynamical time-ordered process. Its physical ideas are similar to thermodynamics. The dynamical properties of a system, however, can also be retrieved by mapping or wavelet transformation. The progress of the multifractal approach lets us have a deeper knowledge of the diffusion-limited aggregation, intermittency in fully developed turbulence, the routes to chaos, disordered systems etc. The paper is a brief review of the current status of multifractal approach with the above mentioned issues detailed.
出处 《物理学进展》 CSCD 北大核心 1991年第3期269-330,共62页 Progress In Physics
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