Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2000-07-14
Fractals, Vol. 9, No. 3 (2001) 317-328
Nonlinear Sciences
Adaptation and Self-Organizing Systems
Final version, PDF
Scientific paper
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically. In these two illustrations branching emerges in the curve of generalized dimensions, and more abnormally, negative values of generalized dimensions arise. Therefore, we classify the random multifractal measures into three classes based on the discrepancy between the curves of generalized dimensions. Other equivalent classifications are also presented.... We apply the cascade processes studied in this paper to characterize two stochastic processes, i.e., the energy dissipation field in fully developed turbulence and the droplet breakup in atomization. The agreement between the proposed model and the experiments are remarkable.
Liu Hai-Feng
Yu Zun-Hong
Zhou Wei-Xing
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