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摘要: 本文利用量纲分析的方法，对分形中周长-面积关系与一般分形曲线的长度公式的量纲进行了分析；给出了普通标度理论与分形中标度变换间的定量关系。我们给出了描述随机耗散系统中分形的一种数学理论与分形结构上的输运过程，并讨论了某些预言性的结果，有待实验上加以证明。Abstract: In this paper, the relation of perimeter-are and the length formula of ordinary fractal curve in fractal are considered by the method of the dimensional analysis; the quantitative relation between the ordinary scaling transformation and scaling transformation in fractal is established. Finally, we give F-P equation of fractional Brownian moton.
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Mandelbrot B B. The Fractal Geometry of Nature. W H Freemann. San Fransico, 1983. Mu Z Q, Lung C W. J Phys D, 1983, 21: 848. Xie H P. Chinese Science Bulletion, 1989, 34: 1292. 穆在勤, 龙期威. 材料科学进展, 1989, 3(2): 110. Feder J. Fractal Plenum Press. New York and London, 1988: 201. Feder J. Fractal Plenum Press. New York and London, 1988: 177. Aharony A. Scaling Phenomena in Disordered System. Ed by R Pynn, A Skjeltop. New York and London: Plenum Publishing Corporation, 1985: 289. -
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