不等概率分形破碎及有限尺度破碎体分形

FRACTAL FRAGMENTATION WITH UNEQUAL PROBABILITY AND THE FRACTAL OF FRAGMENTS IN ALIMITED SCALE

本文讨论了破碎体两种分形分布的一致性，有限尺度破碎体分形的几个特征及不等概率分形破碎等问题。证明，尺度范围足够宽时，两种分形是互为近似的，且其粒级可以是更大尺度范围内的任一段；尺度范围不变时，分形维数不仅反映粒度分布，还决定粒组的粗细；一般情况下，满足分形分布的破碎不一定是等概率的破碎．Ｄ＞３时，必然是有限破碎。Ｄ＜３时，也可能是破碎有限的，决定于初始破碎后的坚固单元与易碎单元的数量分配。最后给出了某些情况下推断实际分形破碎过程的方法。

This paper gives a discussion about the uniformity between two kinds of the fragments fractal,somefeature of the fractals in a limited scale,and the fractal fragmentation with unequal probabitily.It gives ademenstration of the following points.When the scale scope is wide enough,the two fractals are approximate,and the grading of the fractals can be any section of that in a larger scale scope;if the scale scope re-mains consistent,the fractal dimensio n not only reflects the particle distribution,but also desides thefineness of grading;in ordinary circumstances,the fragmentation which meet the requirements of fractaldistribution are not definitely with equal probability,if D>3,the fragmentation must be limited,and mayalso be if D<3,but this depends on the amount allotment between the sound and fragile elements after theinitial fragmentation.In the end,this paper suggests the method to infer the actual fractal fragmentation process in some cases.