Formation of a New Class of Random Fractals in Fragmentation with Mass Loss

Details Formation of a New Class of Random Fractals in Fragmentation with Mass Loss Formation of a New Class of Random Fractals in Fragmentation with Mass Loss

2000-03-31

arxiv.org/abs/cond-mat/0003501v3

Physics

Condensed Matter

Statistical Mechanics

5 pages, Latex, no Figures, bibliography updated and minor corrections to text in this version

Scientific paper

We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact numerical values are given for which $x^{-\theta}$ or $t^{\theta z}$ has the dimension of particle size distribution function c(x,t) where z is the kinetic exponent. We also give explicit scaling solution for special case. Finally, we identify a new class of fractals ranging from random to non-random and show that the fractal dimension increases with increasing order and a transition to strictly self-similar pattern occurs when randomness is completely seized.

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