Transition from random to ordered fractals in fragmentation of particles in an open system

Details Transition from random to ordered fractals in fragmentation of particles in an open system Transition from random to ordered fractals in fragmentation of particles in an open system

2001-06-21

arxiv.org/abs/cond-mat/0106443v1

Phys. Rev. E 64, 016119 (2001)

Physics

Condensed Matter

Statistical Mechanics

5 pages, latex, No figure

Scientific paper

10.1103/PhysRevE.64.016119

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 $\psi(x,t)$, where $z$ is the kinetic exponent. We obtained conditions for which the scaling and fragmentation process altogether break down and 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 completely ceases.

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