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

2000/03/31 by M. K. Hassan, Hassan, M. K.
Environmental Science · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Landslides and related hazards #Pattern Formation and Solitons (nlin.PS) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.cond-mat/0003501

openalex publication_date 2000/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 θ, whose exact numerical values are given for which x^-θ or t^θz 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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• Fractals, Multifractals and the Science of Complexity
• Multifractal spectra and precise rates of decay in homogeneous fragmentation
• Scale invariance and lack of self-averaging in fragmentation
• Asymptotic laws for nonconservative self-similar fragmentations
• Profile of a self-similar growth-fragmentation