Universal elements of fragmentation

• Published in: Journal of experimental and theoretical physics Vol. 110; no. 5; pp. 863 - 876
• Main Authors: Yanovsky, V. V., Tur, A. V., Kuklina, O. V.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01-05-2010; Springer
• Subjects: Analysis; ASYMPTOTIC SOLUTIONS; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSIFICATION; DISTRIBUTION; Elementary Particles; EQUATIONS; FRAGMENTATION; KINETIC EQUATIONS; MASS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; Nonlinear; NONLINEAR PROBLEMS; Particle and Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theory; Relativity Theory; Soft Matter Physics; Solid State Physics; Statistical; SURFACES; Toy industry; Power Exponent; Fragment Size Distribution; Minimal Theory; Fragmentation Theory; Volume Flux
• ISSN: 1063-7761; 1090-6509
• DOI: 10.1134/S1063776110050183

A fragmentation theory is proposed that explains the universal asymptotic behavior of the fragment-size distribution in the large-size range, based on simple physical principles. The basic principles of the theory are the total mass conservation in a fragmentation process and a balance condition for the energy expended in increasing the surface of fragments during their breakup. A flux-based approach is used that makes it possible to supplement the basic principles and develop a minimal theory of fragmentation. Such a supplementary principle is that of decreasing fragment-volume flux with increasing energy expended in fragmentation. It is shown that the behavior of the decreasing flux is directly related to the form of a power-law fragment-size distribution. The minimal theory is used to find universal asymptotic fragment-size distributions and to develop a natural physical classification of fragmentation models. A more general, nonlinear theory of strong fragmentation is also developed. It is demonstrated that solutions to a nonlinear kinetic equation consistent with both basic principles approach a universal asymptotic size distribution. Agreement between the predicted asymptotic fragment-size distributions and experimental observations is discussed.