Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.
Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.
Institute of Ionosphere, National Center of Space Research and Technology, 050020 Almaty, Kazakhstan.
V L
VL
Saveliev
M A
MA
Gorokhovski
D001703:Biophysics / Q000379:methods*; D004247:DNA / Q000737:chemistry*; D053938:DNA Fragmentation; D016014:Linear Models; D009038:Motion; D010316:Particle Size; D011108:Polymers / Q000737:chemistry; D011336:Probability; D013997:Time Factors
D011108:Polymers; D004247:DNA