Physics
Scientific paper
Oct 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996icar..123..450t&link_type=abstract
Icarus, Volume 123, Issue 2, pp. 450-455.
Physics
65
Scientific paper
Dohnanyi (1969, J. Geophys. Res. 74, 2531-2554) analytically obtained the steady-state mass distribution of the collisional fragmentation cascade as n(m) = Am^-alpha, where the power law exponent alpha is very nearly 11/6. In the present study, we investigated the generality of Dohnanyi's result of alpha = 11/6 and clarified what essentially determines the value of the exponent alpha. We first derived new basic equations describing the evolution of the mass distribution in the collision cascade. The new basic equations are independent of the model of collisional outcomes and, hence, enable us to investigate the general properties of the collision cascade. As the steady-state solution to the derived basic equations, we obtained a power law mass distribution under the single assumption that the collisional outcome is self-similar. The results are summarized as follows: the power law exponent alpha of the mass distribution is exactly independent of the collisional outcome model as long as the model is self-similar and the value of alpha is directly determined only by the mass-dependence of the collision rate.
Inaba Satoshi
Nakazawa Kiyoshi
Tanaka Hidekazu
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