Catastrophic fragmentation as a stochastic process: sizes and shapes of fragments |
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| Authors: | A La Spina P Paolicchi |
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| Institution: | Dipartimento di Fisica, Università di Pisa, Piazza Torricelli 2, I-56127, Pisa, Italy |
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| Abstract: | It is rather difficult to understand theoretically and to analyse the experimental data concerning the mass and shape distributions of fragments created by catastrophic collisions. The fragmentation process is discussed as being a purely stochastical phenomenon; the size and shape distributions obtained in this way are compared with the results of laboratory experiments. The results are presented of some computer simulations of random volume fragmentation processes; they are a 3-D generalization of the numerical experiments described in Grady and Kipp (J. Appl. Phys. 58(3), 1210–1222, 1985). The features of the size distribution are discussed, comparing it with the expectations of the Mott-Linfoot and Grady-Kipp theories. In the literature the shape of fragments is defined in terms of the ratios B/A and C/A, where A, B, C are defined as the sizes of a fragment along three orthogonal axes. The definition of the shape of a fragment cannot be considered unique, since it is not obvious in which order to define the three axes when the fragments are not ellipsoidal. A few possible methods are introduced explicity, and the resulting differences are discussed. In this light, the shape results (the mean values and the distribution of the axial ratios) obtained in recent laboratory experiments are rediscussed and critically reviewed. For what concerns the stochastical modelling, the results of various simulations, corresponding to different assumptions regarding fragmentation properties are presented. It is shown that the main features of the shape distributions from laboratory experiments cannot be satisfactorily reproduced. Comparison of the results with the outcomes of the semiempirical fragmentation model by Paolicchi et al. (Icarus 121, 126–157, 1996), as well as with some results coming out from hydrodynamical simulations, shows how only a “global” and physical model, not a purely statistical one (neither global nor “local”), can afford to reproduce the observed data. |
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