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A Fast O(N2) Fragmentation Algorithm

  • Authors: Roman R. Rafikov, Kedron Silsbee, and Richard A. Booth

2020 The Astrophysical Journal Supplement Series 247 65.

  • Provider: AAS Journals

Caption: Figure 4.

Mass spectrum (multiplied by m2 to provide a proxy for a cumulative mass distribution in the system) at four different times indicated on the panels, expressed in units of collisional timescale for the initial mass bin. We use ﹩\tilde{m}﹩ and ﹩\tilde{N}﹩ for m and N, normalized by the initial mass (m = 1) and initial number of objects in the system. Different-colored curves correspond to different numbers of bins in the simulation, labeled in panel (a). Solid lines correspond to the curves from the ﹩{ \mathcal O }\left({N}^{2}\right)﹩ algorithm, and dotted lines to those from the ﹩{ \mathcal O }\left({N}^{3}\right)﹩ algorithm. In the bottom right panel, we show in black the line of slope 1/6 (consistent with Dohnanyi 1969), which provides a good overall fit to the fragment distribution. The superimposed wavy structure is discussed in the text.

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