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    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/81001


    Title: THE COLLISIONAL DYNAMICS OF PARTICULATE DISKS
    Authors: SHU, F.H.;STEWART, G.R.
    教師: 徐遐生
    Date: 1985
    Publisher: Elsevier
    Relation: ICARUS, Elsevier, Volume 62, Issue 3, 1985, Pages 360-383
    Keywords: PARTICULATE DISKS
    Abstract: We use a Krook equation, modified to allow collisions to be inelastic, to describe the dynamics of a particulate disk. By a simple heuristic argument, we compute the effective collision rate in a disk of spherical particles with a power-law distribution of sizes. For Saturn's rings, the effective collision rate for momentum transport is substantially lower than that conventionally estimated on the basis of an observed optical depth at visual wavelengths. We then discuss how the vertically integrated set of moment equations may be closed without the need to discard the third-order moments at the outset; our formulation allows for the possibility of a bent disk. In the limit that the collision frequency is much larger than the orbit frequency, we recover the usual Navier-Stokes equations of viscous hydrodynamics for a thin disk, with an explicit expression for the shear viscosity. For an unperturbed disk, we can solve the krook equation directly, without any assumptions about the magnitude of the collision frequency. Our analytical results, for an unperturbed disk, are in good agreement with the treatments of Hämeen-Anttila, of Goldreich and Tremaine, and of Borderies, Goldreich, and Tremaine, using a Boltzmann description for a collection of identical spheres (assumed to be smooth so that the rotational and translational degrees of freedom do not couple). As a final application of the method, we generalize the formation to include the effects of gravitational scattering. This generalization is not crucial for many applications in planetary rings, but it may be important for the discussion of gas clouds in the disk of a spiral galaxy, and it is probably central to the accumulation of planets from smaller bodies in the primitive solar nebula.
    Relation Link: http://www.elsevier.com/wps/find/homepage.cws_home
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/81001
    Appears in Collections:[ 徐遐生 (2002-2006)] 期刊論文
    [物理系] 期刊論文

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