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Structures Produced by Ballistic Agglomeration: BA, BAM1, and BAM2 Geometries

Bruce T. Draine, Dept. of Astrophysical Sciences, Princeton University

Prescriptions for producing random aggregates of spheres are discussed in Shen, Draine, and Johnson (2008) (ApJ_689_260.pdf), where a simple quantitative measure of "porosity" P is also presented.

"BA" aggregates are the result of simple "ballistic agglomeration", where projectiles approach on random, rectilinear trajectories, and "stick" if the trajectory brings them into contact with the cluster. BA aggregates are obtained if the projectile remains at the point of first contact. BA aggregates are quite porous. If the projectiles are equal-sized spheres, the porosity varies from P = 0.658 +/- 0.053 for N=8, increasing to P=0.871 +/- 0.002 for N=65536. (The "uncertainty" here is the realization-to-realization standard deviation in the porosity.)

"BAM1" aggregates are obtained if the "growth rule" is changed so that, after first contact, the newly-arrived sphere is allowed to "migrate" to make contact with a second sphere from the cluster. BAM1 aggregates are less porous than BA aggregates. N=8 clusters have P=0.480 +/- 0.036, with the porosity increasing to P=0.796 +/- 0.002 as N is increased to N=65536.

"BAM2" aggregates are obtained when the growth rule allows newly-arrived spheres to make, when possible, a second migration to produce contact with a third sphere (while remaining in contact with the first sphere that was contacted). BAM2 aggregates are less porous than BAM1 aggregates. N=8 clusters have P=0.354 +/- 0.023, with P increasing to 0.694 +/- 0.002 as N is increased to N=65536.

Here we make available a "library" of BA, BAM1, and BAM2 clusters of equal-size sphere for N=8, 16, 32, 64, 128, 256, 512, 1024, 2048, and 4096. For N up to 1024, we provide 16 independent random realizations for each growth prescription (BA, BAM1, and BAM2). These are not selected in any way: the initial seed for the random number generator was set to 1,2,3,...,16 . For N=2048 and N=4096 we provide 8 and 4 realizations, respectively. Each ascii file gives the x,y,z locations of the center of each sphere in the cluster, in units of the monomer diameter (column 5 lists the diameter of each sphere, which in all cases here is equal to 1.0000).

Note #1: The clusters are NOT randomly-oriented. Instead, each cluster has been rotated to minimize the volume of a circumscribing rectangular "box" with axes parallel to the x,y,z axes. [This is done because one may wish to carry out calculations of light scattering and absorption using DDSCAT, which will be done more efficiently if the rectangular "computational volume" is minimized.]

Note #2: The coordinate system is centered on the first sphere in the list -- the centroid of the cluster is NOT located at (0,0,0).

We also provide images (gzipped eps) of each cluster in the library. Each target is oriented with the principal axes (a1, a2, a3) of the moment of inertia tensor oriented in fixed directions. Each image file includes the characteristic size R, porosity P, and the quantities alpha_1, alpha_2, and alpha_3 (see Shen et al 2008).

N.B.: The target files that were posted here prior to 2008.07.15 (although they were "random" and "fluffy") did not correspond to BA, BAM1, or BAM2 processes. The incorrect targets were replaced with correctly generated targets on 2008.07.15.

BA clusters of spheres (monodisperse):

  • BA Target files (ascii):

  • Images of BA Targets (encapsulated postscript, gzipped):

    BAM1 clusters of spheres (monodisperse):

  • BAM1 Target files (ascii):

  • Images of BAM1 Targets (encapsulated postscript, gzipped):

    BAM2 clusters of spheres (monodisperse):

  • BAM2 Target files (ascii):

  • Images of BAM2 Targets (encapsulated postscript, gzipped):

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