I have two questions. I am writing two monte carlo models that randomly propagate a square area and a cubic volume with mono sized hard disks and hard spheres. In the model the only criteria is that the disks or spheres can not overlap, but they can touch (however, they are not required to touch each other). This scenario is not close packed and technically it is not loosely packed either since there is no requirement that the disks and spheres touch; however, I do not know the name for this situation. Does anyone know the technical name for this scenario and also if there is any literature describing the packing fractions calculated for this scenario? I am coming up with 52.46% with a standard deviation of 4.32% for disks and 33.82% with a standard deviation of 3.19 for spheres. This is substantially below loose packed, so I know it must be a different scenario and someone else has to have made this same calculation before.

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    $\begingroup$ The top-rated answer to this question (mathoverflow.net/questions/63087/…) says it's called Random Sequential Addition (or Adsorption), and gives links to related literature. $\endgroup$ – mjqxxxx Aug 30 '13 at 5:37
  • $\begingroup$ Thanks, that looks like exactly what I was looking for! $\endgroup$ – Jon Aug 30 '13 at 13:47

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