Apollonian Packing (AP)
Apollonian packing has a long history dating back to Apollonius of
Perga (ca. 200B.C). This packing is formed by placing a circular disc
in the space between three mutually touching discs so that it just
touches the other three.
The procedure is then continually repeated, filling the new gaps
generated by the addition of each new disc.
Random Apollonian Packing
(RAP)
We have studied modern variations on this theme, in which
grains are
sequentially placed at random positions in the pore space (Random
Apollonian Packing). We demonstrate the strong dependence of the
packing efficiency on the grain shape and observe that universal
relations exist between the
grain shape and the fractal properties of the system.
Rotational Random
Apollonian Packing (RRAP)
We have introduced the new Rotational Random Apollonian
Packing (RRAP) model, in which the grains are allowed to rotate during
the
packing process. This additional degree of freedom allows the grains to
pack more densely. An animation can be viewed here.
The
relationship between the packing efficiency and the grain shape in both
the RAP and RRAP models can be understood by identifying the key
constraining length that limits the growth of grain during the packing
process.
Details of this work can be found in our paper:"Relation
Between Grain Shape and Fractal Properties in Random Apollonian Packing
with Grain Rotation" (GW Delaney, S Hutzler and T Aste, Physical Review Letters 2008).
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(Email: gdelaney "AT" gmail "DOT" com)
