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 AstePhysical Review Letters 2008).

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(Email: gdelaney "AT" gmail "DOT" com)