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Relation Between Grain Shape and Fractal Properties in Random Apollonian Packing with Grain Rotation
 

Summary: Relation Between Grain Shape and Fractal Properties in Random Apollonian Packing
with Grain Rotation
Gary W. Delaney,1,2
Stefan Hutzler,2
and Tomaso Aste1
1
Department of Applied Mathematics, Australian National University, Canberra, Australia
2
School of Physics, Trinity College Dublin, Ireland
(Received 9 December 2007; revised manuscript received 11 April 2008; published 16 September 2008)
We extend the common theme of random Apollonian packing of circles to consider orientable grains
with a noncircular shape. Systems of up to 106
grains are examined for a range of polygonal and elliptical
shapes using both the random Apollonian packing model and the new rotational random Apollonian
packing model which takes into account the extra rotational degree of freedom of noncircular grains. We
identify the constraining length Dc that limits growth of the grain during the packing process and find that
a universal relation exists between grain shape and the scaling properties of the system.
DOI: 10.1103/PhysRevLett.101.120602 PACS numbers: 05.10.a, 45.70.n, 61.43.Bn, 81.10.Aj
Scientists have long considered space filling problems in
which nonoverlapping units of smaller and smaller sizes

  

Source: Aste, Tomaso - Department of Applied Mathematics, Australian National University

 

Collections: Physics