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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Circle packing in arbitrary domains - Paolo Amore
(Universidad de Colima)
DTSTART;TZID=Europe/London:20230823T113000
DTEND;TZID=Europe/London:20230823T120000
UID:TALK202621AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/202621
DESCRIPTION:Circle packing is a challenging computational prob
lem\, which has been studied systematically only f
or a handful of domains (the disk\, the square\, t
he rectangle\, regular polygons and few others). F
inding the global maximum of the packing fraction
becomes increasingly difficult as N (number of dis
ks) grows and proofs of \; optimality only exi
st for special domains and limited N. There is con
siderable interest\, however\, in finding good pac
kings in more general domains\, because of the mul
tiple applications of packing to different areas o
f knowledge.\nWe have devised an algorithm that\,
at least in principle\, can be used to obtain dens
ely packed configurations in arbitrary domains (we
will only discuss two dimensional examples but th
e extension to three or even higher dimension is s
traightforward)\, which include ellipses with arbi
trary eccentricity\, rectangles of different propo
rtions\, multiply connected domains (for instance
a concentric circular annulus)\, concave domains (
for example a cross of varying proportions) and ev
en domains with a singularity on the border (the c
ardioid). Numerical results for all these cases wi
ll be presented.\nOur algorithm could be applied w
ith minor modifications to study packing configura
tions in tubular containers or more general contai
ners in three dimensions of arbitrary shape.
LOCATION:External
CONTACT:
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