BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Packing problems\, phyllotaxis and Fibonacci numbers - Adil Mughal
  (Aberystwyth University)\; Denis Weaire (Trinity College Dublin)
DTSTART:20170920T084000Z
DTEND:20170920T092000Z
UID:TALK80271@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We study the optimal packing of hard spheres in an infinitely 
 long cylinder. Our simulations have yielded dozens of periodic\, mechanica
 lly stable\, structures as the ratio of the cylinder (D) to sphere (d) dia
 meter is varied [1\, 2\, 3\, 4]. Up to D/d=2.715 the densest structures ar
 e composed entirely of spheres which are in contact with the cylinder. The
  density reaches a maximum at discrete values of D/d when a maximum number
  of contacts are established. These maximal contact packings are of the cl
 assic "phyllotactic" type\, familiar in biology. However\, between these p
 oints we observe another type of packing\, termed line-slip. We review som
 e relevant experiments with small bubbles and show that such line-slip arr
 angements can also be found in soft sphere packings under pressure. This a
 llows us to compute the phase diagram of columnar structures of soft spher
 es under pressure\, of which the main feature is the appearance and disapp
 earance of line slips\, the shearing of adjacent spirals\, as pressure is 
 increased [5].<br><span><br>We provide an analytical understanding of thes
 e helical structures by recourse to a yet simpler problem: the packing of 
 disks on a cylinder [1\, 2\, 4]. We show that maximal contact packings cor
 respond to the perfect wrapping of a honeycomb arrangement of disks around
  a cylindrical tube. While line-slip packings are inhomogeneous deformatio
 ns of the honeycomb lattice modified to wrap around the cylinder (and have
  fewer contacts per sphere). Finally\, we note that such disk packings are
  of relevance to the spiral arrangements found in stems and flowers\, when
  labelled in a natural way\, which are generally represented by some tripl
 et of successive numbers from the Fibonacci series (1\,1\,2\,3\,5\,8\,13..
 .). This has been an object of wonder for more than a century. We review s
 ome of this history and offer yet another straw in the wind to the never-e
 nding debate [6].</span>
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR