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SUMMARY:Exploring analogies between bubble clusters and particle clusters 
 - Flikkema\, E (Aberystwyth University)
DTSTART:20140227T143500Z
DTEND:20140227T145500Z
UID:TALK51129@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Simon Cox (Aberystwyth University) \n\nThis present
 ation is about the minimal perimeter problem for two-dimensional clusters 
 of equal-area bubbles. The challenge is to find the global minimum of the 
 perimeter with respect to different bubble cluster topologies with a fixed
  number of bubbles N (up to N=42). The free bubble cluster is being consid
 ered\, as well as bubble clusters confined to a circle or to various polyg
 onal shapes. \n\nIn this project\, an analogy between the above-mentioned 
 bubble cluster problem and the problem of the energetic optimisation of cl
 usters of interacting particles is explored. For clusters of atoms\, findi
 ng the global minimum of the energy with respect to the positions of the a
 toms is important\, as it is thermodynamically most likely to be formed. M
 any global optimisation methods have been developed for this problem. \n\n
 More specifically\, in this project\, two dimensional clusters of particle
 s are considered\, interacting via a repulsive pair-wise potential\, combi
 ned with a confining external field. \n\nThe central idea is to use a part
 icle cluster geometry to generate a bubble cluster topology. The procedure
  consists of the construction of Voronoi cells on the basis of the particl
 e positions. A local optimisation of the perimeter is then carried out usi
 ng Surface Evolver. In this way\, minima of the particle cluster problem a
 re used to generate candidates for the global minimal perimeter problem fo
 r two dimensional bubble clusters. Various pair-wise potentials have been 
 tried in combination with different confining potentials (depending on whe
 ther the bubble cluster is free or confined to a circle or polygon). \n\nT
 he success of this procedure in generating good candidates for the global 
 minima of the bubble cluster problem was monitored. The various pair poten
 tials have various success rates. Since the different potentials succeed o
 r fail in different circumstances\, the use of multiple potentials is reco
 mmended.\n
LOCATION:Seminar Room 1\, Newton Institute
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