TY - JOUR
T1 - Minimal perimeter for N identical bubbles in two dimensions
T2 - Calculations and simulations
AU - Cox, S. J.
AU - Graner, F.
AU - Vaz, M. Fátima
AU - Monnereau-Pittet, C.
AU - Pittet, N.
N1 - Funding Information:
ACKNOWLEDGEMENTS We wish to thank Klaus Kassner for his suggestion concerning cluster classification, Manuel Fortes and Renaud Delannay for critically reading the manuscript, Frank Morgan for his patient explanation of energy bounds and Marie-Line Chabanol, Marc Hindry, and Denis Weaire for interesting discussions. F.G. thanks Trinity College, Dublin, and Instituto Superior Técnico, and F.V. thanks Trinity College, Dublin and Laboratoire de Spectrométrie Physique, for their hospitality. N.P. was supported by Enterprise Ireland, C.M.-P. and S.J.C. were supported by Marie Curie fellowships, and F.G. benefited from the ULYSSES France–Ireland exchange programme.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2003/4/11
Y1 - 2003/4/11
N2 - The minimal perimeter enclosing N planar regions, each being simply connected and of the same area, is an open problem, solved only for a few values of N. The problems of how to construct the configuration with the smallest possible perimeter E(N) and how to estimate the value of E(N) are considered. Defect-free configurations are classified and we start with the naïve approximation that the configuration is close to a circular portion of a honeycomb lattice. Numerical simulations and analysis that show excellent agreement to within one free parameter are presented; this significantly extends the range of values of N for which good candidates for the minimal perimeter have been found. We provide some intuitive insight into this problem in the hope that it will help the improvement in future numerical simulations and the derivation of exact results.
AB - The minimal perimeter enclosing N planar regions, each being simply connected and of the same area, is an open problem, solved only for a few values of N. The problems of how to construct the configuration with the smallest possible perimeter E(N) and how to estimate the value of E(N) are considered. Defect-free configurations are classified and we start with the naïve approximation that the configuration is close to a circular portion of a honeycomb lattice. Numerical simulations and analysis that show excellent agreement to within one free parameter are presented; this significantly extends the range of values of N for which good candidates for the minimal perimeter have been found. We provide some intuitive insight into this problem in the hope that it will help the improvement in future numerical simulations and the derivation of exact results.
UR - http://www.scopus.com/inward/record.url?scp=0242334665&partnerID=8YFLogxK
U2 - 10.1080/1478643031000077351
DO - 10.1080/1478643031000077351
M3 - Article
AN - SCOPUS:0242334665
SN - 1478-6435
VL - 83
SP - 1393
EP - 1406
JO - Philosophical Magazine
JF - Philosophical Magazine
IS - 11
ER -