Eur. Phys. J. E 7, 123-127 (2002)
DOI: 10.1140/epje/i200101168
Uniqueness, stability and Hessian eigenvalues for two-dimensional bubble clusters
D. Weaire1, S.J. Cox1 and F. Graner21 Department of Physics, Trinity College, Dublin 2, Ireland
2 Laboratoire de Spectrométrie Physique, Boîte Postale 87, F-38402 St. Martin d'Hères Cedex, France
simon.cox@tcd.ie
(Received 8 November 2001)
Abstract
A recent conjecture on two-dimensional foams suggested that
for fixed topology with given bubble areas there is a unique state of
stable equilibrium. We present counter-examples, consisting of a ring
of bubbles around a central one, which refute this conjecture. The
discussion centres on a novel form of instability which causes
symmetric clusters to become distorted. The stability of these bubble
clusters is examined in terms of the Hessian of the energy.
82.70.Rr - Aerosols and foams.
46.32.+x - Static buckling and instability.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002
