Crystalline Order on a Sphere and the Generalized Thomson Problem
Soft Condensed Matter
2009-03-24 v3
Abstract
We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.
Cite
@article{arxiv.cond-mat/0206144,
title = {Crystalline Order on a Sphere and the Generalized Thomson Problem},
author = {Mark Bowick and Angelo Cacciuto and David R. Nelson and Alex Travesset},
journal= {arXiv preprint arXiv:cond-mat/0206144},
year = {2009}
}
Comments
4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixed