2002/06/30 by Mark J. Bowick, Mark Bowick, Angelo Cacciuto +2 · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Classical mechanics #Condensed matter physics #Disclination #Ground state #Lattice (music) #Liquid crystal #Mathematical Approximation and Integration #Microstructure and mechanical properties #Physics #Quantum mechanics #Theoretical and Computational Physics #Theoretical physics #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.89.185502
published as Phys.Rev.Lett.89:185502,2002 · 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixed
openalex publication_date 2002/10/10 · arxiv created 2002/10/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy E(core) of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0<gamma<2) to four significant figures. The generality of our approach is illustrated by a study of grain boundary proliferation for tilted crystalline order and square lattices on the sphere.