A variational theory for point defects in patterns
arXiv:0706.2917 · doi:10.1007/s00332-008-9035-9
Abstract
We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.
26 pages, 5 figures, submitted to the Journal of Nonlinear Science