A variational theory for point defects in patterns

Details A variational theory for point defects in patterns A variational theory for point defects in patterns

2007-06-20

arxiv.org/abs/0706.2917v1

Mathematics

Analysis of PDEs

26 pages, 5 figures, submitted to the Journal of Nonlinear Science

Scientific paper

10.1007/s00332-008-9035-9

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.

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