Journal of Nonlinear Science

, Volume 19, Issue 3, pp 267–300 | Cite as

A Variational Theory for Point Defects in Patterns

  • N. M. ErcolaniEmail author
  • S. C. Venkataramani


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.


Patterns Defects Calculus of variations 

Mathematics Subject Classification (2000)

35J35 35J60 41A60 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Dept. of Math.Univ. of ArizonaTucsonUSA

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