A Variational Theory for Point Defects in Patterns
- 143 Downloads
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.
KeywordsPatterns Defects Calculus of variations
Mathematics Subject Classification (2000)35J35 35J60 41A60
Unable to display preview. Download preview PDF.
- Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents. U.S. Government Printing Office, Washington (1964). MR MR0167642 (29 #4914) zbMATHGoogle Scholar
- Ercolani, N., Shieh, T.-T., Venkataramani, S.: Calculus of variations for disclinations in harmonic director fields. Unpublished notes (2008) Google Scholar
- Kléman, M.: Points, Lines and Walls. In Liquid Crystals, Magnetic Systems and Various Ordered Media. Wiley, New York (1983). MR MR734901 (85e:82058) Google Scholar
- Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1996). An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Reprint of the fourth (1927) edition. MR MR1424469 (97k:01072) zbMATHGoogle Scholar