On global minimizers for a variational problem with long-range interactions
Author:
Rustum Choksi
Journal:
Quart. Appl. Math. 70 (2012), 517-537
MSC (2010):
Primary 49S05; Secondary 49M30, 35K30, 35K55, 74N15
DOI:
https://doi.org/10.1090/S0033-569X-2012-01316-9
Published electronically:
May 24, 2012
MathSciNet review:
2986133
Full-text PDF Free Access
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Additional Information
Abstract: Energy-driven pattern formation induced by competing short and long-range interactions is common in many physical systems. In these proceedings we report on certain rigorous asymptotic results concerning global minimizers of a nonlocal perturbation to the well-known Ginzburg-Landau/Cahn-Hilliard free energy. We also discuss two hybrid numerical methods for accessing the ground states of these functionals.
References
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References
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- Ren, X. and Wei, J.: Wriggled Lamellar Solutions and their Stability in the Diblock Copolymer Problem. SIAM J. Math. Anal. 37-2, 455–489 (2005). MR 2176111 (2006m:35112)
- Ren, X. and Wei, J.: Droplet solutions in the diblock copolymer problem with skewed monomer composition. Calc. Var. Partial Differential Equations. 25-3, 333–359 (2006). MR 2201676 (2007b:82107)
- Ren, X. and Wei, J.: Existence and Stability of Spherically Layered Solutions of the Diblock Copolymer Equation. SIAM J. Appl. Math. 66-3, 1080–1099 (2006). MR 2216732 (2007a:34088)
- Ren, X. and Wei, J.: Single droplet pattern in the cylindrical phase of diblock copolymer morphology, Journal of Nonlinear Science, Vol. 17, No. 5, 471–503 (2007). MR 2361417 (2008i:82154)
- Ren, X. and Wei, J.: Spherical Solutions to a Nonlocal Free Boundary Problem From Diblock Copolymer Morphology. SIAM J. Math. Anal. 39-5, 1497–1535 (2008). MR 2377287 (2009d:82168)
- Ren, X. and Wei, J.: A toroidal tube solution to a problem involving mean curvature and Newtonian potential, Interfaces and Free Boundaries, Vol. 13, No. 1, 127-154 (2011), MR 2793855
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Additional Information
Rustum Choksi
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Canada
MR Author ID:
604242
Email:
rchoksi@math.mcgill.ca
Keywords:
Global minimizers,
long-range interactions,
diblock copolymers
Received by editor(s):
January 15, 2012
Published electronically:
May 24, 2012
Dedicated:
Dedicated to Constantine M. Dafermos on the occasion of his 70th birthday
Article copyright:
© Copyright 2012
Brown University
The copyright for this article reverts to public domain 28 years after publication.