On the spectra of three-dimensional lamellar solutions of the diblock copolymer problem
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AbstractOne-dimensional free energy local minimizers are viewed as three-dimensional lamellar-type critical points in a box. To determine whether they model the lamellar phase of diblock copolymers in the strong segregation region, we analyze their spectra. We obtain the asymptotic expansions of their eigenvalues and eigenfunctions. Consequently we find that they are stable, i.e., are local minimizers in space, only if they have sufficiently many interfaces. Interestingly the one-dimensional global minimizer is near the borderline of three-dimensional stability.
All Author(s) ListRen XF, Wei JC
Journal nameSIAM Journal on Mathematical Analysis
Volume Number35
Issue Number1
Pages1 - 32
LanguagesEnglish-United Kingdom
Keywordsdiblock copolymer; lamellar solution; spectrum; three-dimensional stability
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2020-26-10 at 23:22