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• W3099061547 abstract "We study the relationship between Onsager’s molecular theory, which involves the effects of nonlocal molecular interactions and the Oseen–Frank theory for nematic liquid crystals. Under the molecular setting, we prove the existence of global minimizers for the generalized Onsager’s free energy, subject to a nonlocal boundary condition which prescribes the second moment of the number density function near the boundary. Moreover, when the re-scaled interaction distance tends to zero, the global minimizers will converge to a uniaxial distribution predicted by a minimizing harmonic map. This is achieved through the investigations of the compactness property and the boundary behaviors of the corresponding second moments. A similar result is established for critical points of the free energy that fulfill a natural energy bound." @default.
• W3099061547 created "2020-11-23" @default.
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• W3099061547 date "2017-11-08" @default.
• W3099061547 modified "2023-09-23" @default.
• W3099061547 title "The Oseen–Frank Limit of Onsager’s Molecular Theory for Liquid Crystals" @default.
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• W3099061547 doi "https://doi.org/10.1007/s00205-017-1180-6" @default.
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