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From Microscopic Theory to Macroscopic Theory: a Systematic Study on Modeling for Liquid Crystals

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Abstract

In this paper, we propose a systematic way of liquid crystal modeling to build connections between microscopic theory and macroscopic theory. In the first part, we propose a new Q-tensor model based on Onsager’s molecular theory for liquid crystals. The Oseen–Frank theory can be recovered from the derived Q-tensor theory by making a uniaxial assumption, and the coefficients in the Oseen–Frank model can be examined. In addition, the smectic-A phase can be characterized by the derived macroscopic model. In the second part, we derive a new dynamic Q-tensor model from Doi’s kinetic theory by the Bingham closure, which obeys the energy dissipation law. Moreover, the Ericksen–Leslie system can also be derived from new Q-tensor system by making an expansion near the local equilibrium.

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Authors and Affiliations

  1. School of Mathematical Sciences and LMAM, Peking University, Beijing, China

    Jiequn Han, Yi Luo, Pingwen Zhang & Zhifei Zhang

  2. Beijing International Center for Mathematical Research, Peking University, Beijing, China

    Wei Wang

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  1. Jiequn Han
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  2. Yi Luo
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  3. Wei Wang
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  4. Pingwen Zhang
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Correspondence to Pingwen Zhang.

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Han, J., Luo, Y., Wang, W. et al. From Microscopic Theory to Macroscopic Theory: a Systematic Study on Modeling for Liquid Crystals. Arch Rational Mech Anal 215, 741–809 (2015). https://doi.org/10.1007/s00205-014-0792-3

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  • DOI: https://doi.org/10.1007/s00205-014-0792-3

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