Archive for Rational Mechanics and Analysis

, Volume 215, Issue 3, pp 741–809 | Cite as

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

  • Jiequn Han
  • Yi Luo
  • Wei Wang
  • Pingwen ZhangEmail author
  • Zhifei Zhang


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.


Liquid Crystal Nematic Liquid Crystal Nematic Phase Microscopic Theory Tensor Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jiequn Han
    • 1
  • Yi Luo
    • 1
  • Wei Wang
    • 2
  • Pingwen Zhang
    • 1
    Email author
  • Zhifei Zhang
    • 1
  1. 1.School of Mathematical Sciences and LMAMPeking UniversityBeijingChina
  2. 2.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina

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