%0 Journal Article
%T From microscopic theory to macroscopic theory: a systematic study on static modeling for liquid crystals
%A Jiequn Han
%A Yi Luo
%A Wei Wang
%A Pingwen Zhang
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00205-014-0792-3
%X In this paper, we propose a systematic way of liquid crystal modeling to build connection between microscopic theory and macroscopic theory. A new Q-tensor theory based on Onsager's molecular theory which leads to liquid crystals with certain shape has been proposed. Making uniaxial assumption, we can recover the Oseen-Frank theory from the derived $Q$-tensor theory, and the Oseen-Frank model coefficients can be examined. In addition, the smectic-A phase can also be characterized by the derived macroscopic model.
%U http://arxiv.org/abs/1305.4889v1