From microscopic theory to macroscopic theory: a systematic study on static modeling for liquid crystals

Abstract

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.

47 pages, 9 figures

References in corpus (2)

• Elastic constants of nematic liquid crystals of uniaxial symmetry
• From microscopic theory to macroscopic theory: symmetries and order parameters of rigid molecules

Cited by in corpus (17)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• Mathematics and liquid crystals
• Analytical structure, dynamics, and coarse-graining of a kinetic model of an active fluid
• OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle
• Phase transitions and macroscopic limits in a BGK model of body-attitude coordination
• Nonstationary models for liquid crystals: A fresh mathematical perspective
• Global solution to the three-dimensional liquid crystal flows of Q-tensor model
• A fast Chebyshev method for the Bingham closure with application to active nematic suspensions
• Solution Landscapes of the Simplified Ericksen--Leslie Model and its Comparison with the Reduced Landau--de Gennes Model
• A Fast Algorithm for the Moments of Bingham Distribution
• Classifying local anisotropy formed by rigid molecules: symmetries and tensors
• Quasi-entropy by log-determinant covariance matrix and application to liquid crystals
• The Oseen-Frank limit of Onsager's molecular theory for liquid crystals
• $\Gamma$-convergence of a mean-field model of a chiral doped nematic liquid crystal to the Oseen-Frank description of cholesterics
• A multiscale approach to liquid crystal nematics via statistical field theory
• Global Well-posedness of the Two Dimensional Beris-Edwards System with General Laudau-de Gennes Free Energy
• Scratching a 50-year itch with elongated rods