摘要：

Liquid crystals are featured by local anisotropy usually described by angular moment tensors. The free energy of tensors needs a stabilizing entropy term. When non-axisymmetric molecules are involved, two classical approaches to write down an entropy term, quartic polynomial and maximum entropy state, both become too complicated. Meanwhile, the maximum entropy state, particularly in cases of non-axisymmetric molecules, seems the only reasonable way of closure approximation in dynamics, but it would make the model not computable.

We propose an elementary-function substitution of the original entropy (by maximum entropy state), called quasi-entropy, aiming to resolve the above problems. The quasi-entropy maintains the essential properties of the original entropy: strict convexity; positive-definiteness of covariance matrix; rotational invariance; consistency in symmetry reduction. Homogeneous phase diagrams of several representative cases match well with classical results. A further application is deriving biaxial frame hydrodynamics from tensor model. Numerical schemes keeping physical constraints can also be constructed naturally using the properties of the quasi-entropy.

简介：

徐劼博士于2010年和2015年在北京大学分别获学士和博士学位，后在普渡大学从事博士后研究，现任职于中国科学院数学与系统科学研究院计算数学与科学工程计算研究所。徐劼博士在液晶建模与模拟、梯度流的数值方法方面取得了突出的研究成果，代表工作包括：针对复杂液晶分子发展了基于分子理论的系统建模方法；独立提出了拟熵使模型可计算化；提出了梯度流的标量辅助变量方法。获2024 ICCM Distinguished Paper Award 和 International Congress of Basic Science 2025 Frontiers of Science Award。