Speaker: 徐劼副研究员

Inviter: 中国科学院数学院学术报告会组委

Title: Quasi-entropy

Language: Chinese

Time & Venue: 2025.03.14 10:40-11:20 数学院南楼N204（数学院交流报告会）

Abstract: Liquid crystals are featured by local anisotropy usually described by angular moment tensors. When the molecule is non-axisymmetric, the free energy and dynamics both involve the maximum entropy state that is too complicated for computation and analysis. The price paid by the complexity does not match the outcome in revealing the physical characteristics and mathematical structures.

The speaker proposes 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. We discuss further applications in modeling and computation, including the derivation of biaxial frame hydrodynamics and physical range preserving numerical schemes.

We would also like to put forward several mathematical problems arising in the models, not limited to the following aspects: 1) The domain of quasi-entropy; 2) The classification of stationary points of the bulk energy (which is now certain elementary function but turns out to be nontrivial); 3) The analysis of hydrodynamics.