Abstract
摘要 |
This talk includes two parts:
Part I: Order Parameters of Liquid Crystal. We propose a systematic molecular modeling of liquid crystals, the models can be used to depict isotropic, nematic, smectic, columnar, cholesterics and blue phases. The tensor model can be reduced from molecular model using Bingham closure and Taylor expansion, the vector model can be reduced from tensor or molecular model using axial symmetry assumption. Using Newton mechanic and virial expansion, we build a generic molecular model to describe phase behaviors of rigid molecules of arbitrary shape. We also clarify the criteria of choosing order parameters, both from theoretical aspects and from results of experiments and simulations.
Part II: Numerical Method of Quasicrystals (QCs), QCs with long-range order and non-crystallographic symmetry, is one kind of fascinatingly ordered structures between period structures (crystals) and disordered structures. There exist several difficult problems in the theoretical research on QCs: how to build mathematical models which make the QCs exist and thermodynamical stability; how to design general numerical methods to capture QCs; how to compare the theoretical results with physical experiments quantitatively. Here, we focus on the development of numerical methods. We provide a systematic numerical method to calculate all QCs where QCs could be treated as projections of a higher-dimensional space. We also present how to compute the energy density exactly without boundary effect. Finally, we take Lifshitz-Petrich model as an example to demonstrate our methods and show some numerical results. |
