We construct static tensor model for nematic phases of bent-core molecules and star molecules from molecular theory. The form of free energy is determined by molecular symmetry, which includes the couplings and derivatives of a vector and two second-order tensors, with the coefficients determined by molecular parameters. Using the static tensor model, we study the nematic phases resulted from the hard-core potential, obtaining the phase diagram and elastic constants about the molecular parameters. Armed with the free energy and taking the molecular-fluid interaction into account, we construct the molecular model for the dynamics of the two molecules in incompressible fluid. The molecular model is also fully determined by molecular parameters and is suitable for inhomogeneous flows. By adopting the quasi-equilibrium approximation, we derive the dynamic tensor model with energy dissipation maintained. We study the shear flow problem using both the molecular and the tensor models. We examine the effect of molecular shape on the flow modes, with the parameters chosen near the transition region of different nematic phases.

徐劼博士2006年至2010年在北京大学数学科学学院学习, 获得学士学位; 从2010年在张平文院士指导下攻读博士, 于2015年获得博士学位。徐劼博士现于美国普渡大学从事博士后研究工作, 他的研究兴趣主要是液晶流的建模与计算、界面问题的数值模拟和梯度流的计算方法。