Solution Landscape: Algorithms and Applications
数学专题报告
报告题目(Title)：Solution Landscape: Algorithms and Applications
报告人(Speaker)：殷鉴远（National University of Singapore）
地点(Place)：后主楼1124
时间(Time)：2023 年 08 月 31 日（周四） 15:00-16:00
邀请人(Inviter)：蔡永强
报告摘要
How do we search for the entire family tree of possible intermediate states, without unwanted random guesses, starting from a stationary point on the energy landscape all the way down to multiple energy minima? Here we introduce a general numerical method that constructs the solution landscape, which is a pathway map connecting all stationary points of the energy. The solution landscape guides our understanding of how a physical system moves on the energy landscape and identifies multiple transition states between energy minima.
As applications, we solve the Landau-de Gennes energy to model nematic liquid crystals confined in a square well; we illustrate the basic concepts by examining multiple stationary points and the connected pathway maps of the model; we further compare the results of the Ericksen-Leslie energy. We also identify non-axisymmetric critical points of the Onsager model with different potential kernels. As another example, we find two possible transition pathways connecting two-dimensional crystalline and quasicrystalline phases with a Lifshitz-Petrich free energy. As a constrained example, we identify vortex states of two-dimensional rotational Bose-Einstein condensates and reveal four excitation mechanisms.
