BIMSA > BIMSA Computational Math Seminar Construction of the solution landscape on a complicated energy landscape
Construction of the solution landscape on a complicated energy landscape
Organizers
Pipi Hu , Xin Liang , Zhiting Ma , Hamid Mofidi , Axel G.R. Turnquist , Li Wang , Fansheng Xiong , Shuo Yang , Wuyue Yang
Speaker
Jianyuan Yin
Time
Thursday, December 4, 2025 3:15 PM - 4:15 PM
Venue
A3-4-312
Online
Zoom 928 682 9093 (BIMSA)
Abstract
Transition pathways represent the most probable routes of transition between metastable states, and index-1 saddle points correspond to transition states. How do we search for a comprehensive graph of possible transition states? I will introduce a general numerical method that constructs the solution landscape, a pathway map of stationary points, starting from a saddle point all the way down to multiple minima. The key idea, downward search, provides convenience for finding multiple transition states systematically. We develop an efficient saddle dynamics method to implement downward search and find saddle points. Several numerical applications will be presented to demonstrate its effectiveness, including liquid crystal molecular equilibrium distribution of the Onsager model, phase transitions in Landau-type phase-field crystal models, and vortex states of Bose-Einstein condensates.