Topic of the report: Building a deconstructed landscape on the energy landscape

Reporter: Zhang Lei, Associate Professor Peking University

Reporting time: December 5, 2020, 10:00-11:00 am

Report location: The second lecture hall on the first floor of the Mathematics Building

School contact: Wang Ruishu wangrs_math@mail.jlu.edu.cn

Report summary:

    Many practical application problems can be classified as the minimum value problem of solving nonlinear energy functions with multiple variables in computational mathematics. The energy landscape of such multi-solution problems usually has multiple minima, so how to find the global minima and how to find the relationship between different minima has always been two key issues in the field of computational mathematics. In the report, we proposed a new concept of solution landscape. The solution landscape describes that different minima are connected by corresponding first-order saddle points, low-order saddle points are connected by corresponding high-order saddle points, and finally connected to a hierarchical structure diagram of the highest-order saddle point. Based on the characteristics of the solution landscape, we use the developed high-order saddle point dynamics, and through the downward search and upward search methods, we can efficiently construct a complete path map on the energy landscape. We take the liquid crystal defect of the soft matter system as an example, and use the Landau-de Gennes model to calculate the defect landscape of the restricted nematic liquid crystal.