PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Becky Halpenny.

Abstract:
Title:	"Shrinking Dimer Dynamics and its Application in Saddle Point Search"
Seminar:	Ph.D. Thesis Defense
Speaker:	Jingyan Zhang, Advisor: Qiang Du, Penn State
Exploring complex energy landscape is a challenging issue encountered in many scientific subjects. Besides locating equilibrium states, it is often also important to identify the transition states given by saddle points. Saddle point search on an energy surface has broad applications in fields like materials science, chemistry and biology. In this dissertation, the shrinking dimer dynamics (SDD) and the constrained shrinking dimer dynamics (CSDD) are developed for effective saddle point search with or without constraints. Some rigorous mathematical theory of the continuous dynamic systems and numerical analysis of their discretizations are presented. Bench-mark numerical experiments are conducted to show the effectiveness and the robustness of newly developed methods. We also study some applications to interesting problems in both finite and infinite dimensional energy spaces, such as the study of critical nuclei morphology in phase transformations, the periodic centroidal Voronoi tessellations, and the discrete interacting particle systems as described by the generalized Thomson problem.