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Carnegie Mellon Center for Nonlinear Analysis
Shrinking Dimer Dynamics and its Applications


Jingyan Zhang
Penn State University
Department of Mathematics

Abstract: In this talk, we present a dynamic system, shrinking dimer dynamics (SDD), that can be applied to locate transition states, which are stationary points where the Hessian matrix has only one negative eigenvalue. A theoretical analysis is provided to show that the stable steady equilibria of SDD are exactly such transition points. Guidance in choosing parameters for the system is also provided to improve the efficiency and robustness of the algorithm, followed by some illustrative numerical experiments and analysis. In addition, linear and quadratic constraints are considered and the corresponding analysis is also presented.