Exploring complex energy landscape is a challenging issue in many
applications. Besides locating equilibrium states, it is often also
important to identify the transition states given by saddle points. In this
talk, we will discuss the mathematics and algorithms, in particular, the
shrinking dimer dynamics, developed to compute transition states. Some
applications will be considered, including the study of critical nuclei
morphology in solid state transformations, optimal photonic crystal design
and the generalized Thomson problem.
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