Many problems in material sciences, physics, chemistry and biology can be abstractly formulated
as a system that navigates over a complex energy landscape of high or infinite dimensions.
The system is confined in metastable states for long times before making transitions from one metastable state
to another. The disparity of time scales makes the study of transition pathways and transition rates
a very challenging task. The string method proposed by E, Ren and Vanden-Eijnden is an efficient way
of identifying transition mechanisms and transition rates between metastable states in systems
with complex energy landscapes. In this talk, I will discuss the string method and its application
to the study of critical nuclei in capillary condensation, dislocation dynamics in crystalline solids, and
the isomerization of alanine dipeptide.
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