Rare Events, Transition Pathways and Reaction Rates

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The dynamics of complex systems are often driven by rare but important events. Well-known examples include nucleation events during phase transitions, conformational changes in macromolecules, and chemical reactions. The long time scale associated with these rare events is a consequence of the disparity between the effective thermal energy and typical energy barrier of the systems. The dynamics proceeds by long waiting periods around metastable states followed by sudden jumps from one state to another.

Common simulation methods like molecular dynamics (MD) are limited by their time-scale. MD simulations resolve individual atomic vibrations and hence require integration time-steps on the order of femto-seconds. In contrast, processes in nature can take place in time scales of milli-seconds to few years. For example time scale for atomic processes such as vacancy diffusion are milli-seconds, where as creep (turbine blades made of Ni3Al, etc) can take as long as few years. To overcome this time constrain it becomes necessary to use methods such as those based on transition state theory to investigate the multi-dimensional potential energy surface (PES).

This web-page contains an algorithm which finds the minimum energy path on the PES connecting the initial and the final states through the saddle point.

Send comments to Amit Samanta: asamanta AT math.princeton.edu or Weinan E: weinan AT math.princeton.edu

-Last updated on May 25, 2010.

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