|Rare Events, Transition Pathways and Reaction Rates|
The dynamics of complex systems are often driven by rare but
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.