The Barrier Method: A Technique for Calculating Very Long Transition Times

Details The Barrier Method: A Technique for Calculating Very Long Transition Times The Barrier Method: A Technique for Calculating Very Long Transition Times

2010-05-21

arxiv.org/abs/1005.3985v1

Physics

Condensed Matter

Statistical Mechanics

20 pages, 8 figures

Scientific paper

In many dynamical systems there is a large separation of time scales between typical events and "rare" events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable practical importance in many fields: for example transition times in chemical physics and extinction times in epidemiology can be very long, but are quite important. We present a very fast numerical technique that can be used to find long transition times (very small rates) in low-dimensional systems, even if they lack detailed balance. We illustrate the method for a bistable non-equilibrium system introduced by Maier and Stein and a two-dimensional (in parameter space) epidemiology model.

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