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

Abstract

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.

20 pages, 8 figures

References in corpus (6)

• Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis
• Disease extinction in the presence of non-Gaussian noise
• Computing stationary distributions in equilibrium and non-equilibrium systems with Forward Flux Sampling
• Homogeneous nucleation under shear in a two-dimensional Ising model: cluster growth, coalescence and breakup
• Harmonic Measure for Percolation and Ising Clusters Including Rare Events
• The Harmonic Measure of Diffusion-Limited Aggregates including Rare Events

Cited by in corpus (7)

• Studying Rare Events using Forward-Flux Sampling: Recent Breakthroughs and Future Outlook
• High-density quantum sensing with dissipative first order transitions
• Pathways to self-organization: crystallization via nucleation and growth
• A primer on noise-induced transitions in applied dynamical systems
• Forward-Flux Sampling with Jumpy Order Parameters
• Statistical behavior of adaptive multilevel splitting algorithms in simple models
• Computation of nucleation of a non-equilibrium first-order phase transition using a rare-event algorithm