势垒法：一种计算超长跃迁时间的技术
The Barrier Method: A Technique for Calculating Very Long Transition Times
摘要：
在许多动力系统中，典型事件和“罕见”事件之间存在很大的时间尺度分离，这可能是感兴趣的情况。稀有事件的发生率很难用数值计算，但在许多领域却具有相当重要的实际意义：例如化学物理中的跃迁时间和流行病学中的灭绝时间可能很长，但却相当重要。我们提出了一个非常快速的数值技术，可以用来找到长的过渡时间（非常小的速率）在低维系统，即使他们缺乏细致平衡。我们说明了一个非平衡系统的方法引入Maier和Stein和一个二维（参数空间）的流行病学模型。
英文摘要：
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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