Minimum action method for the study of rare events
Minimum action method for the study of rare events
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DOI：
10.1002/cpa.20005
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发表时间：
2004-05-01
影响因子：
3
通讯作者：
Vanden-Eijnden, E
中科院分区：
文献类型：
--
作者：
E, W;Ren, WQ;Vanden-Eijnden, E
利用Wentzell-Freidlin大偏差理论的最小作用原理作为一种数值工具，在小噪声驱动的空间扩展系统中找到最佳动力学路径。该方法对离散动作进行离散化，并采用预条件BFGS方法对离散动作进行优化。应用程序中的热激活反转在金斯堡-朗道模型在一个和两个维度，和噪声引起的漂移事件中的反射器作为一个例子，在化学中产生的非梯度系统。在Ginzburg-Landau模型中，反转通过有趣的成核事件进行，随后是畴壁的传播。的成核与传播的问题进行了讨论，和成核事件的数量作为反转时间和其他材料参数的函数的缩放计算。与数值结果吻合良好。在振荡器中，其确定性动力学有一个单一的稳定平衡状态，噪声的存在下，诱导大的偏移，其中系统周期出这个平衡状态。(C)2004 Wiley Periodicals，Inc.
The least-action principle from the Wentzell-Freidlin theory of large deviations is exploited as a numerical tool for finding the optimal dynamical paths in spatially extended systems driven by a small noise. The action is discretized and a preconditioned BFGS method is used to optimize the discrete action. Applications are presented for thermally activated reversal in the Ginzburg-Landau model in one and two dimensions, and for noise-induced excursion events in the Brusselator taken as an example of a nongradient system arising in chemistry. In the Ginzburg-Landau model, the reversal proceeds via interesting nucleation events, followed by propagation of domain walls. The issue of nucleation versus propagation is discussed, and the scaling for the number of nucleation events as a function of the reversal time and other material parameters is computed. Good agreement is found with the numerical results. In the Brusselator, whose deterministic dynamics has a single stable equilibrium state, the presence of noise is shown to induce large excursions by Which the system cycles out of this equilibrium state. (C) 2004 Wiley Periodicals, Inc.