Probing rare physical trajectories with Lyapunov weighted dynamics
Probing rare physical trajectories with Lyapunov weighted dynamics
复制标题
利用李雅普诺夫加权动力学探索罕见的物理轨迹
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Kurchan
中科院分区：
文献类型：
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作者：
J. Tailleur;J. Kurchan
在非线性动力系统中，非典型轨迹往往起着重要的作用。例如，共振和分离决定了行星系统的命运，而孤子和呼吸子等局部物体为玻色-爱因斯坦凝聚体和生物分子等系统提供了能量传输机制。不幸的是，大多数定位这些“稀有”轨迹的数值方法都局限于低维或玩具模型，而统计物理、化学反应或天文学的领域仍然难以达到。在这里，我们实现了一种有效的方法，使我们能够通过选择具有异常混沌性的轨迹来在更高的维度上工作。作为一个例子，我们研究了平衡状态下的Fermi-Pasta-Ulam非线性链，结果表明该算法在寻找低混沌水平的轨迹时能够快速地挑出孤子解，而在相反的情况下则能够快速地挑出混沌呼吸者。我们期望该方案在天体力学和湍流中有自然的应用，它可以很容易地与现有的数值方法相结合。
In nonlinear dynamical systems, atypical trajectories often play an important role. For instance, resonances and separatrices determine the fate of planetary systems, and localized objects such as solitons and breathers provide mechanisms of energy transport in systems such as Bose–Einstein condensates and biological molecules. Unfortunately, most of the numerical methods to locate these ‘rare’ trajectories are confined to low-dimensional or toy models, whereas the realms of statistical physics, chemical reactions or astronomy are still hard to reach. Here we implement an efficient method that enables us to work in higher dimensions by selecting trajectories with unusual chaoticity. As an example, we study the Fermi–Pasta–Ulam nonlinear chain in equilibrium and show that the algorithm rapidly singles out the soliton solutions when searching for trajectories with low levels of chaoticity, and chaotic breathers in the opposite situation. We expect the scheme to have natural applications in celestial mechanics and turbulence, where it can readily be combined with existing numerical methods.