论文标题
Lévy飞行作为空间扩展系统中的新兴现象
Lévy flights as an emergent phenomenon in a spatially extended system
论文作者
论文摘要
在大量的自然和工程系统中观察到以随机离散跳跃为特征的异常扩散和Lévy飞行，其特征是从分子的运动到气候信号。数学家最近揭示了在随机和确定性上产生异常扩散的机制。但是，据我们所知，没有任何明确的示例，即空间扩展系统，该系统表现出异常扩散而不会明确地被Lévy噪声驱动。我们在这里表明，尽管仅由高斯白噪声驱动，但Landau-lifshitz-gilbert方程是一种随机部分微分方程（SPDE），但表现出超级延伸的行为。异常的扩散是一种完全紧急的行为，并在其行进前溶液的位置跳跃。使用集体坐标方法，我们将SPDE降低到由高斯白噪声驱动的一组合适微分方程（SDE）。这使我们能够确定导致异常扩散的机制，因为前界面的随机扩大事件。
Anomalous diffusion and Lévy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate signals. Mathematicians have recently unveiled mechanisms to generate anomalous diffusion, both stochastically and deterministically. However, there exists to the best of our knowledge no explicit example of a spatially extended system which exhibits anomalous diffusion without being explicitly driven by Lévy noise. We show here that the Landau-Lifshitz-Gilbert equation, a stochastic partial differential equation (SPDE), despite only driven by Gaussian white noise, exhibits superdiffusive behaviour. The anomalous diffusion is an entirely emergent behaviour and manifests itself in jumps in the location of its travelling front solution. Using a collective coordinate approach we reduce the SPDE to a set of stochastic differential equations (SDEs) driven by Gaussian white noise. This allows us to identify the mechanism giving rise to the anomalous diffusion as random widening events of the front interface.
