论文标题
非本地时间动态和扩散状态的跨界
Nonlocal-in-time dynamics and crossover of diffusive regimes
论文作者
论文摘要
我们研究了一个简单的非本地时间动态系统，该系统为异质介质中复杂扩散状态的有效建模而提出。我们介绍其解决方案及其常见研究的统计数据，例如均方距离。这个有趣的模型采用非本地运算符来替换常规的一阶时间衍生。它引入了通过内核函数编码的恒定长度的有限记忆效应。非局部时间运算符与一方面依赖整个时间历史的分数时间衍生物有关，而如果内存窗口的长度减小，则还原为经典时间衍生物。这使我们能够证明非局部模型在捕获自然界在初始亚扩散和长时间正常扩散之间广泛观察到的分频器方面的有效性。
We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance. This interesting model employs a nonlocal operator to replace the conventional first-order time-derivative. It introduces a finite memory effect of a constant length encoded through a kernel function. The nonlocal-in-time operator is related to fractional time derivatives that rely on the entire time-history on one hand, while reduces to, on the other hand, the classical time derivative if the length of the memory window diminishes. This allows us to demonstrate the effectiveness of the nonlocal-in-time model in capturing the crossover widely observed in nature between the initial sub-diffusion and the long time normal diffusion.
