Luca Angelani, Alessandro De Gregorio, Roberto Garra, Francesco Iafrate
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引用次数: 0
摘要
随机飞行(也称奔跑和翻滚行走或传输过程)表示在任何泊松时间内改变方向的有限速度随机运动。这些 d 维模型的研究给出了在任何空间维度上都有效的问题的一般表述。本文的目的是将这种一般分析扩展到动力学方程的非局部广义化所产生的时间分数过程。时间分数方程解的概率解释导致了原始传输过程的时间变化版本。所获得的结果清楚地说明了时间分数导数在这种随机运动中所起的作用。它们显示出一种反常行为,有助于描述统计物理学和生物学中出现的若干复杂系统。我们尤其关注被称为电报过程的一维随机飞行,研究经典电报方程的时间分数版本,并为其随机解提供合适的解释。
Anomalous Random Flights and Time-Fractional Run-and-Tumble Equations
Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provide a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.