Transient Anomalous Diffusion in Run-and-Tumble Dynamics
Transient Anomalous Diffusion in Run-and-Tumble Dynamics
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DOI：
10.3389/fphy.2019.00120
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发表时间：
2019-09-18
影响因子：
3.1
通讯作者：
Rieger, Heiko
中科院分区：
文献类型：
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作者：
Shaebani, M. Reza;Rieger, Heiko
研究了具有两种不同运动状态的粒子的随机动力学。每一个都由两个参数表征：一个代表平均速度，另一个代表量化保持当前运动方向的趋势的持久性。我们考虑一个运行和翻滚的过程，这是一个积极的快速运动模式（持续运动）和被动的缓慢模式（扩散）的组合。假设两个运动状态之间的随机过渡，我们推导出的均方位移的时间演化的解析表达式。的关键参数和初始条件的相互作用，例如，最初开始在运行或翻滚状态的概率导致各种瞬态制度的异常运输在不同的时间尺度上接近渐近扩散动力学。我们估计的交叉时间的长期扩散制度，并证明了渐近扩散常数是独立的最初开始在运行或翻滚状态。
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain the current direction of motion. We consider a run-and-tumble process, which is a combination of an active fast motility mode (persistent motion) and a passive slow mode (diffusion). Assuming stochastic transitions between the two motility states, we derive an analytical expression for the time evolution of the mean square displacement. The interplay of the key parameters and the initial conditions as for instance the probability of initially starting in the run or tumble state leads to a variety of transient regimes of anomalous transport on different time scales before approaching the asymptotic diffusive dynamics. We estimate the crossover time to the long-term diffusive regime and prove that the asymptotic diffusion constant is independent of initially starting in the run or tumble state.