Establishing the kinetics of ballistic-to-diffusive transition using directional statistics.
Establishing the kinetics of ballistic-to-diffusive transition using directional statistics.
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使用方向统计建立弹道到扩散转变的动力学。
DOI：
10.1103/physreve.97.042102
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
R. Chakrabarty
中科院分区：
文献类型：
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作者：
Pai Liu;W. Heinson;B. Sumlin;kuan;R. Chakrabarty
我们利用方向统计建立了在二维随机游动中观察到的弹道到扩散(BD)转变的动力学。使用步行器的转角分布对方向相关性进行参数化，该分布遵循通常采用的包裹柯西分布(WCD)函数。在BD相变过程中，观察到控制WCD形状的浓度因子(ρ)较其初始值有所下降。接下来，我们解析地推导出有效ρ与时间之间的关系，这本质上量化了BD转换率。我们的动力学表达式的预测与相关随机游走模拟得到的经验数据集符合得很好。我们进一步将我们的公式与通常使用的步行者均方位移与时间之间的标度关系联系起来。
We establish the kinetics of ballistic-to-diffusive (BD) transition observed in two-dimensional random walk using directional statistics. Directional correlation is parameterized using the walker's turning angle distribution, which follows the commonly adopted wrapped Cauchy distribution (WCD) function. During the BD transition, the concentration factor (ρ) governing the WCD shape is observed to decrease from its initial value. We next analytically derive the relationship between effective ρ and time, which essentially quantifies the BD transition rate. The prediction of our kinetic expression agrees well with the empirical datasets obtained from correlated random walk simulation. We further connect our formulation with the conventionally used scaling relationship between the walker's mean-square displacement and time.