Relations between anomalous diffusion and fluctuation scaling: the case of ultraslow diffusion and time-scale-independent fluctuation scaling in language
Relations between anomalous diffusion and fluctuation scaling: the case of ultraslow diffusion and time-scale-independent fluctuation scaling in language
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DOI：
10.1140/epjb/s10051-021-00236-2
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发表时间：
2021-11-01
影响因子：
1.6
通讯作者：
Watanabe，Hayafumi
中科院分区：
文献类型：
--
作者：
Watanabe，Hayafumi
涨落标度（FS）和反常扩散在不同的背景下进行了讨论，即使两者都经常在复杂系统中观察到。为了澄清这些概念之间的关系，我们调查了大约30亿日本博客文章在六年的时间内，并分析了相应的泊松过程驱动的随机游走模型与幂律遗忘，再现了异常扩散和FS。通过对模型的分析，我们确定了FS的时间尺度依赖性与反常扩散特性之间的关系，并表明时间尺度无关的FS基本上对应于对数扩散（即，一种超低扩散）。此外，我们证实，这种关系也适用于实际数据。这一发现可能有助于发现超低速扩散的实际例子，尽管有许多数学理论，但几乎没有观察到，因为我们可以更容易和更明显地检测到与时间尺度无关的FS，而不是通过直接检测基于均方位移的对数扩散。
Fluctuation scaling (FS) and anomalous diffusion have been discussed in different contexts, even though both are often observed in complex systems. To clarify the relationship between these concepts, we investigated approximately three billion Japanese blog articles over a period of six years and analyzed the corresponding Poisson process driven by a random walk model with power-law forgetting, which reproduces both the anomalous diffusion and the FS. From the analysis of the model, we have identified the relationship between the time-scale dependence of FS and characteristics of anomalous diffusion and showed that the time-scale-independent FS corresponds to essentially a logarithmic diffusion (i.e., a kind of ultraslow diffusion). In addition, we confirmed that this relationship is also valid for the actual data. This finding may contribute to the discovery of actual examples of ultraslow diffusion, which have been nearly unobserved in spite of many mathematical theories, because we can detect the time-scale-independent FS more easily and more distinctly than through direct detection of the logarithmic diffusion based on the mean squared displacement.