Relations between anomalous diffusion and fluctuation scaling: The case of ultraslow diffusion and time-scale-independent fluctuation scaling in language

10/26/2021
by   Hayafumi Watanabe, et al.
0

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.

READ FULL TEXT
research
07/21/2017

Ultraslow diffusion in language: Dynamics of appearance of already popular adjectives on Japanese blogs

What dynamics govern a time series representing the appearance of words ...
research
01/02/2023

Preface: Characterisation of Physical Processes from Anomalous Diffusion Data

Preface to the special issue "Characterisation of Physical Processes fro...
research
10/05/2020

Identification of Anomalous Diffusion Sources by Unsupervised Learning

Fractional Brownian motion (fBm) is a ubiquitous diffusion process in wh...
research
08/07/2021

Unsupervised learning of anomalous diffusion data

The characterization of diffusion processes is a keystone in our underst...
research
05/06/2021

Extreme Learning Machine for the Characterization of Anomalous Diffusion from Single Trajectories

The study of the dynamics of natural and artificial systems has provided...
research
11/27/2018

Large deviations of time-averaged statistics for Gaussian processes

In this paper we study the large deviations of time averaged mean square...

Please sign up or login with your details

Forgot password? Click here to reset