Disentangling the origins of anomalous diffusion in data: the Moses/ Noah and Joseph effects

  Erez Aghion  ,  Philipp G. Meyer  ,  Vidushi Adlakha  ,  Holger Kantz  ,  Kevin E. Bassler  
Max-Planck institute for physics of complex systems, Dresden, Germany

We study a method for detecting the precise factors that lead to anomalous diffusion, when it is observed in a experimental data,

and we do not have exact knowledge about the underlying dynamics.

The reasons for anomalous scaling of the mean-squared displacement are decomposed into three effects:

Increment correlations are expressed by the “Joseph effect”, fat-tails of the increment probability density lead to a “Noah effect”,

and non-stationarity, to the “Moses effect”. Telling these three effects apart is crucial when one tries to infer the underlying structure of the system,

and build a model to describe it. We present this decomposition by analyzing the example of a widely-applicable model for coupled L \'evy walk.

We infer the properties of the dynamics from the data using methods of time-series analysis, and compare our results to theoretical predictions.