Unravelling the origins of anomalous diffusion: From molecules to migrating storks

Ohad Vilk, Erez Aghion, Tal Avgar, Carsten Beta, Oliver Nagel, Adal Sabri, Raphael Sarfati, Daniel K. Schwartz, Matthias Weiss, Diego Krapf, Ran Nathan, Ralf Metzler, Michael Assaf

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations ("Joseph effect"), fat-tailed probability density of increments ("Noah effect"), and nonstationarity ("Moses effect"). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.

Original languageEnglish
Article number033055
JournalPhysical Review Research
Issue number3
StatePublished - 1 Jul 2022
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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