Abstract
The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by ‘viscoelastic’ anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of ‘viscoelastic yet non-Gaussian’ diffusion.
Highlights
Gaussianity is so fundamentally engrained in statistics that we almost take it for granted
A more advanced modelling approach is associated with the concept of generalised grey Brownian motion [12] and leads to the underdamped HEBP model which displays anomalous diffusion at short times and normal diffusion at long times [13]
We present detailed results for this non-universality in the viscoelastic anomalous diffusion case in terms of the time evolution of the mean squared displacement (MSD), the effective diffusivities, and the probability density function (PDF) of these processes
Summary
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Wei Wang1,2, Flavio Seno3, Igor M Sokolov4, Aleksei V Chechkin2,5 and Ralf Metzler2,6 Keywords: diffusion, anomalous diffusion, non-Gaussianity, fractional Brownian motion
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