2018/03/14 by Vittoria Sposini, V. Sposini, A. V. Chechkin +7 · 2 citations
Biochemistry, Genetics and Molecular Biology · Materials Science · Mathematics · Physics and Astronomy · #Anomalous diffusion #Brownian motion #Diffusion #Diffusion and Search Dynamics #Diffusion process #Exponential function #Fractional Brownian motion #Fractional Differential Equations Solutions #Gaussian #Laplace transform #Material Dynamics and Properties #Mathematical analysis #Mathematics #Mean squared displacement #Physics #Probability density function #Quantum mechanics #Statistical physics #Statistics #Stochastic modelling #Stochastic process #Thermal diffusivity #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1367-2630/aab696
published as New J. Phys. 20, 043044 (2018) · 33 pages, 13 figures, IOP LaTeX
openalex publication_date 2018/03/14 · arxiv created 2018/11/23 · arxiv updated 2018/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.