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Anomalous diffusion originated by two Markovian hopping-trap mechanisms
(2022)
We show through intensive simulations that the paradigmatic
features of anomalous diffusion are indeed the features of
a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms.
If $p ...
The Fokker–Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm
(2022)
By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live Escherichia coli cells, we obtain the ...
Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
(2021-07-24)
In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the ...
A generalized Stefan model accounting for system memory and non-locality
(2020-05)
The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the ...
Gaussian processes in complex media: new vistas on anomalous diffusion
(2019-09)
Normal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions ...
Single-trajectory spectral analysis of scaled Brownian motion
(2019-06)
A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the ...
Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
(2019-02)
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite ...
Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
(2019-02-01)
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly ...
Stochastic processes for anomalous diffusion
(2019)
Anomalous diffusion is a diffusion process which Mean Square Displacement (MSD)
is not a linear funtion of time, what is known as normal diffusion.
When the relation is faster than linear, it is called superdiffusion and ...
Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion
(2018-10-25)
We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass ...