Related papers: Langevin equation in complex media and anomalous d…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent…
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…
Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…
In this paper we revisit the Brownian motion on the basis of {the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo in 1966. The importance of our approach is to…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism…
Anomalous diffusion often arises in complex environments where viscoelastic or crowded conditions influence particle motion. In many biological and soft-matter systems, distinct components of the medium exhibit unique viscoelastic…
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…
We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the…
This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…
We review the latest advances in the analytical modelling of single file diffusion. We focus first on the derivation of the fractional Langevin equation that describes the motion of a tagged file particle. We then propose an alternative…
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…