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The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the…
We propose an interpolation expression using the difference moment (Kolmogorov transient structural function) of the second order as the average characteristic of displacements for identifying the anomalous diffusion in complex processes…
Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…
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 present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and…
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…
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 $p \in (0,1/2)$ and $1-p$…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…