Anomalous diffusion originated by two Markovian hopping-trap mechanisms

Abstract

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 $1-p$ are the probabilities of occurrence of each Markovian mechanism, then the anomalousness parameter $\beta \in (0,1)$ results to be $\beta \simeq 1-1/\{1+\log [(1-p)/p]\}$. Ensemble and single-particle observables of this model have been studied and they match the main characteristics of anomalous diffusion as they are typically measured in living systems. In particular, the celebrated transition of the walker's distribution from exponential to stretched-exponential and finally to Gaussian distribution is displayed by including also the Brownian yet non-Gaussian interval.

arXiv commentAccepted for publication in J. Phys. A

References in corpus (33)

• Anomalous transport in the crowded world of biological cells
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Fractional calculus and continuous-time finance
• Lévy walks
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations
• Fractional calculus and continuous-time finance II: the waiting-time distribution
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• Physical Pictures of Transport in Heterogeneous Media: Advection-Dispersion, Random Walk and Fractional Derivative Formulations
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells
• Brownian subordinators and fractional Cauchy problems
• The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook
• Packets of Diffusing Particles Exhibit Universal Exponential Tails
• Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
• Fractional Calculus as a Macroscopic Manifestation of Randomness
• Stochastic calculus for uncoupled continuous-time random walks
• Fractional kinetics emerging from ergodicity breaking in random media
• Analytic approaches of the anomalous diffusion: a review
• Breakdown of the Onsager principle as a sign of aging
• Weak ergodicity breaking in an anomalous diffusion process of mixed origins
• On relation between generalized diffusion equations and subordination schemes
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Large deviations for continuous time random walks
• Superstatistical modelling of protein diffusion dynamics in bacteria
• Short note on the emergence of fractional kinetics
• Non-Gaussian diffusion of mixed origins
• Random-time processes governed by differential equations of fractional distributed order
• Models for characterizing the transition among anomalous diffusions with different diffusion exponents
• Should I stay or should I go? Zero-size jumps in random walks for Lévy flights
• Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
• Anomalous diffusion and FRAP dynamics in the random comb model

Cited by in corpus (5)

• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift
• Machine Learning Analysis of Anomalous Diffusion
• Preface: Characterisation of Physical Processes from Anomalous Diffusion Data
• A non-homogeneous, non-stationary and path-dependent Markov anomalous diffusion model