Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

Abstract

We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport.

Non-Markovian diffusion of excitons in layered perovskites and transition metal dichalcogenides

“…For instance, similar non-Markovian rest states with Mittag–Leffler distribution have been proposed recently for self-reinforced transport of particles. 94 In a geophysical context the non-Markovian MIM model has been recently used in ref. 87 for the description of the movement of a tracer which can switch between the mobile zone (the bulk water of a river) and immobile zone (dead-end pores, the hyporheic zone, or biofilms).…”

Stochastic Model of Virus–Endosome Fusion and Endosomal Escape of pH-Responsive Nanoparticles

“…For example, one can take into account multiplicative noises that might lead to noise-induced transitions [25] for a nonlinear cutoff switch model [18]. It would be interesting to take into account the stochastic anomalous intracellular transport of viruses and nanoparticles along microtubules to the perinuclear region [26][27][28][29]. Certainly, the anomalous endosomal movements have implications on their fusion and fission inside cells and therefore Rab5 to Rab7 conversion.…”

Population heterogeneity in the fractional master equation, ensemble self-reinforcement, and strong memory effects

“…More recently, it was shown that strong memory and reinforcement can generate superdiffusion in a continuous-time and finite-velocity strong memory model [31], even in the presence of rests [32]. However, when including a trapping state, the superdiffusion caused by reinforcement was only transient [33].…”