Self-reinforcing directionality generates Lévy walks without the power-law assumption
arXiv:2005.00498 · doi:10.1103/PhysRevE.103.022132
Abstract
We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Lévy walks observed in active intracellular transport by Chen et. al. [\textit{Nat. mat.}, 2015]. We derive the non-homogeneous in space and time, hyperbolic PDE for the probability density function (PDF) of particle position. This PDF exhibits a bimodal density (aggregation phenomena) in the superdiffusive regime, which is not observed in classical linear hyperbolic and Lévy walk models. We find the exact solutions for the first and second moments and criteria for the transition to superdiffusion.
References in corpus (18)
- Statistical Mechanics of Interacting Run-and-Tumble Bacteria
- Lévy walks
- First-passage times in complex scale-invariant media
- Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
- Lattice Models of Nonequilibrium Bacterial Dynamics
- Towards deterministic equations for Levy walks: the fractional material derivative
- From the area under the Bessel excursion to anomalous diffusion of cold atoms
- First-passage time of run-and-tumble particles
- Theory of fractional-Lévy kinetics for cold atoms diffusing in optical lattices
- Optimizing persistent random searches
- Asymptotic densities of ballistic Lévy walks
- Exact moments in a continuous time random walk with complete memory of its history
- Memory effects and Lévy walk dynamics in intracellular transport of cargoes
- Emergence of Lévy Walks in Systems of Interacting Individuals
- Single integro-differential wave equation for Lévy walk
- Persistent random walk of cells involving anomalous effects and random death
- Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate
- A Fractional Diffusion Equation for an n-Dimensional Correlated Levy Walk
Cited by in corpus (5)
- Langevin picture of anomalous diffusion processes in expanding medium
- Population heterogeneity in the fractional master equation, ensemble self-reinforcement and strong memory effects
- Superdiffusion in self-reinforcing run-and-tumble model with rests
- Telomeres in Lamin-A Depleted Cells Exhibit Directed Motion and Dynamic Coherence
- Anomalous stochastic transport of particles with self-reinforcement and Mittag-Leffler distributed rest times