2021/10/10 by Daniel Han, Dmitri V. Alexandrov, Anna Gavrilova +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Applied mathematics #Continuous-time random walk #Diffusion and Search Dynamics #Limit (mathematics) #Mathematical analysis #Mathematics #Moment (physics) #Monte Carlo method #Physics #Quantum mechanics #Random walk #Rest (music) #Statistical physics #Statistics #Stochastic differential equation #Stochastic process #Stochastic processes and statistical mechanics #cond-mat.stat-mech #q-bio.QM #stochastic dynamics and bifurcation
paper · pdf · doi:10.3390/fractalfract5040221
arxiv created 2021/10/10 · openalex publication_date 2021/11/15 · arxiv updated 2021/11/16 · openalex created_date 2021/11/22 · openalex updated_date 2026/08/06
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.