Investigating the interplay between mechanisms of anomalous diffusion via fractional Brownian walks on a comb-like structure

Abstract

The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of the particle is zero. Here, we propose an extension for the comb model via Langevin-like equations driven by fractional Gaussian noises (long-range correlated). By carrying out computer simulations, we show that the correlations in the y-direction affect the diffusive behavior in the x-direction in a non-trivial fashion, resulting in a quite rich diffusive scenario characterized by usual, superdiffusive or subdiffusive scaling of second moment in the x-direction. We further show that the long-range correlations affect the probability distribution of the particle positions in the x-direction, making their tails longer when noise in the y-direction is persistent and shorter for anti-persistent noise. Our model thus combines and allows the study/analysis of the interplay between different mechanisms of anomalous diffusion (geometric constraints and long-range correlations) and may find direct applications for describing diffusion in complex systems such as living cells.

Accepted for publication in New Journal of Physics

References in corpus (4)

• Anomalous transport in the crowded world of biological cells
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
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• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Quenched and Annealed Disorder Mechanisms in Comb-Models with Fractional Operators
• Long-range correlations and fractal dynamics in C. elegans: changes with aging and stress
• Langevin dynamics for ramified structures
• Interplay between particle trapping and heterogeneity in anomalous diffusion
• Machine Learning Analysis of Anomalous Diffusion
• Dynamics of soft interacting particles on a comb
• Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model