2025/03/19 by House, Jonathan, Bakhshizada, Rashad, Janušonis, Skirmantas +2 · 2 citations
#Biological Physics (physics.bio-ph) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2503.15255
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of particles undergoing fractional Brownian motion. Specifically, we introduce a mean-density interaction in which each particle in the ensemble is coupled to the gradient of the total, time-integrated density produced by the entire ensemble. We report the results of extensive computer simulations for the mean-squared displacements and the probability densities of particles undergoing one-dimensional fractional Brownian motion with such a mean-density interaction. We find two qualitatively different regimes, depending on the anomalous diffusion exponent α characterizing the fractional Gaussian noise. The motion is governed by the interactions for α< 4/3 whereas it is dominated by the fractional Gaussian noise for α> 4/3. We develop a scaling theory explaining our findings. We also discuss generalizations to higher space dimensions and nonlinear interactions, the relation of our process to the ``true'' or myopic self-avoiding walk, as well as applications to the growth of strongly stochastic axons (e.g., serotonergic fibers) in vertebrate brains.