ArticlePhysical review. E2020
Reflected fractional Brownian motion in one and higher dimensions.
Article in Physical review. E, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed, 45 citations in OpenAlex.
- Article
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- Extract latent features of single-particle trajectories with historical experience learning.Biophysical journal · 2023Article
- Predicting the distribution of serotonergic axons: a supercomputing simulation of reflected fractional Brownian motion in a 3D-mouse brain model.Frontiers in computational neuroscience · 2023Article
- An experimental platform for stochastic analyses of single serotonergic fibers in the mouse brain.Frontiers in neuroscience · 2023Article
- Weak Point of SARS-CoV-2: Human and Viral Ion Channels under External Physical Fields.International journal of molecular sciences · 2022Article
- High-resolution spatiotemporal analysis of single serotonergic axons in anFrontiers in neuroscience · 2022Article
- Brain serotonergic fibers suggest anomalous diffusion-based dropout in artificial neural networks.Frontiers in neuroscience · 2022Article
- Article
- Serotonergic Axons as Fractional Brownian Motion Paths: Insights Into the Self-Organization of Regional Densities.Frontiers in computational neuroscience · 2020Article
Corrections and comments
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Authors and funding
6 authors at 3 institutions in 2 countries.
Funding
Abstract
Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic process with long-ranged correlations, represents a widely applied, paradigmatic mathematical model of anomalous diffusion. We report the results of large-scale computer simulations of FBM in one, two, and three dimensions in the presence of reflecting boundaries that confine the motion to finite regions in space. Generalizing earlier results for finite and semi-infinite one-dimensional intervals, we observe that the interplay between the long-time correlations of FBM and the reflecting boundaries leads to striking deviations of the stationary probability density from the uniform density found for normal diffusion. Particles accumulate at the boundaries for superdiffusive FBM while their density is depleted at the boundaries for subdiffusion. Specifically, the probability density P develops a power-law singularity, P∼r^{κ}, as a function of the distance r from the wall. We determine the exponent κ as a function of the dimensionality, the confining geometry, and the anomalous diffusion exponent α of the FBM. We also discuss implications of our results, including an application to modeling serotonergic fiber density patterns in vertebrate brains.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.