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Updated: Dec 5, 2025
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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
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Reflected fractional Brownian motion in one and higher dimensions
Thomas Vojta1, Samuel Halladay1, Sarah Skinner1
1Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA.
Physical Review. E
|October 20, 2020
Summary
Computer simulations reveal how reflecting boundaries alter anomalous diffusion. Particles accumulate at boundaries for superdiffusion and deplete for subdiffusion, deviating from normal diffusion patterns.
Area of Science:
- Physics
- Mathematics
- Computational Science
Background:
- Fractional Brownian motion (FBM) models anomalous diffusion with long-range correlations.
- Reflecting boundaries confine FBM to finite spatial regions.
Purpose of the Study:
- Investigate FBM behavior in confined spaces.
- Analyze deviations from uniform probability density due to boundary interactions.
Main Methods:
- Large-scale computer simulations of FBM in 1D, 2D, and 3D.
- Analysis of stationary probability density near reflecting boundaries.
Main Results:
- FBM exhibits striking deviations from uniform density near boundaries.
- Particles accumulate at boundaries for superdiffusive FBM (α > 1).
- Particle density depletes at boundaries for subdiffusive FBM (α < 1).
Conclusions:
- The interplay of FBM correlations and boundaries creates power-law singularities in probability density.
- The exponent of this singularity depends on dimensionality, geometry, and the FBM diffusion exponent.
- Findings have implications for modeling biological systems, such as brain fiber density.
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