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An empirical method to characterize displacement distribution functions for anomalous and transient diffusion

Author

Listed:
  • Qiao, Le
  • Ilow, Nicholas
  • Ignacio, Maxime
  • Slater, Gary W.

Abstract

We propose a practical empirical fitting function to characterize the non-Gaussian displacement distribution functions (DispD) often observed for heterogeneous diffusion problems. We first test this fitting function with the problem of a colloidal particle diffusing between two walls using Langevin Dynamics (LD) simulations of a raspberry particle coupled to a lattice Boltzmann (LB) fluid. We also test the function with a simple model of anomalous diffusion on a square lattice with obstacles. In both cases, the fitting parameters provide more physical information than just the Kurtosis (which is often the method used to quantify the degree of anomaly of the dynamics), including a length scale that marks where the tails of the DispD begin. In all cases, the fitting parameters smoothly converge to Gaussian values as the systems become less anomalous.

Suggested Citation

  • Qiao, Le & Ilow, Nicholas & Ignacio, Maxime & Slater, Gary W., 2022. "An empirical method to characterize displacement distribution functions for anomalous and transient diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    • Handle: RePEc:eee:phsmap:v:604:y:2022:i:c:s0378437122004526
    DOI: 10.1016/j.physa.2022.127676
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    References listed on IDEAS

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    1. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
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