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Advective transport in percolation clusters.

Matthew E Rhodes1, Martin J Blunt

  • 1Department of Earth Science and Engineering, Imperial College London, South Kensington, London, United Kingdom. rhodes@imperial.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
Summary

We simulated advective transport in percolation clusters, finding that negative velocity moments are ill-defined in large systems. Flux-weighted analysis reveals anomalous transport linked to multifractal properties.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Advective transport is crucial in disordered media.
  • Percolation theory describes connectivity at critical points.
  • Multifractality characterizes complex systems with varying properties.

Purpose of the Study:

  • To simulate advective transport in bond percolation clusters at the critical point.
  • To investigate the velocity distribution and multifractal spectrum.
  • To understand anomalous transport using continuous time random walk theory.

Main Methods:

  • Simulating advective transport in percolation clusters.
  • Computing flow speed histograms and multifractal spectra.
  • Applying continuous time random walk theory.

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Main Results:

  • Negative moments of the velocity distribution become ill-defined in large systems.
  • Flux-weighted velocity histograms yield well-defined mean travel times.
  • Anomalous transport is observed and linked to multifractal properties.

Conclusions:

  • Advective transport in percolation clusters exhibits complex behavior at the critical point.
  • Flux weighting is essential for accurate transport modeling.
  • Multifractality governs the characteristics of anomalous transport.