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Related Experiment Videos

Transport with multiple-rate exchange in disordered media.

V Cvetkovic1, R Haggerty

  • 1Division of Water Resources Engineering, Royal Institute of Technology, Stockholm, Sweden. vdc@hth.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary

Particle transport with exchange is modeled using continuous-time random walks. Disorder influences transition and exchange, defining transport dominance regions based on power-law exponents.

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Area of Science:

  • Statistical Physics
  • Transport Phenomena
  • Complex Systems

Background:

  • Particle transport is fundamental in various scientific disciplines.
  • Understanding the interplay of transition and exchange dynamics is crucial for modeling complex systems.
  • Disorder at micro and macro scales significantly impacts transport behavior.

Purpose of the Study:

  • To investigate particle transport under exchange mechanisms using the continuous-time random-walk (CTRW) framework.
  • To analyze how macroscale and microscale disorder influence particle transition and exchange.
  • To determine the conditions under which transition or exchange dominates asymptotic transport.

Main Methods:

  • Utilized the continuous-time random-walk (CTRW) framework to model particle transport.

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  • Employed the multiple-rate exchange model to represent diverse exchange mechanisms.
  • Derived the crossing-time density, h(t;L), dependent on microscale (g) and joint (f) disorder functions.

    • Main Results:

    • Identified two distinct regions of asymptotic transport dominance based on power-law exponents (eta, alpha(tau), alpha(mu)).
    • Demonstrated that microscale disorder (eta) and macroscale disorder (alpha(tau), alpha(mu)) jointly define transport behavior.
    • Showed that for uniform exchange, both transition and exchange influence late-time behavior, with microscale exchange dominating if eta<0 or if eta>0 and transition is asymptotically Gaussian.

    Conclusions:

    • The CTRW framework effectively models particle transport with exchange influenced by multi-scale disorder.
    • The interplay between transition and exchange dynamics, governed by disorder characteristics, dictates transport regimes.
    • Specific conditions on disorder exponents determine whether transition or exchange ultimately dominates particle movement.