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Related Experiment Videos

Strong anomaly in diffusion generated by iterated maps.

J Dräger1, J Klafter

  • 1School of Chemistry, Tel-Aviv University, Tel-Aviv 69978, Israel.

Physical Review Letters
|September 16, 2000
PubMed
Summary
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This study explores deterministic diffusion using periodic iterated maps. We found that mean squared displacement grows logarithmically, revealing anomalous diffusion behavior with broad waiting times.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Deterministic systems can exhibit complex behaviors, including anomalous diffusion.
  • Understanding diffusion anomalies is crucial for modeling various physical phenomena.

Purpose of the Study:

  • To investigate deterministic diffusion generated by periodic iterated maps.
  • To analyze the scaling properties of mean squared displacement and propagators.

Main Methods:

  • Utilizing periodic iterated maps of the form x(t+1) = x(t)+ax(z)(t)exp[-(b/x(t))(z-1)].
  • Applying a scaling approach to connect map properties with diffusion characteristics.

Main Results:

  • Mean squared displacement exhibits logarithmic growth: sigma(2)(t) ~ ln(t).

Related Experiment Videos

  • Propagator decays exponentially with a scaling variable |x|/sqrt(sigma(2)(t)).
  • Identified anomalously broad waiting time distributions causing diffusion anomalies.

    • Conclusions:

    • The studied maps generate strong anomalous diffusion.
    • The findings relate to diffusion in random local fields.
    • A scaling approach effectively links map dynamics to diffusion outcomes.