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Anomalous diffusion with log-periodic modulation in a selected time interval.

L Padilla1, H O Mártin, J L Iguain

  • 1Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR) and Departamento de Física FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina. lorenapadilla.r@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 17, 2011
PubMed
Summary
This summary is machine-generated.

Disordered random walks on self-similar substrates lose oscillations but retain subdiffusion. Introducing disorder selectively can localize these oscillations in time, with exponents and periods determined analytically and by simulation.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Random walks on self-similar substrates exhibit logarithmic-periodic oscillations.
  • These oscillations modulate the time behavior across all scales.

Purpose of the Study:

  • To investigate the effect of introducing disorder on these oscillations.
  • To determine if subdiffusion persists under averaged self-similarity.
  • To explore the localization of oscillations through controlled disorder distribution.

Main Methods:

  • Analytical derivation of random walk exponents and oscillation periods.
  • Monte Carlo simulations to confirm theoretical findings.
  • Modeling disorder in a way that preserves average self-similarity.

Main Results:

  • Disorder washes out oscillations when self-similarity is only averaged.
  • Subdiffusion behavior remains consistent with the perfectly self-similar case.
  • Oscillations can be localized to specific time intervals with appropriate disorder.

Conclusions:

  • Averaged self-similarity in disordered systems eliminates global oscillations while preserving subdiffusion.
  • The study provides analytical tools to predict random walk behavior and oscillation characteristics.
  • Controlled disorder offers a method to manipulate temporal dynamics in complex systems.