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Relaxation processes in a system with logarithmic growth.

Mark O Brown1, Robert H Galyean1, Xiangwen Wang1

  • 1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2015
PubMed
Summary

This study explores coarsening and aging in ABC models, revealing logarithmic domain growth and distinct formation regimes. Dynamical scaling is observed in long-time behavior, with complex early-time effects.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Driven diffusive systems exhibit complex emergent behaviors.
  • Understanding relaxation and aging is crucial in many physical systems.

Purpose of the Study:

  • To investigate relaxation and aging dynamics in 1D and 2D ABC models.
  • To characterize the coarsening process and domain growth.
  • To identify different regimes in domain formation and evolution.

Main Methods:

  • Analysis of one- and two-dimensional ABC models.
  • Utilizing driven diffusive systems with biased particle exchanges.
  • Employing time-dependent length derived from spatial correlators.
  • Calculating mean particle displacement.
  • Examining two-time correlation and response functions.

Main Results:

  • Biased exchanges lead to coarsening with logarithmic domain growth in the long-time limit.
  • Ordered domains form as stripes.
  • Distinct regimes in domain formation and growth were identified.
  • Dynamical scaling observed in asymptotic logarithmic growth.
  • Complex finite-time and finite-size effects noted in early/intermediate regimes.

Conclusions:

  • The ABC model exhibits characteristic coarsening and aging phenomena.
  • Logarithmic growth and stripe formation are key features of long-time behavior.
  • Early and intermediate time dynamics are influenced by finite-time and size effects, requiring detailed analysis.