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Relaxation after a change in the interface growth dynamics.

T A de Assis1, F D A Aarão Reis2

  • 1Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115, Salvador, BA, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 15, 2014
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Summary

Sudden changes in interface growth dynamics were studied for Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) models. The research predicts how interface roughness changes over time after such dynamic shifts, offering insights into surface smoothing.

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Area of Science:

  • Surface growth dynamics
  • Statistical physics
  • Condensed matter physics

Background:

  • Interface growth models like Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) are crucial for understanding various physical phenomena.
  • Sudden changes in growth dynamics can significantly alter surface properties, but their effects are not fully understood.

Purpose of the Study:

  • To investigate the global effects of abrupt changes in interface growth dynamics.
  • To develop predictive models for the relaxation of interface roughness after dynamic shifts.
  • To analyze these effects in one and two dimensions for EW and KPZ models.

Main Methods:

  • Combined scaling arguments and simulation results to analyze interface roughness relaxation.
  • Reviewed analytical solutions for EW-EW dynamics and numerically discussed them in lattice models.
  • Predicted scaling laws for KPZ-KPZ dynamics and analyzed crossovers between different dynamics (KPZ-EW).

Main Results:

  • Predicted relaxation of interface roughness difference as ΔW²∼sᶜt⁻<0xC9><0x83>, with specific exponents for EW-EW and KPZ-KPZ changes.
  • Observed good agreement between predicted scaling and simulation results in d=1 and d=2.
  • Ruled out a simplified time shift hypothesis for KPZ-EW changes in d=2, identifying a crossover time and different scaling behavior.

Conclusions:

  • The study provides a framework for understanding how sudden changes in growth dynamics affect interface roughness.
  • Results offer insights into differences in surface smoothing for correlated and uncorrelated surfaces.
  • The approach can be extended to analyze sudden transitions between other interface growth dynamics.