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Related Experiment Videos

Stochastic growth models for driven interfaces through random media in two and three dimensions.

Hyun-Joo Kim1, Kwangho Park, In-mook Kim

  • 1Department of Physics, Korea University, Seoul, 136-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
Summary

We developed two stochastic growth models for interface motion in random media. Computer simulations confirm these models align with the quenched Edwards-Wilkinson and quenched Kardar-Parisi-Zhang universality classes in 2D and 3D.

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Area of Science:

  • Physics
  • Materials Science
  • Complex Systems

Background:

  • Interface dynamics in random media are crucial for understanding phenomena like diffusion and pattern formation.
  • Existing models often simplify the complexities of anisotropic and isotropic media.

Purpose of the Study:

  • To introduce and analyze two novel stochastic growth models for interface motion.
  • To investigate interface dynamics in both isotropic and anisotropic random media.
  • To classify the universality classes of these models in two and three dimensions.

Main Methods:

  • Development of two distinct stochastic growth models.
  • Utilizing computer simulations to observe interface behavior.
  • Analysis of simulation data to determine universality classes.

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Main Results:

  • One model accurately describes interface motion in isotropic media, aligning with the quenched Edwards-Wilkinson (QEW) equation.
  • The second model captures interface dynamics in anisotropic media, corresponding to the quenched Kardar-Parisi-Zhang (QKPZ) equation.
  • Simulations confirm the 2D and 3D universality classes for the respective models.

Conclusions:

  • The proposed models provide a robust framework for studying interface dynamics in random environments.
  • The findings validate the applicability of QEW and QKPZ equations in specific random media conditions.
  • This work contributes to the understanding of scaling behaviors in complex systems.