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Pseudospectral approach to inverse problems in interface dynamics.

A Giacometti1, M Rossi

  • 1INFM, Unitá di Venezia, Dipartimento di Chimica Fisica, Universitá di Venezia, Calle Larga Santa Marta DD 2137, I-30123 Venice, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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A new spectral method accurately computes Kardar-Parisi-Zhang equation coupling parameters from interface profiles. This approach improves upon real-space methods for analyzing growth models.

Area of Science:

  • Physics
  • Materials Science
  • Computational Science

Background:

  • The Kardar-Parisi-Zhang (KPZ) equation describes driven interfaces and surface growth.
  • Accurate computation of KPZ coupling parameters is crucial for understanding growth dynamics.
  • Existing real-space methods for parameter extraction have limitations.

Purpose of the Study:

  • To present an improved spectral method for calculating KPZ equation coupling parameters.
  • To validate the method using simulated and microscopic growth models.
  • To compare the new technique with existing real-space approaches.

Main Methods:

  • A spectral representation of the Kardar-Parisi-Zhang equation is employed.
  • An appropriate Fourier-based discretization scheme is developed.

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  • The method is tested on 1D KPZ-generated profiles and microscopic growth models.

    • Main Results:

    • The spectral method accurately reproduces input coupling parameters for 1D KPZ simulations.
    • Parameter values are successfully extracted for microscopic growth models.
    • The technique demonstrates favorable comparison against established real-space schemes.

    Conclusions:

    • The presented spectral approach offers a robust and accurate way to compute KPZ coupling parameters.
    • This method provides a valuable tool for analyzing surface growth phenomena.
    • The Fourier-based discretization is an effective byproduct of the spectral scheme.