Kardar-Parisi-Zhang Asymptotics for the Two-Dimensional Noisy Kuramoto-Sivashinsky Equation Articles uri icon

publication date

  • October 2010

start page

  • 45202

issue

  • 4, Pt 2

volume

  • 82

International Standard Serial Number (ISSN)

  • 1539-3755

Electronic International Standard Serial Number (EISSN)

  • 1539-3755

abstract

  • We study numerically the Kuramoto-Sivashinsky equation forced by external white noise in two space dimensions, that is a generic model for, e.g., surface kinetic roughening in the presence of morphological
    instabilities. Large scale simulations using a pseudospectral numerical
    scheme allow us to retrieve Kardar-Parisi-Zhang (KPZ) scaling as the
    asymptotic state of the system, as in the one-dimensional (1D) case.
    However, this is only the case for sufficiently large values of the
    coupling and/or system size, so that previous conclusions on non-KPZ
    asymptotics are demonstrated as finite size effects. Crossover effects
    are comparatively stronger for the two-dimensional case than for the 1D
    system.