Pseudospectral method for the Kardar-Parisi-Zhang equation.
نویسندگان
چکیده
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudospectral approximation of the nonlinear term. The method is tested in (1+1) and (2+1) dimensions, where it is shown to reproduce the current most reliable estimates of the critical exponents based on restricted solid-on-solid simulations. In particular, it allows the computations of various correlation and structure functions with high degree of numerical accuracy. Some deficiencies that are common to all previously used finite-difference schemes are pointed out and the usefulness of the present approach in this respect is discussed.
منابع مشابه
Pseudospectral approach to inverse problems in interface dynamics.
An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dime...
متن کاملKardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation.
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-dime...
متن کاملMinimum action method for the Kardar-Parisi-Zhang equation.
We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for the height profile of a growing interface. In one dimension we find that the transition pathway between different height configurations is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls ...
متن کاملImproved discretization of the Kardar-Parisi-Zhang equation
We propose a spatial discretization of the Kardar-Parisi-Zhang ~KPZ! equation in 111 dimensions. The exact steady state probability distribution of the resulting discrete surfaces is explained. The effective diffusion coefficient, nonlinearity, and noise strength can be extracted from three correlators, and are shown to agree exactly with the nominal values used in the discrete equations. Impli...
متن کاملA Modified Kardar–parisi–zhang Model
A one dimensional stochastic differential equation of the form dX = AXdt+ 1 2 (−A) ∂ξ[((−A)X)]dt+ ∂ξdW (t), X(0) = x is considered, where A = 1 2∂ 2 ξ . The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar–Parisi–Zhang model. For α 6= 0, this equation conserves two important properties of the Kardar–Parisi–Zhang model: it contains a quadratic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 65 3 Pt 2A شماره
صفحات -
تاریخ انتشار 2002