Nicoli Matteo, Vivo Edoardo, Cuerno Rodolfo
Laboratoire de Physique de la Matière Condensée, École Polytechnique-CNRS, 91128 Palaiseau, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Oct;82(4 Pt 2):045202. doi: 10.1103/PhysRevE.82.045202. Epub 2010 Oct 21.
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.
我们对二维空间中由外部白噪声驱动的Kuramoto-Sivashinsky方程进行了数值研究，该方程是例如存在形态不稳定性时表面动力学粗糙化的一个通用模型。使用伪谱数值格式进行的大规模模拟使我们能够像在一维（1D）情况下一样，将Kardar-Parisi-Zhang（KPZ）标度作为系统的渐近状态恢复出来。然而，这仅在耦合和/或系统尺寸足够大时成立，因此之前关于非KPZ渐近性的结论被证明是有限尺寸效应。二维情况的交叉效应比一维系统的交叉效应相对更强。
