de Castro C P, Luković M, Pompanin G, Andrade R F S, Herrmann H J
Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federacção, Salvador, BA, 40170-115, Brazil.
Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093, Zurich, Switzerland.
Sci Rep. 2018 Mar 27;8(1):5286. doi: 10.1038/s41598-018-23489-x.
Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated surfaces in the framework of Schramm-Loewner evolution (SLE). We show numerically that in the continuum limit the external perimeter of a percolating cluster of correlated surfaces with H ∈ [-1, 0] is statistically equivalent to SLE curves. Our results suggest that the external perimeter also retains the Markovian properties, confirmed by the absence of time correlations in the driving function and the fact that the latter is Gaussian distributed for any specific time. We also confirm that for all H the variance of the winding angle grows logarithmically with size.
鉴于许多物理景观具有由赫斯特指数H量化的长程高度-高度相关性这一事实，我们在施拉姆-洛厄纳演化（SLE）框架下研究相关曲面等高线的统计特性。我们通过数值计算表明，在连续极限下，赫斯特指数H∈[-1, 0]的相关曲面渗流簇的外周在统计上等同于SLE曲线。我们的结果表明，外周也保留了马尔可夫性质，这通过驱动函数中不存在时间相关性以及驱动函数在任何特定时间呈高斯分布这一事实得到证实。我们还证实，对于所有的H，缠绕角的方差随尺寸呈对数增长。
