相关景观侵蚀海岸线的分形
Fractality of eroded coastlines of correlated landscapes
摘要：
使用一个简单的海洋海岸机械侵蚀模型的数值模拟，我们调查的影响，在相应的海岸线上的分形行为的岩性的海岸景观的空间长程相关性。在该模型中，海岸段的抗侵蚀性取决于当地的岩性配置以及相邻的海岸的数量。对于弱的海上力量，海洋被海岸线困住，侵蚀过程在一段时间后停止。因为强大的海上力量，侵蚀是永久性的。这两种制度之间的过渡发生在一个关键的海上力量，其特征在于分形海岸线前。对于不相关的景观，我们得到，在临界值，分形维数D=1.33，这是一致的，在二维渗流的跨越集群的可访问的外部周长的尺寸。对于临界值以上的海力，我们的结果表明，海岸线是自仿射的，属于Kardar-Parisi-Zhang普适类。在幂律空间长程相关的景观的情况下，海岸线的分形维数不断变化的赫斯特指数H，从D=1.34下降到1.04，H=0和1，分别。这种非普遍的行为是兼容的众多分形维数发现真正的海岸线。
英文摘要：
Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
