Fractional Stochastic Loewner Evolution and Scaling Curves
Fractional Stochastic Loewner Evolution and Scaling Curves
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分数随机 Loewner 演化和缩放曲线
DOI：
10.1016/j.physa.2022.127309
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
M. G. Nezhadhaghighi
中科院分区：
文献类型：
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作者：
M. G. Nezhadhaghighi
在二维统计力学中，由Oded Schramm引入的随机Loewner方程提供了一种强大的技术来研究和分类临界随机曲线和界面。首次提出了一种新的随机Loewner方程，称为分数阶随机Loewner演化（FSLE）。我们引入了广泛的一类分形曲线使用分数时间序列作为驱动函数的Loewner方程和局部分数积分微分算子。我们认为，除了分形维数估计，赫斯特指数的驱动函数导致FSLE曲线的显着差异。这种修改引入了一种新的方法来分类不同类型的缩放曲线的基础上的赫斯特指数的驱动功能。这种形式化似乎是适当的研究范围广泛的二维曲线中看到的统计力学和自然现象。
In two-dimensional statistical mechanics, the Stochastic Loewner equation, introduced by Oded Schramm, provides a powerful technique to study and categorize critical random curves and interfaces. For the first time, a new type of stochastic Loewner equation entitled fractional stochastic Loewner evolution (FSLE) has been proposed. We introduce a wide class of fractal curves using the fractional time series as the driving function of the Loewner equation and local fractional integrodifferential operators. We suggest that, in addition to fractal dimension estimations, the Hurst index of the driving function leads significant differences in the FSLE curves. This modification introduces a new approach to categorize different types of scaling curves based on the Hurst index of the driving function. Such formalizations appear to be appropriate for studying a wide range of two-dimensional curves seen in statistical mechanics and natural phenomena.