Evidence for Geometry-Dependent Universal Fluctuations of the Kardar-Parisi-Zhang Interfaces in Liquid-Crystal Turbulence
Evidence for Geometry-Dependent Universal Fluctuations of the Kardar-Parisi-Zhang Interfaces in Liquid-Crystal Turbulence
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DOI：
10.1007/s10955-012-0503-0
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发表时间：
2012-03
影响因子：
1.6
通讯作者：
K. Takeuchi;M. Sano
中科院分区：
文献类型：
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作者：
K. Takeuchi;M. Sano
我们提供了一个全面的报告尺度不变的波动生长界面的液晶湍流，我们最近发现的证据表明，他们属于Kardar-Parisi-Zhang（KPZ）的普适性类为1+1维[竹内和佐野在物理。104：230601，2010; Takeuchi等人，Sci. 1：34，2011]。在这里，我们调查了圆形和平面接口，并详细报告了它们的统计数据。首先，我们证明，他们的波动不仅显示KPZ标度指数，但超越：他们渐近共享，甚至精确的形式的分布函数和空间相关函数共同可解模型的KPZ类，也展示了一个密切的关系，随机矩阵理论。然后，我们确定其他统计特性，没有确切的理论预测，特别是时间相关函数和持久性概率。有限时间效应和极值统计的实验结果。在整个文件中，重点放在如何普遍的统计性质取决于全球几何的接口，即，无论界面是圆形的还是平面的。因此，我们证实了强大的几何依赖的普遍性KPZ类，它管理着不断增长的接口驱动的平衡。
We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1 dimensions [Takeuchi and Sano in Phys. Rev. Lett. 104:230601, 2010; Takeuchi et al. in Sci. Rep. 1:34, 2011]. Here we investigate both circular and flat interfaces and report their statistics in detail. First we demonstrate that their fluctuations show not only the KPZ scaling exponents but beyond: they asymptotically share even the precise forms of the distribution function and the spatial correlation function in common with solvable models of the KPZ class, demonstrating also an intimate relation to random matrix theory. We then determine other statistical properties for which no exact theoretical predictions were made, in particular the temporal correlation function and the persistence probabilities. Experimental results on finite-time effects and extreme-value statistics are also presented. Throughout the paper, emphasis is put on how the universal statistical properties depend on the global geometry of the interfaces, i.e., whether the interfaces are circular or flat. We thereby corroborate the powerful yet geometry-dependent universality of the KPZ class, which governs growing interfaces driven out of equilibrium.