Torres-Guzmán José C, Martínez-Mekler Gustavo, Müller Markus F
Centro de Investigación en Ciencias, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001, 62209 Cuernavaca, Morelos, Mexico.
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Mexico.
J Chem Phys. 2016 May 7;144(17):174702. doi: 10.1063/1.4946792.
We present a statistical analysis of Liesegang-type patterns formed in a gaseous HCl-NH3 system by ammonium chloride precipitation along glass tubes, as described in Paper I [J. C. Torres-Guzmán et al., J. Chem. Phys. 144, 174701 (2016)] of this work. We focus on the detection and characterization of short and long-range correlations within the non-stationary sequence of apparently irregular precipitation bands. To this end we applied several techniques to estimate spatial correlations stemming from different fields, namely, linear auto-correlation via the power spectral density, detrended fluctuation analysis (DFA), and methods developed in the context of random matrix theory (RMT). In particular RMT methods disclose well pronounced long-range correlations over at least 40 bands in terms of both, band positions and intensity values. By using a variant of the DFA we furnish proof of the nonlinear nature of the detected long-range correlations.
如本研究的第一篇论文[J. C. 托雷斯 - 古兹曼等人，《化学物理杂志》144, 174701 (2016)]所述，我们对气态HCl - NH₃系统中沿玻璃管氯化铵沉淀形成的李泽冈型图案进行了统计分析。我们专注于检测和表征明显不规则沉淀带的非平稳序列中的短程和长程相关性。为此，我们应用了几种技术来估计源自不同领域的空间相关性，即通过功率谱密度的线性自相关、去趋势波动分析（DFA）以及在随机矩阵理论（RMT）背景下开发的方法。特别是，RMT方法在带位置和强度值方面都揭示了至少40个带的明显长程相关性。通过使用DFA的一种变体，我们提供了检测到的长程相关性非线性性质的证据。
