Irregular Liesegang-type patterns in gas phase revisited. II. Statistical correlation analysis.

Area of Science:

• Chemical Physics
• Statistical Mechanics
• Pattern Formation

Background:

• Liesegang-type patterns are complex precipitation phenomena.
• Previous work established a gaseous HCl-NH3 system for ammonium chloride precipitation.
• The non-stationary nature of these patterns suggests underlying correlations.

Purpose of the Study:

• To statistically analyze spatial correlations in Liesegang-type patterns.
• To characterize short and long-range correlations in precipitation bands.
• To investigate the nature of these correlations using advanced analytical techniques.

Main Methods:

• Linear auto-correlation via power spectral density.
• Detrended Fluctuation Analysis (DFA).
• Random Matrix Theory (RMT) methods.

Main Results:

• Random Matrix Theory methods revealed pronounced long-range correlations (over at least 40 bands) in band positions and intensities.
• A variant of Detrended Fluctuation Analysis provided evidence for the nonlinear nature of these long-range correlations.

Conclusions:

• The study demonstrates the presence of significant long-range, nonlinear correlations in gaseous ammonium chloride precipitation patterns.
• These findings contribute to understanding complex pattern formation in chemical systems.
• Advanced statistical methods like RMT and DFA are effective tools for analyzing such complex phenomena.