Homological Characterizations of Spiral Defect Chaos in Rayleigh-Benard Convection

TL;DR

This paper introduces a topological method to analyze complex patterns in Rayleigh-Benard convection, revealing structural differences and ergodic behavior in spiral defect chaos that traditional statistics miss.

Contribution

It presents a novel homological approach to characterize and distinguish attractors in turbulent convection patterns, uncovering new insights into their geometric and dynamic properties.

Findings

Different attractors distinguished by homology

Pattern asymmetries detected beyond statistical measures

Global stochastic ergodicity observed in certain parameters

Abstract

We use a quantitative topological characterization of complex dynamics to measure geometric structures. This approach is used to analyze the weakly turbulent state of spiral defect chaos in experiments on Rayleigh-Benard convection. Different attractors of spiral defect chaos are distinguished by their homology. The technique reveals pattern asymmetries that are not revealed using statistical measures. In addition we observe global stochastic ergodicity for system parameter values where locally chaotic dynamics has been observed previously.