Network structure of chaotic patterns

TL;DR

This paper models chaotic patterns in Rayleigh-Benard convection as a topological network of defects, analyzing their distribution, boundary effects, and interactions to understand pattern dynamics.

Contribution

It introduces a novel network-based approach to characterize and analyze defects in chaotic convection patterns, providing new insights into their spatial and temporal organization.

Findings

Defects follow an exponential distribution in edge length.

Boundary influence significantly affects defect dynamics.

A systematic method for studying defect hierarchies is proposed.

Abstract

We reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. We present statistics on the spatial and temporal distribution of defects within the state of spiral defect chaos state in experiments on Rayleigh Benard convection. These measure the role of boundary influence on the dynamics, and suggest an exponential distribution for the length of edges in the pattern. We also indicate a systematic method to study hierarchies of defect interactions based on the network structure.