Unusual synchronization phenomena during electrodissolution of silicon: the role of nonlinear global coupling

TL;DR

This paper investigates complex spatio-temporal patterns, including chimera states, during silicon electrodissolution, highlighting the role of nonlinear global coupling in modeling these phenomena with the complex Ginzburg-Landau equation.

Contribution

It introduces a nonlinear global coupling into the complex Ginzburg-Landau equation to accurately model experimentally observed patterns in silicon electrodissolution.

Findings

Nonlinear global coupling explains pattern formation.

Simulations match experimental dynamics.

Spatially averaged oxide-layer oscillations are nearly harmonic.

Abstract

The photoelectrodissolution of n-type silicon constitutes a convenient model system to study the nonlinear dynamics of oscillatory media. On the silicon surface, a silicon oxide layer forms. In the lateral direction, the thickness of this layer is not uniform. Rather, several spatio-temporal patterns in the oxide layer emerge spontaneously, ranging from cluster patterns and turbulence to quite peculiar dynamics like chimera states. Introducing a nonlinear global coupling in the complex Ginzburg-Landau equation allows us to identify this nonlinear coupling as the essential ingredient to describe the patterns found in the experiments. The nonlinear global coupling is designed in such a way, as to capture an important, experimentally observed feature: the spatially averaged oxide-layer thickness shows nearly harmonic oscillations. Simulations of the modified complex Ginzburg-Landau equation capture the experimental dynamics very well.