Pattern generation by dissipative parametric instability

TL;DR

This paper introduces a novel dissipative parametric instability mechanism that induces pattern formation in nonlinear systems through periodic spectral loss modulation, differing from classical instabilities like Benjamin-Feir and Faraday.

Contribution

It proposes a new instability mechanism based on spectral loss modulation, expanding understanding of pattern formation in nonlinear systems.

Findings

Demonstrates stable pattern formation in 1D and 2D systems

Shows the mechanism differs from classical modulation instabilities

Highlights the generic applicability of the instability

Abstract

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems based on a periodic antiphase modulation of spectrally-dependent losses arranged in a zig-zag way: an effective filtering is imposed at symmetrically located wavenumbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of the both key classical concepts of modulation instabilities: the Benjamin-Feir, and the Faraday instability. We demonstrate how dissipative parametric instability can lead to the formation of stable patterns in one and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.