Universality in spectral condensation

Abstract

Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.

Universality of oscillatory instabilities in fluid mechanical systems

“…Recently, it was reported that the amplitude A of the dominant mode of oscillations increases and follows a universal scaling law A ∝ H −2.0±0.2 [15]. A spectral measure µ, which quantifies the sharpening of peaks in the power spectrum as the system dynamics approaches OI, has also been introduced and another universal scaling law A ∝ µ −0.66±0.10 [37,38] has been discovered. In both cases, the scaling exponents are invariant across aero-acoustic, thermoacoustic and aeroelastic systems.…”

Critical transitions and their early warning signals in thermoacoustic systems

“…Furthermore, the transition to oscillatory instability via intermittency follows universal scaling behaviours across different turbulent fluid mechanical systems [45,46]. These scaling behaviours during the emergence of oscillatory instabilities are elaborated in Sect.…”

“…The transition from stable operating conditions to thermoacoustic instability is viewed as the emergence of ordered patterns from a disordered state. This transition is often accompanied by a phenomenon known as spectral condensation [46], which is the sharpening and the amplification of the peak corresponding to the dominant mode of oscillations in the power spectrum. During the transition, the energy distributed over a wide range of frequencies gets condensed into the dominant frequency of oscillations.…”

“…To describe the common behaviour observed during the transition in such disparate systems, Pavithran et al [45,46] used Hurst exponent and spectral measures. We notice that this transition follows a universal scaling relation between the Hurst exponent and the amplitude of the dominant mode, A ∝ H −2 , in turbulent thermoacoustic, aeroacoustic, and aeroelastic systems (Fig.…”

“…b The universal power law scaling relation across different systems are shown and power law exponent k is noted for each system. Reproduced from Pavithran et al[46]…”