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

“…Here P(F) is the power corresponding to the modified frequency F = f − f 0 , where f indicates the frequency of oscillations, f 0 is the frequency corresponding to the dominant peak in the power spectrum, and P 0 := P(f 0 ). A universal scaling relationship relating the normalized amplitude A/A I of the dominant mode of oscillations and the spectral measure µ has been obtained from experiments as A ∝ µ −0.66±0.10 [37]. In figure 3 the normalized amplitude of the dominant Fourier mode is plotted as a function of the spectral measure µ for the ensemble of time series obtained from the GCGLE model (equations ( 1)-( 3)).…”

“…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.…”

“…Furthermore, a transition of power spectra from a broad peak to a sharp one is obtained as the onset of the OI is approached [37]. Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced.…”

“…Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced. They are calculated as the product of different moments of the normalized power spectrum raised to integer powers, and they follow inverse power law relations with the corresponding peak power [37]. The most prominent spectral measure µ is defined as…”

Universality of oscillatory instabilities in fluid mechanical systems

“…Here P(F) is the power corresponding to the modified frequency F = f − f 0 , where f indicates the frequency of oscillations, f 0 is the frequency corresponding to the dominant peak in the power spectrum, and P 0 := P(f 0 ). A universal scaling relationship relating the normalized amplitude A/A I of the dominant mode of oscillations and the spectral measure µ has been obtained from experiments as A ∝ µ −0.66±0.10 [37]. In figure 3 the normalized amplitude of the dominant Fourier mode is plotted as a function of the spectral measure µ for the ensemble of time series obtained from the GCGLE model (equations ( 1)-( 3)).…”

“…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.…”

“…Furthermore, a transition of power spectra from a broad peak to a sharp one is obtained as the onset of the OI is approached [37]. Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced.…”

“…Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced. They are calculated as the product of different moments of the normalized power spectrum raised to integer powers, and they follow inverse power law relations with the corresponding peak power [37]. The most prominent spectral measure µ is defined as…”

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.…”

Universality of oscillatory instabilities in fluid mechanical systems

“…Here P(F) is the power corresponding to the modified frequency F = f − f 0 , where f indicates the frequency of oscillations, f 0 is the frequency corresponding to the dominant peak in the power spectrum, and P 0 := P(f 0 ). A universal scaling relationship relating the normalized amplitude A/A I of the dominant mode of oscillations and the spectral measure µ has been obtained from experiments as A ∝ µ −0.66±0.10 [37]. In figure 3 the normalized amplitude of the dominant Fourier mode is plotted as a function of the spectral measure µ for the ensemble of time series obtained from the GCGLE model (equations ( 1)-( 3)).…”

“…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.…”

“…Furthermore, a transition of power spectra from a broad peak to a sharp one is obtained as the onset of the OI is approached [37]. Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced.…”

“…Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced. They are calculated as the product of different moments of the normalized power spectrum raised to integer powers, and they follow inverse power law relations with the corresponding peak power [37]. The most prominent spectral measure µ is defined as…”

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.…”

Universality of oscillatory instabilities in fluid mechanical systems

“…Here P(F) is the power corresponding to the modified frequency F = f − f 0 , where f indicates the frequency of oscillations, f 0 is the frequency corresponding to the dominant peak in the power spectrum, and P 0 := P(f 0 ). A universal scaling relationship relating the normalized amplitude A/A I of the dominant mode of oscillations and the spectral measure µ has been obtained from experiments as A ∝ µ −0.66±0.10 [37]. In figure 3 the normalized amplitude of the dominant Fourier mode is plotted as a function of the spectral measure µ for the ensemble of time series obtained from the GCGLE model (equations ( 1)-( 3)).…”

“…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.…”

“…Furthermore, a transition of power spectra from a broad peak to a sharp one is obtained as the onset of the OI is approached [37]. Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced.…”

“…Spectral measures which quantify the sharpening of peaks in the power spectrum have been introduced. They are calculated as the product of different moments of the normalized power spectrum raised to integer powers, and they follow inverse power law relations with the corresponding peak power [37]. The most prominent spectral measure µ is defined as…”

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.…”