2022/10/18 by van Kan, Adrian, Pétrélis, François
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2210.10197
On-off intermittency occurs in nonequilibrium physical systems close to bifurcation points and is characterised by an aperiodic switching between a large-amplitude "on" state and a small-amplitude "off" state. Lévy on-off intermittency is a recently introduced generalisation of on-off intermittency to multiplicative Lévy noise, which depends on a stability parameter α and a skewness parameter β. Here, we derive two novel results on Lévy on-off intermittency by leveraging known exact results on the first-passage time statistics of Lévy flights. First, we compute anomalous critical exponents explicitly as a function of arbitrary Lévy noise parameters (α,β) for the first time, by a heuristic method, complementing previous results. The predictions are verified using numerical solutions of the fractional Fokker-Planck equation. Second, we derive the power spectrum S(f) of Lévy on-off intermittency and show that it displays a power law S(f)∝ fκ at low frequencies f, where κ∈ (-1,0) depends on the noise parameters α,β. An explicit expression for κ is obtained in terms of (α,β). The predictions are verified using long time series realisations of Lévy on-off intermittency. Our findings help shed light on instabilities subject to non-equilibrium, power-law-distributed fluctuations, emphasizing that their properties can differ starkly from the case of Gaussian fluctuations.