Anomalous exponents at the onset of an instability

Abstract

Critical exponents are calculated exactly at the onset of an instability, using asymptotic expansiontechniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous, i.e. the mode amplitude X scales with departure from onset μas $<X>{\mu }^{\beta }$ with an exponent $\beta$ different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability and our results provide a possible explanation to recent experimental observations.

References in corpus (5)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Directed percolation criticality in turbulent liquid crystals
• On the magnetic fields generated by experimental dynamos
• Low frequency noise controls on-off intermittency of bifurcating systems
• Nonlinear dynamos at infinite magnetic Prandtl number

Cited by in corpus (4)

• Lévy on-off intermittency
• Intermittency of three-dimensional perturbations in a point-vortex model
• Critical exponents in zero dimensions
• Decay rates of magnetic modes below the threshold of a turbulent dynamo