Abstract
We apply a new threshold detection method based on the extreme value theory (EVT) to the von Kármán sodium (VKS) experiment data. The VKS experiment is a successful attempt to get a dynamo magnetic field in a laboratory liquid-metal experiment. We first show that the dynamo threshold is associated with a change of the probability density function of the extreme values of the magnetic field. This method does not require the measurement of response functions from applied external perturbations and thus provides a simple threshold estimate. We apply our method to different configurations in the VKS experiment, showing that it yields a robust indication of the dynamo threshold as well as evidence of hysteretic behaviors. Moreover, for the experimental configurations in which a dynamo transition is not observed, the method provides a way to extrapolate an interval of possible threshold values.
Highlights
We apply our method to different configurations in the von Kármán sodium (VKS) experiment, showing that it yields a robust indication of the dynamo threshold as well as evidence of hysteretic behaviors
We suggest that the statistical approach based on the extreme value theory (EVT) proposed in [14] could provide a robust determination of the threshold even in the presence of turbulence
Applying our method to several different configurations, we show in the present article that it provides a robust indication of the dynamo threshold as well as evidence of hysteretic behaviors
Summary
We use the statistical approach based on the EVT proposed in [14] as a criterion allowing the determination of the dynamo threshold. The interest of the EVL statistics in bifurcation detection relies on the change of the nature of the fluctuations of a given system, when going from a situation with one stable attractor to a situation with two competing attractors, with a jump between the two allowed either under the effect of external noise or due to internal chaotic fluctuations. In such a case, two time scales are present: a short one related to transitive dynamics within an attracting component and a long one corresponding to intermittent jumps from one to the other component. Physical observables will display deviations of greater amplitude in the direction of the state the system is doomed to tumble— that is, the basin of attraction observed after the transition—than in, the opposite direction; one expects to observe this switching either in the maxima or in the minima
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
