Small-scale Induced Large-scale Transitions in Solar Wind Magnetic Field

Alberti, Tommaso; Faranda, Davide; Donner, Reik V.; Caby, Théophile; Carbone, Vincenzo; Consolini, Giuseppe; Dubrulle, Bérengère; Vaienti, Sandro

doi:10.3847/2041-8213/ac0148

Cited by 8 publications

(4 citation statements)

References 46 publications

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“…As for d, since we can explore all states ζ (i.e., all time instants), an instantaneous view of the residence time of the system into the different states is obtained. The instantaneous dimension d and the extremal index θ allow one to provide novel insights and an innovative view of extreme phenomena into different fields as transient events in the atmospheric circulation [37][38][39][40], in the ocean dynamics [41], transient disturbances of the geomagnetic field due to geomagnetic storms and magnetospheric substorms [16], localized energy transfers in hydrodynamic [42] and magnetohydrodynamic [43] turbulence and earthquake dynamics [44,45].…”

Section: Methodsmentioning

confidence: 99%

Tracking Geomagnetic Storms with Dynamical System Approach: Ground-Based Observations

et al. 2023

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Using a dynamical systems approach, we examine the persistence and predictability of geomagnetic perturbations across a range of different latitudes and levels of geomagnetic activity. We look at the horizontal components of the magnetic field measured on the ground between 13 and 24 March 2015, at approximately 40 observatories in the Northern Hemisphere. We introduced two dynamical indicators: the extremal index θ, which quantifies the persistence of the system in a particular state and the instantaneous dimension d, which measures the active number of degrees of freedom of the system. The analysis revealed that during disturbed periods, the instantaneous dimension of the horizontal strength of the magnetic field, which depends on latitude, increases, indicating that the geomagnetic response is externally driven. Furthermore, during quiet times, the instantaneous dimension values fluctuate around the state-space dimension, indicating a more stochastic and thus less predictable nature system.

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Section: Methodsmentioning

confidence: 99%

Tracking Geomagnetic Storms with Dynamical System Approach: Ground-Based Observations

et al. 2023

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“…Firstly, it should have a clear scale separation in time, that is, one should be able to distinguish a time scale gap between two (or more) phenomena in the dynamics, as, for instance, in standard fast-slow systems. Scale separation can be estimated in several different ways, depending on the availability of data and on the existence of differential equations to describe the dynamics [24][25][26][27] . Secondly, the system needs a (near-)neutral direction along trajectories which is invariant under the linear(ized) dynamics: indeed, if the system does not have any neutral direction, the angle θ is no longer a relevant quantity to evaluate the stability of a state.…”

Section: Observations and Guidelinesmentioning

confidence: 99%

Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors

Viennet¹,

Vercauteren²,

Engel³

et al. 2022

Preprint

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We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The underlying models are built from data by the dynamical clustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximated based on these models. We test this data-based numerical approach at the hand of three well-understood example systems with increasing dynamical complexity, identifying crucial properties that allow for a successful application of the method: in particular, it turns out that the method requires a clear multiple time scale structure with fast transitions between slow subsystems which can be dynamically characterized by invariant neutral directions of the linear approximation model.

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“…Firstly, (a) it should have a clear scale separation in time, that is, one should be able to distinguish a time scale gap between two (or more) phenomena in the dynamics, as, for instance, in standard fast-slow systems. Scale separation can be estimated in several different ways, depending on the availability of data and on the existence of differential equations to describe the dynamics [28][29][30][31] . Secondly, (b)…”

Section: Observations and Guidelinesmentioning

confidence: 99%

Guidelines for data-driven approaches to study transitions in multiscale systems: The case of Lyapunov vectors

Viennet¹,

Vercauteren

Engel³

et al. 2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This study investigates the use of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric sciences applications. In a first step, the needed underlying dynamical models are derived from data using a non-parametric model-based clustering framework. The covariant Lyapunov vectors are then approximated based on these data-driven models. The data-based numerical approach is tested using three well-understood example systems with increasing dynamical complexity, identifying properties that allow for a successful application of the method: in particular, the method is identified to require a clear multiple time scale structure with fast transitions between slow subsystems. The latter slow dynamics should be dynamically characterized by invariant neutral directions of the linear approximation model.

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Small-scale Induced Large-scale Transitions in Solar Wind Magnetic Field

Cited by 8 publications

References 46 publications

Tracking Geomagnetic Storms with Dynamical System Approach: Ground-Based Observations

Tracking Geomagnetic Storms with Dynamical System Approach: Ground-Based Observations

Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors

Guidelines for data-driven approaches to study transitions in multiscale systems: The case of Lyapunov vectors

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