Generality of Deterministic Chaos, Exponential Spectra, and Lorentzian Pulses in Magnetically Confined Plasmas

Maggs, J. E.; Morales, G. J.

doi:10.1103/physrevlett.107.185003

Cited by 49 publications

(74 citation statements)

References 24 publications

(26 reference statements)

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“…Also in the IBC case, the log-linear plot of hj/ðk y Þj 2 i t shows the hint of an exponentially decaying scaling with k y , which has been seen in other experiments and simulations, 11,29 and attributed to the presence of coherent structures. 30,31 We conclude that both the frequency and the wavenumber spectra show the characteristics of the nonlinear cascade in the IBC case. The peak value of k y can be compared in the simulation and the experiment.…”

Section: A Basic Propertiesmentioning

confidence: 88%

Effect of parallel currents on drift-interchange turbulence: Comparison of simulation and experiment

et al. 2012

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Two-dimensional (2D) turbulence simulations are reported in which the balancing of the parallel and perpendicular currents is modified by changing the axial boundary condition (BC) to vary the sheath conductivity. The simulations are carried out using the 2D scrape-off-layer turbulence (SOLT) code. The results are compared with recent experiments on the controlled shear de-correlation experiment (CSDX) in which the axial BC was modified by changing the composition of the end plate. Reasonable qualitative agreement is found between the simulations and the experiment. When an insulating axial BC is used, broadband turbulence is obtained and an inverse cascade occurs down to low frequencies and long spatial scales. Robust sheared flows are obtained. By contrast, employing a conducting BC at the plate resulted in coherent (drift wave) modes rather than broadband turbulence, with weaker inverse cascade, and smaller zonal flows. The dependence of the two instability mechanisms (rotationally driven interchange mode and drift waves) on the axial BC is also discussed.

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Section: A Basic Propertiesmentioning

confidence: 88%

Effect of parallel currents on drift-interchange turbulence: Comparison of simulation and experiment

et al. 2012

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“…(The conjectured bound would instead imply λ L ≤ πω 0 .) In numerous classical systems, the power spectrum decay of time series has been used as an empirical probe of deterministic chaos [57][58][59][60][61][62][63]. To the best of our knowledge, the bound (44) provides the first quantitative justification for this usage.…”

Section: A (Weaker) Bound On Classical Chaosmentioning

confidence: 99%

A Universal Operator Growth Hypothesis

et al. 2019

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We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate α in generic systems, with an extra logarithmic correction in 1d. The rate α -an experimental observable -governs the exponential growth of operator complexity in a sense we make precise. This exponential growth prevails beyond semiclassical or large-N limits. Moreover, α upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents λL ≤ 2α, which complements and improves the known universal low-temperature bound λL ≤ 2πT . We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants. CONTENTS

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“…It is important to note that an exponential behaviour for the PSD is usually associated with deterministic chaotic systems (see e.g. [Maggs & Morales, 2011] and references therein) which indicates that the gKS solution is clearly chaotic for small values of δ. For δ = 0.4 multiple peaks appear (2f m , 3f m , 4f m .…”

Section: Power Spectral Densitymentioning

confidence: 99%

Nonlinear Forecasting of the Generalized Kuramoto–Sivashinsky Equation

Gotoda

Pradas

Kalliadasis

2015

Int. J. Bifurcation Chaos

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We study the emergence of pattern formation and chaotic dynamics in the one-dimensional (1D) generalized Kuramoto-Sivashinsky (gKS) equation by means of a time-series analysis, in particular a nonlinear forecasting method which is based on concepts from chaos theory and appropriate statistical methods. We analyze two types of temporal signals, a local one and a global one, finding in both cases that the dynamical state of the gKS solution undergoes a transition from high-dimensional chaos to periodic pulsed oscillations through low-dimensional deterministic chaos with increasing the control parameter of the system. Our results demonstrate that the proposed nonlinear forecasting methodology allows to elucidate the dynamics of the system in terms of its predictability properties.

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Generality of Deterministic Chaos, Exponential Spectra, and Lorentzian Pulses in Magnetically Confined Plasmas

Cited by 49 publications

References 24 publications

Effect of parallel currents on drift-interchange turbulence: Comparison of simulation and experiment

Effect of parallel currents on drift-interchange turbulence: Comparison of simulation and experiment

A Universal Operator Growth Hypothesis

Nonlinear Forecasting of the Generalized Kuramoto–Sivashinsky Equation

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