A Coupled Map Lattice model for geomagnetic polarity reversals that exhibits realistic scaling

Seki, Masayuki; Ito, Keisuke

doi:10.1186/bf03352243

Cited by 5 publications

(5 citation statements)

References 22 publications

(30 reference statements)

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“…A similar physical model, the Rikitake disk dynamo (Rikitake 1958, Seki & Ito 1999 has been favored to explain the statistical distribution of Earth's magnetic field reversals. Under certain parameter ranges, this system of equations has been shown to undergo "Lorenz-type" nonlinear evolution, with projections of the flow onto two-dimensional phase space planes showing two regions organizing the flow (McMillen 1999).…”

Section: Disk Magnetic Fieldsmentioning

confidence: 99%

The Long‐Term Light Curves of X‐Ray Binaries Contain Simultaneous Periodic and Random Components

Boyd

Smale

2004

ApJ

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LMC X-3 and Cyg X-2 show large amplitude X-ray fluctuations that have been attributed to a warped accretion disk. Cyg X-3 displays high amplitude, apparently nonperiodic oscillations. We reanalyze these systems using RXTE ASM data and timefrequency decomposition techniques. We find that the long-term variations in Cyg X-2 can be completely characterized by excursions whose durations are integer multiples of the orbital period, including one essentially identical to the reported "period" of 78 days. Cyg X--3 can be characterized in terms of integer multiples of a 71-day fundamental period, unrelated to the 4.8 day orbital period, but suggestively close to the 2 60 day reported precession period of the relativistic jet inferred from recent radio observations. The long-term excursions of LMC X-3 are related to each other by rational fractions, suggesting the characteristic time scale is 10.594 days, shorter than any observed excursion to date. We explore the phase space evolution of the light curves using a natural embedding and find that all three systems possess two rotation centers that organize the phase space trajectories, one of low luminosity and the other of high luminosity. The implications of this repeatable behavior on generic models of accretion disk dynamics and mass transfer variability are explored.

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Section: Disk Magnetic Fieldsmentioning

confidence: 99%

The Long‐Term Light Curves of X‐Ray Binaries Contain Simultaneous Periodic and Random Components

Boyd

Smale

2004

ApJ

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“…[39] Hypothetically, the random walk description could be linked to local and statistically independent dynamo processes in the Earth's outer core, similar to those envisaged by Mazaud and Laj [1989] or Seki and Ito [1999]. If each process creates a chaotically switching dipole field, essentially aligned with the rotation axis, either parallel or antiparallel, then their sum undergoes a one-dimensional random walk.…”

Section: Discussionmentioning

confidence: 99%

“…For α ≤ 2 the average polarity duration for (1) becomes infinite for observation times T → ∞ , leading to the appearance of strong fluctuations in t , which can be mistaken for nonstationary behavior. Accordingly, the observed superchrons—instead of being outliers—would be an intrinsic feature of the distribution [ Seki and Ito , 1999; Pelletier , 1999; Jonkers , 2007]. The idea that the appearance of superchrons are a consequence of the nonlinear nature of the geodynamo was also defended by Hulot and Gallet [2003] on the grounds of their analysis of the GPTS and by Aubert et al [2009] who concluded that results of their numerical simulations of the geodynamo work “support the idea of superchrons being integral to the variety of timescales spontaneously produced by the dynamo.”…”

Section: Introductionmentioning

confidence: 99%

The geodynamo as a random walker: A view on reversal statistics

Щербаков

Fabian

2012

J. Geophys. Res.

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[1] The sequence of durations of the geomagnetic polarity intervals is often described in terms of a nonhomogenous Poisson process with time-dependent reversal rate, reflecting the nonstationarity of the underlying geodynamo process. This view has recently been challenged, and here we show that the first-passage time statistics of random walks taking place on a flat potential relief yields a much more consistent interpretation of the distribution of geomagnetic polarity intervals. A possible physical explanation suggests that the stability of a polarity chron of the Earth's magnetic field is controlled by a sum of statistically independent, randomly behaving, dynamo processes in the outer core. The random-walk hypothesis naturally includes the observed occurrences of very long superchrons, and it provides a new, considerably longer statistical estimate for the total duration of the present Brunhes chron predicting that the probability for a geomagnetic field reversal within the next 30 Ka is ≈5% and the probability that we live in a chron longer than 2 Ma is about 30%.Citation: Shcherbakov, V., and K. Fabian (2012), The geodynamo as a random walker: A view on reversal statistics, J. Geophys.

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“…By numerical simulation, they found that intervals of polarity reversals in the model follow a power law at a critical state. They also improved their model (Seki and Ito, 1999) to make it more realistic and to obtain a power exponent closer to the observed value. The revised model is a coupled map lattice where the elements themselves evolve and reverse polarity autonomously according to the Lorentz map obtained from Rikitake dynamo dynamics.…”

Section: Introductionmentioning

confidence: 99%

Some new approaches to the study of the Earth's magnetic field reversals

Michelis¹,

Consolini²

2010

Annals of Geophysics

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Paleomagnetic studies clearly show that the polarity of the magnetic fi eld has been subject to reversals. It is generally assumed that polarity intervals are exponentially distributed. Here, the geomagnetic polarity reversal record, for the past 166 Ma, is analysed and a new approach to the study of the reversals is presented. In detail, the occurrence of 1/ƒ-noise in the Power Spectral Density (PSD), relative to geomagnetic fi eld reversals, the existence of a Zipf's law behaviour for the cumulative distribution of polarity intervals, and the occurrence of punctuated equilibrium, as shown by a sort of Devil's staircase for the reversal time series, are investigated. Our results give a preliminary picture of the dynamical state of the geomagnetic dynamo suggesting that the geodynamo works in a marginally stable out-of-equilibrium confi guration, and that polarity reversals are equivalent to a sort of phase transition between two metastable states.

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A Coupled Map Lattice model for geomagnetic polarity reversals that exhibits realistic scaling

Cited by 5 publications

References 22 publications

The Long‐Term Light Curves of X‐Ray Binaries Contain Simultaneous Periodic and Random Components

The Long‐Term Light Curves of X‐Ray Binaries Contain Simultaneous Periodic and Random Components

The geodynamo as a random walker: A view on reversal statistics

Some new approaches to the study of the Earth's magnetic field reversals

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