Multiscale behavior and fractional kinetics from the data of solar wind–magnetosphere coupling

Zaslavsky, G. M.; Guzdar, P. N.; Edelnman, M.; Sitnov, M. I.; Sharma, A. S.

doi:10.1016/j.cnsns.2006.04.003

Cited by 6 publications

(6 citation statements)

References 39 publications

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“…In this case, the assumption of monoscaling is rather dubious, since it is not possible to identify a convincing scaling regime over any substantial time window. This is in line with findings presented by Zaslavsky et al [2008]. Nevertheless, we attempted a linear regression fit up to τ ≈ 70 minutes.…”

Section: Estimation Of Flm Parameters H J and αsupporting

confidence: 86%

“…Scaling of the peak P (Δ τ ε = 0, τ ) . There is some indication of a small modulation of the scaling law, which would imply that monoscaling is violated [ Zaslavsky et al , 2008]. …”

Section: Estimation Of Flm Parameters H J and αmentioning

confidence: 99%

“…We discuss this in the context of a fractional Lévy motion (fLm) model where the noise is additive [ Samorodnitsky and Taqqu , 1994; Embrechts and Maejima , 2002; Calvo et al , 2009; Watkins et al , 2009], sometimes called linear fractional stable motion, which has been proposed as a model for the Akasofu ε parameter [ Watkins et al , 2005] and is considered an archetype of a dependent heavy‐tailed process in the mathematical theory of stochastic processes. In particular, in space physics Lévy motions have been used to model, e.g., magnetic field line transport [ Pommois et al , 1998], fluctuations in various solar wind parameters [ Hnat et al , 2003a; Bruno et al , 2004; Zaslavsky et al , 2008] and auroral indices [ Watkins et al , 2005; Zaslavsky et al , 2008] making our analysis of general interest.…”

Section: Introductionmentioning

confidence: 99%

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Extreme value statistics in the solar wind: An application to correlated Lévy processes

Moloney

Davidsen

2010

J. Geophys. Res.

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[1] The interplay between the solar wind and the Earth's magnetosphere is a longstanding and challenging problem. An estimate of the energy influx into the magnetosphere is given by the Akasofu parameter. Extreme values of this parameter are of interest not only for magnetospheric response but also for the design of satellites, space stations, and considerations of astronaut safety. For the time series derived from ACE spacecraft measurements for the years 2000-2007, we find that its distribution of extreme values over time windows of about 18 h and longer can be accurately described by parametric models based on the mathematical theory of generalized extreme value statistics. These models predict that significantly larger values than observed to date can be expected during any 50 year period. While our findings seem to suggest that correlations and/or nonstationarities do not play a significant role for the extreme value statistics of the Akasofu parameter, we show that the contrary is in fact true. To isolate the effect of correlations and finite observation periods, we also consider the distribution of maximal changes in the parameter and compare it to the extreme value statistics of a recently proposed fractional Lévy motion-type model. However, we find that fractional Lévy motion does not reliably capture the extremal behavior of the time series.Citation: Moloney, N. R., and J. Davidsen (2010), Extreme value statistics in the solar wind: An application to correlated Lévy processes,

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Section: Estimation Of Flm Parameters H J and αsupporting

confidence: 86%

“…Scaling of the peak P (Δ τ ε = 0, τ ) . There is some indication of a small modulation of the scaling law, which would imply that monoscaling is violated [ Zaslavsky et al , 2008]. …”

Section: Estimation Of Flm Parameters H J and αmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extreme value statistics in the solar wind: An application to correlated Lévy processes

Moloney

Davidsen

2010

J. Geophys. Res.

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“…The ambivalent process they used for illustration, and fitted to data, was the well-studied fully fractional continuous time random walk [3] which incorporates both effects via fractional orders of the spatial and temporal derivatives in its kinetic equation. Zaslavsky et al [26,27] also advocated use of the same process in space physics for modelling the auroral index time series. They explicitly contested [27] the applicability of a time series model [23] based on a self-similar stable processlinear fractional stable motion (lfsm) [13,14]-in this role.…”

Section: Introductionmentioning

confidence: 99%

Kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts

et al. 2009

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Lévy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and longranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion ͑lfsm͒ is a model process of this type, combining ␣-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk ͑CTRW͒, with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst "sizes" and "durations" in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.

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“…In space physics, such heavy-tailed distributions have been used to model e.g. magnetic field line transport [Pommois et al, 1998], fluctuations in various solar wind parameters [Hnat et al, 2003;Bruno et al, 2004;Zaslavsky et al, 2008] and auroral indices [Watkins et al, 2005;Zaslavsky et al, 2008]. Other examples include, size distributions in geology [Caers et al, 1999], meteorology [Taqqu, 1987], or sediments [Painter and Paterson, 1994].…”

Section: Introductionmentioning

confidence: 99%

Extreme Value and Record Statistics in Heavy-Tailed Processes With Long-Range Memory

Schumann

Moloney

Davidsen

2012

Extreme Events and Natural Hazards: The Complexity Perspective

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Abstract. Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to independent extreme events as often observed in natural systems. Here, we focus on this case and consider stationary stochastic processes that are characterized by long-range memory and heavytailed distributions, often called fractional Lévy noise. While the size distribution of extreme events is not affected by the long-range memory in the asymptotic limit and remains a Fréchet distribution, there are strong finite-size effects if the memory leads to persistence in the underlying dynamics. Moreover, we show that this persistence is also present in the extreme events, which allows one to make a time-dependent hazard assessment of future extreme events based on events observed in the past. This has direct applications in the field of space weather as we discuss specifically for the case of the solar power influx into the magnetosphere. Finally, we show how the statistics of records, or record-breaking extreme events, is affected by the presence of long-range memory.

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Multiscale behavior and fractional kinetics from the data of solar wind–magnetosphere coupling

Cited by 6 publications

References 39 publications

Extreme value statistics in the solar wind: An application to correlated Lévy processes

Extreme value statistics in the solar wind: An application to correlated Lévy processes

Kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts

Extreme Value and Record Statistics in Heavy-Tailed Processes With Long-Range Memory

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