Articles | Volume 25, issue 1
https://doi.org/10.5194/npg-25-207-2018
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the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-25-207-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review article
| 
12 Mar 2018
Review article |
| 12 Mar 2018
| 12 Mar 2018
Evolution of fractality in space plasmas of interest to geomagnetic activity
Víctor Muñoz
CORRESPONDING AUTHOR
Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
Macarena Domínguez
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
Juan Alejandro Valdivia
Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
Centro para la Nanociencia y la Nanotecnología, CEDENNA, Santiago, Chile
Simon Good
Department of Physics, University of Helsinki, Helsinki, Finland
The Blackett Laboratory, Imperial College London, London, UK
Giuseppina Nigro
Dipartimento di Fisica, Università della Calabria, Rende, Italy
Vincenzo Carbone
Dipartimento di Fisica, Università della Calabria, Rende, Italy
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Gurbax S. Lakhina and Bruce T. Tsurutani
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Chris M. Hall
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Y. Zou, R. V. Donner, N. Marwan, M. Small, and J. Kurths
Nonlin. Processes Geophys., 21, 1113–1126, https://doi.org/10.5194/npg-21-1113-2014, https://doi.org/10.5194/npg-21-1113-2014, 2014
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We use visibility graphs to characterize asymmetries in the dynamics of sunspot areas in both solar hemispheres. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between effects due to statistical versus dynamical properties of the observed data. Temporal changes in the hemispheric predominance of the graph connectivity are found to lag those directly associated with the total hemispheric sunspot areas themselves.
A. Ojeda González, W. D. Gonzalez, O. Mendes, M. O. Domingues, and R. R. Rosa
Nonlin. Processes Geophys., 21, 1059–1073, https://doi.org/10.5194/npg-21-1059-2014, https://doi.org/10.5194/npg-21-1059-2014, 2014
C. M. Hall
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A. Shapoval, J. L. Le Mouël, M. Shnirman, and V. Courtillot
Nonlin. Processes Geophys., 21, 797–813, https://doi.org/10.5194/npg-21-797-2014, https://doi.org/10.5194/npg-21-797-2014, 2014
Cited articles
ACE Science Center: ACE data, Caltech, available at:
http://www.srl.caltech.edu/ACE/ASC/index.html, last access: 6 March
2018. a
Aschwanden, M. J. and Aschwanden, P. D.: Solar Flare Geometries. I. The
Area Fractal Dimension, Astrophys. J., 674, 530–543, 2008. a
Balasis, G., Daglis, I. A., Kapiris, P., Mandea, M., Vassiliadis, D., and
Eftaxias, K.: From pre-storm activity to magnetic storms: a transition
described in terms of fractal dynamics, Ann. Geophys., 24, 3557–3567,
https://doi.org/10.5194/angeo-24-3557-2006, 2006. a
Balasis, G., Daglis, I. A., Papadimitriou, C., Kalimeri, M., Anastasiadis,
A.,
and Eftaxias, K.: Investigating Dynamical Complexity in the Magnetosphere
using Various Entropy Measures, J. Geophys. Res., 114, A00D06, https://doi.org/10.1029/2008JA014035,
2009. a, b
Berger, M. A. and Asgari-Targhi, M.: Self-Organized Braiding and the
Structure
of Coronal Loops, Astrophys. J., 705, 347–355, 2009. a
Borovsky, J. E.: A Model for the MHD Turbulence in the Earth's Plasma
Sheet: Building Computer Simulations, in: Multiscale Processes in the
Earth's Magnetosphere: From Interball to Cluster, edited by: Sauvaud,
J.-A. and Němeček, Z., vol. 178, NATO Science Series. II. Mathematics, Physics and Chemistry, 217–253, Kluwer Academic
Publishers, Dordrecht, the Netherlands, 2004. a
Burlaga, L. F., Sittler, E., Mariani, F., and Schwenn, R.: Magnetic Loop
Behind
and Interplanetary Shock: Voyager, Helios, and IMP 8 Observations, J.
Geophys. Res., 86, 6673–6684, 1981. a
Cadavid, A. C., Lawrence, J. K., Ruzmaikin, A. A., and Kayleng-Knight, A.:
Multifractal Models of Small-Scale Solar Magnetic Fields, Astrophys. J.,
429, 391–399, 1994. a
Chang, T.: Self-Organized Criticality, Multi-Fractal Spectra, Sporadic
Localized Reconnection and Intermittent Turbulence in the Magnetotail, Phys.
Plasmas, 6, 4137, https://doi.org/10.1023/A:1002486121567, 1999. a, b
Chang, T. and Wu, C. C.: Rank-Ordered Multifractal Spectrum for Intermittent
Fluctuations, Phys. Rev. E, 77, 045401, https://doi.org/10.1103/PhysRevE.77.045401, 2008. a
Chapman, S. C., Hnat, B., and Kiyani, K.: Solar cycle dependence of scaling
in solar wind fluctuations, Nonlin. Processes Geophys., 15, 445–455,
https://doi.org/10.5194/npg-15-445-2008, 2008. a, b, c, d
Conlon, P. A., Gallagher, P. T., McAteer, R. T. J., Ireland, J., Young,
C. A.,
Kestener, P., Hewett, R. J., and Maguire, K.: Multifractal Properties of
Evolving Active Regions, Solar Phys., 248, 297–309, 2008. a
Dendy, R. O., Chapman, S. C., and Paczuski, M.: Fusion, Space and Solar
Plasmas
as Complex Systems, Plasma Phys. Contr. F., 49, A95–A108, 2007. a
Dias, V. H. A. and Papa, A. R. R.: Statistical Properties of Global
Geomagnetic
Indexes as a Potential Forecasting Tool for Strong Perturbations, J. Atmos.
Sol.-Terr. Phy., 72, 109–114, 2010. a
Ditlevsen, P. D.: Turbulence and Shell Models, Cambridge University Press,
Cambridge, UK, 2011. a
El-Alaoui, M., Richard, R. L., Ashour-Abdalla, M., Walker, R. J., and
Goldstein, M. L.: Turbulence in a global magnetohydrodynamic simulation of
the Earth's magnetosphere during northward and southward interplanetary
magnetic field, Nonlin. Processes Geophys., 19, 165–175,
https://doi.org/10.5194/npg-19-165-2012, 2012. a
Gallagher, P. T., Phillips, K. J. H., Harra-Murnion, L. K., and Keenan,
F. P.:
Properties of the Quiet Sun EUV Network, Astron. Astrophys., 335,
733–745, 1998. a
Gledzer, E. B.: System of Hydrodynamic Type Allowing 2 Quadratic Integrals of
Motion, Sov. Phys. Dokl. SSSR, 18, 216–217, 1973. a
Gloaguen, C., Léorat, J., Pouquet, A., and Grappin, R.: A scalar model
for
MHD turbulence, Physica D, 17, 154–182, 1985. a
Gonzalez, W. D., Joselyn, J. A., Kamide, Y., Kroehl, H. W., Rostoker, G.,
Tsurutani, B. T., and Vasyliunas, V. M.: What Is A Geomagnetic Storm?, J.
Geophys. Res., 93, 5771–5792, 1994. a
Hwang, K.-J., Kuznetsova, M. M., Sahraoui, F., Goldstein, M. L., Lee, E., and
Parks, G. K.: Kelvin-Helmholtz Waves under Southward Interplanetary
Magnetic Field, J. Geophys. Res., 116, 1978–2012, 2011. a
Kiyani, K., Chapman, S. C., Hnat, B., and Nicol, R. M.: Self-Similar
Signature
of the Active Solar Corona within the Inertial Range of Solar-Wind
Turbulence, Phys. Rev. Lett., 98, 211101, https://doi.org/10.1103/PhysRevLett.98.211101, 2007. a
Klimas, A. J., Valdivia, J. A., Vassiliadis, D., N. Baker, D., Hesse,
M., and Takalo, J.: Self-Organized Criticality in the Substorm Phenomenon and
its Relation to Localized Reconnection in the Magnetospheric Plasma Sheet, J.
Geophys. Res., 105, 18765–18780, 2000. a
Kozelov, B. V.: Fractal approach to description of the auroral structure,
Ann. Geophys., 21, 2011–2023, https://doi.org/10.5194/angeo-21-2011-2003,
2003. a, b
Lawrence, J. K., Ruzmaikin, A. A., and Cadavid, A. C.: Multifractal Measure
of
the Solar Magnetic Field, Astrophys. J., 417, 805–811, 1993. a
Macek, W. M.: Chaos and Multifractals in the Solar Wind, Adv. Space Res., 46,
526–531, 2010. a
McAteer, R. T. J., Gallagher, P. T., and Conlon, P. A.: Turbulence,
Complexity,
and Solar Flares, Adv. Space Res., 45, 1067–1074, 2010. a
Nigro, G., Malara, F., Carbone, V., and Veltri, P.: Nanoflares and MHD
Turbulence in Coronal Loops: A Hybrid Shell Model, Phys. Rev. Lett., 92,
194501, https://doi.org/10.1103/PhysRevLett.92.194501, 2004. a
Nykyri, K., Grison, B., Cargill, P. J., Lavraud, B., Lucek, E., Dandouras,
I., Balogh, A., Cornilleau-Wehrlin, N., and Rème, H.: Origin of the
turbulent spectra in the high-altitude cusp: Cluster spacecraft observations,
Ann. Geophys., 24, 1057–1075, https://doi.org/10.5194/angeo-24-1057-2006,
2006. a
Obukhov, A. M.: Some General Properties of Equations Describing The Dynamics
of the Atmosphere, Akad. Nauk. SSSR, Izv. Serria Fiz. Atmos. Okeana, 7,
695–704, 1971. a
Osella, A., Favetto, A., and Silbergleit, V.: A Fractal Temporal Analysis of
Moderate and Intense Magnetic Storms, J. Atmos. Sol.-Terr. Phy., 59,
445–451, 1997. a
Papa, A. R. R. and Sosman, L. P.: Statistical Properties of Geomagnetic
Measurements as a Potential Forecast Tool for Strong Perturbations, J.
Atmos. Sol.-Terr. Phy., 70, 1102–1109, 2008. a
Sundkvist, D., Krasnoselskikh, V., Shukla, P. K., Vaivads, A.,
André,
M., Buchert, S., and Rème, H.: In Situ Multi-Satellite Detection of
Coherent Vortices as a Manifestation of Alfvénic Turbulence, Nature,
436, 825–828, 2005. a
Takalo, J., Timonen, J., Klimas, A., Valdivia, J., and Vassiliadis, D.:
Nonlinear Energy Dissipation in a Cellular Automaton Magnetotail Field Model,
Geophys. Res. Lett., 26, 1813–1816, 1999. a
Theiler, J.: Estimating Fractal Dimension, J. Opt. Soc. Am. A, 7,
1055–1073, 1990. a
Tsurutani, B. T. and Gonzalez, W. D.: The Causes of Geomagnetic Storms during
Solar Maximum, EOS, Transactions, American Geophysical Union, 75, 49–53,
1994. a
Valdivia, J. A., Milikh, G. M., and Papadopoulos, K.: Model of Red Sprites
Due
to Intracloud Fractal Lightning Discharges, Radio Sci., 33, 1655–1666,
1988. a
Valdivia, J. A., Klimas, A., Vassiliadis, D., Uritsky, V., and Takalo, J.:
Self-Organization in a Current Sheet Model, Space Sci. Rev., 107, 515–522,
2003. a
Valdivia, J. A., Rogan, J., Muñoz, V., Toledo, B., and Stepanova, M.: The
Magnetosphere as a Complex System, Adv. Space Res., 51, 1934–1941,
https://doi.org/10.1016/j.asr.2012.04.004, 2013. a
World Data Center for Geomagnetism: Dst data, Kyoto University, available at:
http://wdc.kugi.kyoto-u.ac.jp/caplot/index.html, last access: 6 March
2018. a
Witte, R. S. and Witte, J. S.: Statistics, chap. 6, 9 edn., Wiley,
Crawfordsville, USA, 2009. a
Yamada, M. and Ohkitani, K.: Lyapunov Spectrum of a Model of Two-Dimensional
Turbulence, Phys. Rev. Lett., 60, 983–986, 1988. a
Zimbardo, G., Greco, A., Veltri, P., Vörös, Z., and Taktakishvili,
A. L.: Magnetic Turbulence in and Around the Earth's Magnetosphere,
Astrophys. Space Sci. Trans., 4, 35–40, 2008. a
Short summary
Fractals are self-similar objects (which look the same at all scales), whose dimensions can be noninteger. They are mathematical concepts, useful to describe various physical systems, as the fractal dimension is a measure of their complexity. In this paper we study how these concepts can be applied to some problems in space plasmas, such as the activity of the Earth's magnetosphere, simulations of plasma turbulence, or identification of magnetic structures ejected from the Sun.
Fractals are self-similar objects (which look the same at all scales), whose dimensions can be...
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