Skip to main content
SpringerLink
Log in

Complexity Phenomena and ROMA of the Earth’s Magnetospheric Cusp, Hydrodynamic Turbulence, and the Cosmic Web

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

“Dynamic complexity” is a phenomenon observed for a nonlinearly interacting system within which multitudes of different sizes of large scale coherent structures emerge, resulting in a globally nonlinear stochastic behavior vastly different from that which could be surmised from the underlying equations of interaction. A characteristic of such nonlinear, complex phenomena is the appearance of intermittent fluctuating events with the mixing and distribution of correlated structures on all scales. We briefly review here a relatively recent method, ROMA (rank-ordered multifractal analysis), explicitly developed for analysis of the intricate details of the distribution and scaling of such types of intermittent structure. This method is then used for analysis of selected examples related to the dynamic plasmas of the cusp region of the Earth’s magnetosphere, velocity fluctuations of classical hydrodynamic turbulence, and the distribution of the structures of the cosmic gas obtained by use of large-scale, moving mesh simulations. Differences and similarities of the analyzed results among these complex systems will be contrasted and highlighted. The first two examples have direct relevance to the Earth’s environment (i.e., geoscience) and are summaries of previously reported findings. The third example, although involving phenomena with much larger spatiotemporal scales, with its highly compressible turbulent behavior and the unique simulation technique employed in generating the data, provides direct motivation for applying such analysis to studies of similar multifractal processes in extreme environments of near-Earth surroundings. These new results are both exciting and intriguing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  • Bird, S., Vogelsberger, M., Sijacki, D., Zaldarriaga, M., Springel, V., and Hernquist, L. (2013), Moving mesh cosmology: properties of neutral hydrogen in absorption, Mon. Not. R. Astron., Soc., 429, 3341.

  • Chang, T. (2014), An Introduction to Space Plasma Complexity, Cambridge University Press, New York, NY.

  • Chang, T., Wu, C. C., Podesta, Echim, M., Lamy, H., and Tam, S. W. Y. (2010), ROMA (rank-ordered multifractal analyses) of intermittency in space plasmas – a brief tutorial review, Nonlinear Processes in Geophysics, 17, 545.

  • Chang, T., and Wu, C. C. (2008), Rank-ordered multifractal spectrum for intermittent fluctuations, Phys. Rev. E, 77, 045401(R), doi:10.1103/Phys. Rev. E.77045401.

  • Chang, T., Tam, S. W. Y., and Wu, C. C. (2004), Complexity induced anisotropic bimodal intermittent turbulence in space plasmas, Phys. Plasmas, 11, 1287.

  • Chang, T., Hankey, A., and Stanley, H. E. (1973) Generalized scaling hypothesis in multicomponent systems. 1. Classification of critical points by order and scaling at tricriical points, Phys. Rev. B, 8, 346.

  • Consolini, G. and De Michelis, P. (2011), Rank ordering multifractal analysis of the auroral electrojet index, Nonlinear Processes in Geophysics, 18, 277.

  • Echim, M. M., Lamy, H., and Chang, T. (2007), Multipoint observations of intermittency in the cusp regions, Nonlinear Processes in Geophysics, 14, 325.

  • Echim, M, and Lamy, H. (2010), private communication

  • Eisenstein, D.J., and Hu, W. (1999), Power Spectra for Cold Dark Matter and Its Variants, Ap. J., 511, 5, doi:10.1086/306640.

  • Fang, F. (2006), Information of structures in galaxy distribution, Ap. J., 644, 678.

  • Frisch, U. (1995), Turbulence, Cambridge University Press, Cambridge, UK.

  • Hernquist, L., Katz, N., Weinberg, D. H., and Miralda-Escudé, J. (1996), The Lyman-Alpha forest in the cold dark matter model, Ap. J., 457, L51.

  • Hnat, B., Chapman, S. C., Rowlands, G., Watkins, N. W., and Farrell, W. M. (2002), Finite size scaling in the solar wind magnetic field energy density as seen by WIND, Geophys. Res. Lett., 29, 1446, doi:10.1029/2001GL014587.

  • Komatsu, E., et al. (2011), Seven-year Wilkinson microwave anisotropy probe (WMAP) observations: cosmological interpretation, Ap. JS, 192, 18.

  • Lamy, H., M. Echim, and T. Chang (2008), Rank-ordered multifractal spectrum of intermittent fluctuations in the cusp: a case study with Cluster data, 37th COSPAR Scientific Assembly, Paper D31-0017-08, p. 1686.

  • Li, Y., Perlman, E., Wan, M., Yang, Y., Burns, R., and Meneveau, C. (2008), A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turbulence, 9, 1, 2008.

  • Liddle, A. (2013), An Introduction to Modern Cosmology, Wiley, Chichester, West Sussex, UK

  • Lovejoy, S., Garrido, P., and Schertzer, D. (2000), Multifractal absolute galactic luminosity distributions and the multifractal Hubble 3/2 law, Physica A, 287, 49.

  • Peebles, P. (1980), The large Scale Structure of the Universe, Princeton University Press, Princeton, NJ.

  • Perlman, E., Burns, R., Li, Y., and Meneveau, C. (2007), Data exploration of turbulence simulations using a database cluster, Supercomputing SC07, ACM, IEEE, doi:10.1145/1362622, 1362654.

  • Permutter, S., et al., (1999), Measurements of Ω and Λ from 42 high-redshift supernovae, Ap. J., 517, 565.

  • Press, W. H., and Schechter, P. (1974), Formation of galaxies and clusters of galaxies by self-similar gravitational condensation, Ap. J., 187, 425.

  • Riess, a., et al. (1999), The rise time of nearby Type Ia supernovae, Ap. J., 118, 2268.

  • Springel, V. (2010), E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh, Mon. Not. R. Astron., Soc., 401, 791.

  • Springel, V., and Hernquist, L. (2003), The history of star formation in a Λ cold dark matter universe, Mon. Not. R. Astron., Soc., 339, 312.

  • Tam, S. W. Y., et al. (2010), Rank ordered multifractal analysis for intermittent fluctuations with global crossover behavior, Phys. Rev. E, 81, 036404.

  • Taylor, G. I. (1938), The spectrum of turbulence, Proc. Royal Soc. London A, 164, 476.

  • Torrey, P., Vogelsberger, M., Genel, S., Sijacki, D., Springel, V., and Hernquist, L. (2013), A physical model for cosmological simulations of galaxy formation: multi-epoch, arXiv:1305.4931v1.

  • Vogelsberger, M., Sijacki, D., Kereš, D., Springel, V., Hernquist, L. (2012), Moving mesh cosmology: numerical techniques and global statistics, Mon. Not. R. Astron., Soc., 425, 3024.

  • Vogelsberger, M., Genel, S., Sijacki, D., Torrey, P., Springel, V., and Hernquist, L. (2013), A model for cosmological simulations of galaxy formation physics, arXiv:1305.2913v3.

  • Wu, C. C., and Chang, T. (2011), Rank-ordered multifractal analysis (ROMA) of probability distributions in fluid turbulence, Nonlinear Processes in Geophysics, 18, 261.

  • Yordanova, E., Grezesiak, M, Wernik, A.W., Popielawska, B. and Stasiewicz, K. (2004), Multifractal structure of turbulence in the magnetospheric cusp, Ann. Geophys., 22, 2431.

  • Yordanova, E., Bergman, J., Consolini, G., Kretzschmar, M., Materassi, M., Popielawska, B., Roca-Sogorb, M., Stasiewicz, K., and Wernik, A.W., Anisotropic scaling features and complexity in magnetospheric-cusp: a case study, Nonlinear Processes in Geophysics, 12, 817, 2005.

  • Zhu, W., Feng, L.-L., and Fang, L.Z. (2011), Intermittence of the map of the kinetic Sunyaev-Zel’dovich effect and turbulence of the intergalactic medium, Ap. J. Lett., 734, L14.

Download references

Acknowledgments

This research is partially supported by the US National Science Foundation and the European Community’s Seventh Framework Programme (FP7/2007–2013) under Grant agreement no. 313038/STORM. Tom Chang wishes to thank Dr. Diego Perigini for inviting him to present this combined review and report of new findings related to ROMA at the 6th International Conference on Fractals and Dynamic Systems in Geoscience in the spirit of providing cross-discipline fertilization/exchange of scientific techniques and ideas in modern fractal analysis.

Author information

Authors and Affiliations

  1. Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Tom Chang & Mark Vogelsberger

  2. Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, CA, 90095, USA

    Cheng-chin Wu

  3. Belgian Institute for Space Aeronomy, 1180, Brussels, Belgium

    Marius Echim & Hervé Lamy

  4. Institute for Space Sciences, 077125, Bucharest, Romania

    Marius Echim

  5. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, 02138, USA

    Lars Hernquist

  6. Institute of Astronomy, University of Cambridge, Cambridge, CB3 OHA, UK

    Debora Sijacki

Authors
  1. Tom Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cheng-chin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marius Echim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hervé Lamy
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mark Vogelsberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Lars Hernquist
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Debora Sijacki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tom Chang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, T., Wu, Cc., Echim, M. et al. Complexity Phenomena and ROMA of the Earth’s Magnetospheric Cusp, Hydrodynamic Turbulence, and the Cosmic Web. Pure Appl. Geophys. 172, 2025–2043 (2015). https://doi.org/10.1007/s00024-014-0874-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-014-0874-z

Keywords

Search

Navigation