Chaos and multifractals in the solar wind

Advances in Space Research

Volumn 46, Issue 4, 2010, Pages 526-531

  MacEk, Wiesław M ^a,b  

^a CARDINAL STEFAN WYSZY SKI UNIVERSITY   (Poland)

^b Polish Academy of Sciences   (Poland)

Author keywords

Fractal and multifractal systems; Nonlinear dynamics and chaos; Solar wind plasma; Turbulence

Indexed keywords

CHAOTIC SYSTEMS; PLASMA DIAGNOSTICS; PLASMA TURBULENCE; SOLAR WIND; STREAM FLOW; TOPOLOGY; TURBULENCE;

DETERMINISTIC COMPONENT; MULTI FRACTALS; MULTI-FRACTAL SPECTRUM; NEAREST NEIGHBOURS METHOD; NON-UNIFORM COMPRESSION; PHENOMENOLOGICAL MODELING; SOLAR WIND PLASMAS; TOPOLOGICAL EMBEDDING;

FRACTALS;

EID: 77955418507     PISSN: 02731177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.asr.2008.12.026     Document Type: Article

References (37)

1. R. Bruno, V. Carbone, P. Veltri, E. Pietropaolo, and B. Bavassano Identifying intermittency events in the solar wind Planet. Space Sci. 49 2001 1201 1210
2. Burlaga, L.F. Multifractal structure of the interplanetary magnetic field: Voyager 2 observations near 25 AU, 1987-1988. Geophys. Res. Lett. 18, 69-72, 1991.
3. L.F. Burlaga Lognormal and multifractal distributions of the heliospheric magnetic field J. Geophys. Res. 106 2001 15917 15927 10.1029/2000JA000107, 2001
4. V. Carbone Cascade model for intermittency in fully developed magnetohydrodynamic turbulence Phys. Rev. Lett. 71 1993 1546 1548 10.1103/PhysRevLett.71.1546
5. K. Falconer Fractal Geometry: Mathematical Foundations and Applications 1990 J. Wiley New York
6. P. Grassberger Generalized dimensions of strange attractors Phys. Lett. A 97 1983 227 230 doi: 10.1016/0375-9601(83)90753-3
7. P. Grassberger, and I. Procaccia Measuring the strangeness of strange attractors Physica D 9 1983 189 208 doi: 10.1016/0167-2789(83)90298-1
8. T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I. Shraiman Fractal measures and their singularities: the characterization of strange sets Phys. Rev. A 33 1986 1141 1151 10.1103/PhysRevA.33.1141
9. H.G.E. Hentschel, and I. Procaccia The infinite number of generalized dimensions of fractals and strange attractors Physica D 8 1983 435 444 doi: 10.1016/0167-2789(83)90235-X
10. B. Hnat, S.C. Chapman, and G. Rowlands Intermittency, scaling, and the Fokker-Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft Phys. Rev. E 67 2003 056404 10.1103/PhysRevE.67. 056404
11. B. Hnat, S.C. Chapman, K. Kiyani, G. Rowlands, and N.W. Watkins On the fractal nature of the magnetic field energy density in the solar wind Geophys. Res. Lett. 34 2007 L15108 10.1029/2007GL029531
12. T.S. Horbury, and A. Balogh Evolution of magnetic field fluctuations in high-speed solar wind streams: Ulysses and Helios observations J. Geophys. Res. 106 2001 15929 15940 10.1029/2000JA000108
13. K. Kiyani, S.C. Chapman, B. Hnat, and R.M. Nicol Self-similar signature of the active solar corona within the inertial range of solar-wind turbulence Phys Res. Lett. 98 2007 211101 10.1103/PhysRevLett98.211101
14. W.M. Macek Testing for an attractor in the solar wind flow Physica D 122 1998 254 264 doi: 10.1016/S0167-2789(98)00098-0
15. W.M. Macek Multifractality and chaos in the solar wind S. Boccaletti, B.J. Gluckman, J. Kurths, L.M. Pecora, M.L. Spano, Experimental Chaos vol. 622 2002 American Institute of Physics New York 74 79 doi: 10.1063/1.1487522
16. W.M. Macek The multifractal spectrum for the solar wind flow M. Velli, R. Bruno, F. Malara, Solar Wind 10, 679 2003 American Institute of Physics New York 530 533 doi: 10.1063/1.1618651
17. W.M. Macek Modeling multifractality of the solar wind Space Sci. Rev. 122 2006 329 337 10.1007/s11214-006-8185-z
18. Macek, W.M. Multifractality and intermittency in the solar wind. Nonlin. Processes Geophys. 14, 695-700, 2007. Available from: < http://www.nonlin- processes-geophys.net/14/695/2007/ >.
19. W.M. Macek, and S. Redaelli Estimation of the entropy of the solar wind flow Phys. Rev. E 62 2000 6496 6504 10.1103/PhysRevE.62.6496
20. W.M. Macek, and M. Strumik Testing for nonlinearity and low-dimensional dynamics in the slow solar wind Adv. Space Res. 37 2006 1544 1549 10.1016/j.asr.2005.07.038
21. W.M. Macek, and A. Szczepaniak Generalized two-scale weighted Cantor set model for solar wind turbulence Geophys. Res. Lett. 35 2008 L02108 10.1029/2007GL032263
22. W.M. Macek, R. Bruno, and G. Consolini Generalized dimensions for fluctuations in the solar wind Phys. Rev. E 72 2005 017202 10.1103/PhysRevE.72. 017202
23. W.M. Macek, R. Bruno, and G. Consolini Testing for multifractality of the slow solar wind Adv. Space Res. 37 2006 461 466 10.1016/j.asr.2005.06.057
24. Mandelbrot, B.B. Multifractal measures, especially for the geophysicist. Pure Appl. Geophys. 131, Birkhäuser Verlag, Basel, pp. 5-42, doi:10.1007/BF00874478, 1989.
25. E. Marsch, and C.-Y. Tu Non-Gaussian probability distributions of solar wind fluctuations Ann. Geophys. 12 1994 1127 1138
26. Marsch, E., Tu, C.-Y. Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind. Nonlin. Processes Geophys. 4, 101-124, 1997. Available from: < http://www.nonlin-processes-geophys.net/4/ 101/1997/ >.
27. E. Marsch, C.-Y. Tu, and H. Rosenbauer Multifractal scaling of the kinetic energy flux in solar wind turbulence Ann. Geophys. 14 1996 259 269
28. C. Meneveau, and K.R. Sreenivasan Simple multifractal cascade model for fully developed turbulence Phys. Rev. Lett. 59 1987 1424 1427 10.1103/PhysRevLett.59.1424
29. C. Meneveau, and K.R. Sreenivasan The multifractal nature of turbulent energy dissipation J. Fluid Mech. 224 1991 429 484 10.1017/S0022112091001830
30. E. Ott Chaos in Dynamical Systems 1993 Cambridge University Press Cambridge
31. J.M. Polygiannakis, and X. Moussas Fractal properties of the interplanetary magnetic field fluctuations: indications of chaotic dynamics Astron. Astrophys. 283 1994 990 996
32. J.M. Polygiannakis, and X. Moussas On experimental evidence of chaotic dynamics over short time scales in solar wind and cometary data using nonlinear prediction techniques Solar Phys. 151 1994 341 350
33. R. Schwenn Large-scale structure of the interplanetary medium R. Schwenn, E. Marsch, Physics of the Inner Heliosphere vol. 20 1990 Springer-Verlag Berlin 99 181
34. L. Sorriso-Valvo, R. Marino, V. Carbone, F. Lepreti, P. Veltri, A. Noullez, R. Bruno, B. Bavassano, and E. Pietropaolo Observation of inertial energy cascade in interplanetary space plasma Phys. Rev. Lett. 99 2007 115001 10.1103/PhysRevE.71.066313
35. S.H. Strogatz Nonlinear Dynamics and Chaos 1994 Addison-Wesley Reading
36. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J.D. Farmer Testing for nonlinearity in time series: the method of surrogate data Physica D 58 1992 77 94 doi: 10.1016/0167-2789(92)90102-S
37. Y.-K. Tsang, E. Ott, T.M. Antonsen Jr., and P.N. Guzdar Intermittency in two-dimensional turbulence with drag Phys. Rev. E 71 2005 066313 10.1103/PhysRevLett.99.115001