FRACTAL RADIOPHYSICS. Part 4. PRACTICAL APPLICATIONS
Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed in radiophysics — fractal radiophysics. The subject of this review is the main practical ideas of "fractalization" in radio physics. The purpose of the work is a systematic presen...
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| Дата: | 2024 |
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Видавничий дім «Академперіодика»
2024
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| Назва журналу: | Radio physics and radio astronomy |
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Radio physics and radio astronomy| Резюме: | Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed in radiophysics — fractal radiophysics. The subject of this review is the main practical ideas of "fractalization" in radio physics. The purpose of the work is a systematic presentation of the main results of the practical application of fractal theory in radiophysics, as well as a detailed analysis of the originality, novelty, and practical value of the obtained results.Methods and Methodology. The results of using the fractal approach in various fields of modern radiophysics are presented. The results of the application of fractal and multifractal analysis methods for various radiophysical objects, phenomena and processes are considered. The main features, advantages and disadvantages of this approach, as well as existing problems, are highlighted.Results. The main practical results of applying the fractal approach in radio physics are considered. The main features of solving the problem of radio wave propagation in fractal media are also discussed. The usage of fractals in applied electrodynamics is demonstrated by the example of fractal antennas, resonators, filters, capacitors, transistors, diplexers, frequency-selective surfaces and metamaterials, etc. Fractals in semiconductor and vacuum electronics are described by the example of the fractal structures of the cathode spot and the cathodes themselves, fractal electrodes and diffusers, as well as the avalanche breakdown of the p-n junction. The features of the application of fractal ideas in statistical and nonlinear radiophysics are considered. To illustrate the "fractalization" of physics and radiophysics of the geospace, the fractal processes that occur during earthquakes, in the atmosphere, ionosphere and magnetosphere, etc., are used.Conclusions. The main directions of practical application of the theory of fractals in modern radiophysics are analyzed, as well as the features of the new results obtained, which reflect one of the main properties of the surrounding world — its fractality, are discussed.Keywords: fractal, fractal electrodynamics, fractal medium, fractal electronics, fractal process, fractal characteristicsManuscript submitted 12.09.2023Radio phys. radio astron. 2024, 29(3): 180-205REFERENCES 1. Lazorenko, O.V., and Chernogor, L.F., 2020. Fractal Radio Physics. 1. Theoretical Bases. Radio Phys. Radio Astron., 25(1), pp. 3—77 (in Russian). DOI: https://doi.org/10.15407/rpra25.01.003 2. Lazorenko, O.V., and Chernogor, L.F., 2023. Fractal Radio Physics. 2. Fractal and Multifractal Analyses of Signals and Processes. Radio Phys. Radio Astron., 28(1), pp. 5—70 (in Ukrainian). DOI: https://doi.org/10.15407/rpra28.01.005 3. Lazorenko, O.V., and Chernogor, L.F., 2024. Fractal Radio Physics. 3. Fractional Calculus in Electrodynamics. Radio Phys. Radio Astron., 29(1), pp. 46—67 (in Ukrainian). DOI: https://doi.org/10.15407/rpra29.01.046 4. Nanjo, K., and Nagahama, H., 2004. Fractal properties of spatial distributions of aftershocks and active faults. Chaos Solit. Frac- tals, 19(2), pp. 387—397. DOI: https://doi.org/10.1016/S0960-0779(03)00051-1 5. Quadfeul, S.-A., ed., 2012. Fractal Analysis and Chaos in Geosciences. Rijeka, Croatia: InTech Press. DOI: https://doi.org/10.5772/3309 6. Goltz, C., 1997. Fractal and Chaotic Properties of Earthquakes. Berlin, Heidelberg: Springer-Verlag. DOI: https://doi.org/10.1007/BFb0028315 7. Takayasu, H., 1990. Fractals in the Physical Sciences. Nonlinear Science: Theory and Applications., Manchester, New York: Man- chester University Press. 8. Dimri, V.P., ed., 2005. Fractal Behavior of the Earth System. Berlin, Heidelberg: Springer-Verlag. DOI: https://doi.org/10.1007/b137755 9. Gil’mutdinov, A.K., Ushakov, P.A., and El-Kharazi, R., 2017. Fractal Elements and their Applications. Cham, Switzerland: Springer Int. Publ. 10. Bandt, C., Barnsley, M., Devaney, R., Falconer, K.J., Kannan, V., and Vinod Kumar, P.B., eds. Fractals, Wavelets, and their Appli- cations: Contributions from the International Conference and Workshop on Fractals and Wavelets (Springer Proceedings in Mathe- matics & Statistics). Switzerland: Springer Int. Publ., 2014. DOI: https://doi.org/10.1007/978-3-319-08105-2 11. Di Ieva, A., ed., 2016. The Fractal Geometry of the Brain. New York: Springer-Verlag. DOI: https://doi.org/10.1007/978-1-4939-3995-4 12. Werner, D.H., and Mittra, R., 1999. Frontiers in Electromagnetics, IEEE Press Series on Microwave Technology and RF. New York: Wiley–IEEE Press. DOI: https://doi.org/10.1109/9780470544686 13. Jaggard, D.L., 1997. Fractal Electrodynamics: From Super Antennas to Superlattices. In: Levy-Vehel, J., Lutton, E., and Tricot, C., 1997. Fractals in Engineering. New York: Springer-Verlag, pp. 204—221. DOI: https://doi.org/10.1007/978-1-4471-0995-2_16 14. Berry, M.V., 1979. Diffractals. J. Phys., A12, pp. 781—797. DOI: https://doi.org/10.1088/0305-4470/12/6/008 15. Tatarskii, V.I., 1961. Wave Propagation in a Turbulent Medium. New York: McGraw-Hill. DOI: https://doi.org/10.1063/1.3057286 16. Chernov, L.A., 1960. Wave Propagation in a Random Medium. New York: McGraw-Hill. DOI: https://doi.org/10.1063/1.3056748 17. Kolmogorov, A.N., 1961. The local structure of turbulence in incompressible viscous fluid for very large reynolds’ number, and Dissipation of energy in the locally isotropic turbulence. In: Friedlander, S.K., and Topper, L., eds., 1961. Turbulence, Classical Papers on Statistical Theory. New York: Interscience. 18. Jaggard, D.L., and Sun, X., 1989. Scattering from bandlimited fractal fibers. IEEE Trans. Antennas Propag., 37(12), pp. 1591— 1597. DOI: https://doi.org/10.1109/8.45102 19. Franceschetti, G., and Riccio, D., 2007. Scattering, natural surfaces, and fractals. Elsevier. https://doi.org/10.1016/B978-012265655-2/50000-3 20. Werner, D.H., and Ganguly, S., 2003. An overview of fractal antenna engineering research. IEEE Antennas Propag. Mag., 45(1), pp. 38—57. DOI: https://doi.org/10.1109/MAP.2003.1189650 21. Cohen, N., 1995. Fractal Antennas: Part 1. Commun. Q., pp. 7—22. 22. Puente, C., Romeu, J., Pous, R., Garcia, X., and Benitez, F., 1996. Fractal multiband antenna based on the Sierpinski gasket. Elec- tron. Lett., 32(1), pp. 1—2. DOI: https://doi.org/10.1049/el:19960033 23. Puente, C., Navarro, M., Romeu, I., and Pous, R., 1998. Variations on the fractal Sierpinski antenna flare angle. In: IEEE Antennas and Propagation Society International Symposium. 1998. Digest. Antennas: Gateways to the Global Network. Held in Conjunc- tion with: USNC/URSI National Radio Science Meeting (Cat. No.98CH36194). Atlanta, Georgia, 21—26 June 1998. IEEE, 1998, pp. 1—4. DOI: https://doi.org/10.1109/APS.1998.701794 24. Cohen, N., 1996. Fractal Antennas. Part 2. Commun. Q., pp. 53—66. 25. Karmakar, A., 2020. Fractal antennas and arrays: a review and recent developments. Int. J. Microw. Wirel. Technol., pp. 1—25. DOI: https://doi.org/10.1017/S1759078720000963 26. Cohen, N., Hohifeld, R., Moschella, D., and Salkind, P., 2003. Fractal wideband antennas for software defined radio, UWB, and multiple platform applications. In: Radio and Wireless Conference, RAWCON ‘03. Proc. Boston, MA, USA, 8—13 Aug. 2003. IEEE, 2003. DOI: https://doi.org/10.1109/RAWCON.2003.1227902 27. Walker, G.J., and James, J.R., 1998. Fractal Volume Antennas. Electron. Lett., 34(16), pp. 1536—1537. DOI: https://doi.org/10.1049/el:19981135 28. Al-Zabee, A.A.K., Jabbar, S.Q., and Wang, D., 2016. Fractal Antennas (Study and Review). Int. J. Comput. Technol., 15(13), pp. 7387—7400. DOI: https://doi.org/10.24297/ijct.v15i13.31 29. Frame, M., and Urry, A., 2016. Fractal Worlds: Grown, Built, and Imagined. New Haven, London: Yale University Press. 30. FRACTALCOMS: Exploring the limits of Fractal Electrodynamics for the future telecommunication technologies IST-2001- 33055. Final Report Task 4.3 by J.M. Gonz´Alez, J. Romeu, E. Cabot, and J.R. Mosig. 31. Sabban, A., 2018. Novel Wearable Antennas for Communication and Medical Systems. Taylor & Francis Group. DOI: https://doi.org/10.1201/b22261 32. Even, C., Russ, S., Repain, V., Pieranski, P., and Sapoval, B., 1999. Localizations in Fractal Drums: An Experimental Study. Phys. Rev. Lett., 83(4), pp. 726—729. DOI: https://doi.org/10.1103/PhysRevLett.83.726 33. Crnojevic-Bengin, V., and Budimir, D., 2004. Novel microstrip resonators with embedded 3-D curves. In: Asia-Pacific Microwave Conf. (APMC’, 2004). New Delhi, India, 15—18 Dec. 2004. 34. Crnojevic-Bengin, V., and Budimir, D., 2005. Novel 3-D Hilbert microstip resonators. Microwave Technol. Lett., 46(3), pp. 195— 197. DOI: https://doi.org/10.1002/mop.20943 35. Zemlyakov, K., and Crnojevic-Bengin, V., 2012. Planar low-pass filters based on Hilbert fractal. Microwave Opt. Technol. Lett.,54(11), pp. 2577—2581. DOI: https://doi.org/10.1002/mop.27158 36. Bagmanov, V.Kh., Potapov, A.A., Sultanov, A.Kh., and Zang, W., 2018. Fractal Filters Intended for Signal Detection during Re- mote-Sensing Data Processing. J. Commun. Technol. Electron., 63(10), pp. 1163—1169. DOI: https://doi.org/10.1134/S1064226918100030 37. Samavati, H., Hajimiri, A., Shahani, A.R., Nasserbakht, G.N., and Lee, T.H., 1998. Fractal Capacitors. IEEE J. Solid-State Circuits,33(12), pp. 2035—2041. DOI: https://doi.org/10.1109/4.735545 38. Gassmann, F., Koеtz, R., and Wokaun, A., 2003. Supercapacitors boost the fuel cell car. Europhys. News, 34(5), pp. 176—180. Available from: http://ecl.web.psi.ch/index.html DOI: https://doi.org/10.1051/epn:2003502 39. Shahani, A.R., Lee, T.H., Samavati, H., Shaeffer, D.K., and Walther, S. Lateral flux capacitor having fractal-shaped perimeters. US Patent 6084285. 40. Xu, H., Wang, G., and An, H., 2010. Hilbert fractal curves form compact diplexer. Microwaves & RF, 49(8), pp. 92—95. 41. Parker, E.A., and El Sheikh, A.N.A., 1991. Convoluted Array Elements and Reduced Size Unit Cells for Frequency-Selective Surfaces. IEE Proc. H: Microw., Antennas Propag., 138(1), pp. 19—22. DOI: https://doi.org/10.1049/ip-h-2.1991.0004 42. Werner, D.H., Bretones, A.R., and Long, B.R., 1999. Radiation Characteristics of Thin-wire Ternary Fractal Trees. Eleciron. Lett., 35(8), pp. 609—610. DOI: https://doi.org/10.1049/el:19990478 43. Dmitruk, N.L., Goncharenko, A.V., and Venger, E.F., 2009. Optics of Small Particles and Composite Media. Kyiv: Naukova Dumka Publ. 44. Kozar, A.I., 2014. Resonant metacrystals from small magnetodielectric spheres. Monograph. Kharkov: KhNURE Publ. (in Rus- sian). 45. Kozar, A.I. and Khizhnyak, N.A., 1970. Reflection of electromagnetic waves from a resonant dielectric sphere in a waveguide.Ukr. Fiz. Zh., 15, pp. 847—849 (in Russian). 46. Bolotov, V.N., Kirichok, A.V., and Tkach, Yu.V., 1998. Experimental Research of Fractal Antennas. Electromagnetic Phenomena,1(4), pp. 483—498. 47. Bolotov, V.N., and Tkach, Yu.V., 2006. Signal generation with fractal spectra. Zh. Tekh. Fiz., 76(4), pp. 91—98 (in Russian). 48. Bao, Y.-J., Zhang, B., Wu, Z., Si, J.-W., Wang, M., Peng, R.-W., Lu, X., Shao, J., Li, Zh.-F., Hao, X.-P., Ming, N.-B., 2007. Sur- face-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array. Appl. Phys. Lett., 90(25), 251914. DOI: https://doi.org/10.1063/1.2750528 49. Carlier, F., and Akulin, V.M., 2004. Quantum interference in nanofractals and its optical manifestation. Phys. Rev. B, 69(11), 115433. DOI: https://doi.org/10.1103/PhysRevB.69.115433 50. Burioni, R., Cassi, D., and Neri, F.M., 2004. Electrical circuits on mesoscopic Sierpinski gaskets. J. Phys. A: Math. Gen., 37(37), pp. 8823–8833. DOI: https://doi.org/10.1088/0305-4470/37/37/005 51. Marlow, C.A., Taylor, R.P., Martin, T.P., Scannell, B.C., Linke, H., Fairbanks, M.S., Hall, G.D.R., Shorubalko, I., Samuelson, L., Fromhold, T.M., Brown, C.V., Hackens, B., Faniel, S., Gustin, C., Bayot, V., Wallart, X., Bollaert, S., and Cappy, A., 2006. Unified model of fractal conductance fluctuations for diffusive and ballistic semiconductor devices. Phys. Rev. B, 73(19), 195318. DOI: https://doi.org/10.1103/PhysRevB.73.195318 52. Fairbanks, M.S., Mccarthy, D.N., Scott, S.A., Brown, S.A., and Taylor, R.P., 2011. Fractal electronic devices: simulation and im- plementation. Nanotechnology, 22(36), 365304. DOI: https://doi.org/10.1088/0957-4484/22/36/365304 53. Fan, J.A., Yeo, W.H., Su, Y., Hattori, Y., Lee, W., Jung, S.Y., Zhang, Y., Liu, Z., Cheng, H., Falgout, L., Bajema, M., Coleman, T., Gregoire, D., Larsen, R.J., Huang, Y., Rogers, J.A., 2014. Fractal design concepts for stretchable electronics. Nat. Commun., 5(1), 3266. DOI: https://doi.org/10.1038/ncomms4266 54. Kuznetsov, A.P., and Kuznetsov, S.P., 1992. Fractal signal generator. Pis’ma v ZhTF, 18(24), pp. 19—21 (in Russian). 55. Francis, T.S., and Yu, S.J., 1996. Optical Storage and Retrieval: Memory: Neural Networks, and Fractals. CRC Press. 56. Allain, C., and Cloitre, M., 1986. Optical diffraction on fractals. Phys. Rev. B, 33(5), pp. 3566—3569. DOI: https://doi.org/10.1103/PhysRevB.33.3566 57. Uozumi, U., Kimura, H., and Asakura, T., 1991. Fraunhofer diffraction by Koch fractals: the dimensionality. J. Mod. Opt., 38, pp. 1335—347. DOI: https://doi.org/10.1080/09500349114551501 58. Tanida, J., Uemoto, A., and Ichioka, Y., 1993. Optical fractal synthesizer: concept and experimental verification. Appl. Opt., 32, pp. 653—658. DOI: https://doi.org/10.1364/AO.32.000653 59. Berry, M., 2001. Fractal modes of unstable lasers with polygonal and circular mirrors. Opt. Commun., 200, pp. 321—330. DOI: https://doi.org/10.1016/S0030-4018(01)01613-3 60. Sroor, H., Naidoo, D., Miller, S.W., Nelson, J., Courtial, J., and Forbes, A., 2019. Fractal light from lasers. Phys. Rev. A, 99(1). DOI: https://doi.org/10.1103/PhysRevA.99.013848 61. Anders, A., 2008. Cathodic Arcs: From Fractal Spots to Energetic Condensation. Springer Science + Business Media, LLC. DOI: https://doi.org/10.1007/978-0-387-79108-1 62. Solntsev, V.A., 1998. Nonlinear phenomena in vacuum microelectronic structures. Izv. Vyssh. Uchebn. Zaved. Appl. Nonlinear Dynamics, 6(1), p. 54. DOI: https://doi.org/10.18500/0869-6632-1998-6-1-54-74 63. Isaeva, O.B., Eliseev, M.V., Rozhnev, A.G., and Ryskin, N.M., 1999. Simulation of field emission from fractal surface. Izv. Vyssh. Uchebn. Zaved. Appl. Nonlinear Dynamics, 7(5), pp. 33—43. DOI: https://doi.org/10.18500/0869-6632-1999-7-5-33-43 64. Iijima, S., and Ichihashi, T., 1993. Single-shell carbon nanotubes of 1-nm diameter. Nature, 363(6430), pp. 603—605. DOI: https://doi.org/10.1038/363603a0 65. Chernogor, L.F., 2011. Sun — interplanetary medium — magnetosphere — ionosphere — atmosphere — Earth as an open non-equilibrium non-linear physical system. Zhurnal problem evoljutsiy otkrytykh system, 13, pp. 22—58 (in Russian). 66. Chernogor, L.F., 2003. Physics of the Earth, atmosphere, geocosmos in the light of the system paradigm. Radiofizika i radioas- tronomiya, 8, pp. 59—101 (in Russian). 67. D’Amico, S., ed., 2012. Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology. Rijeka: InTech. DOI: https://doi.org/10.5772/1117 68. Cello, G., Marchegiani, L., and Tondi, E., 2006. Evidence for the existence of a simple relation between earthquake magni- tude and the fractal dimension of seismogenic faults: a case study from central Italy. In: Cello, G., and Malamud, B.D., eds., 2006. Fractal Analysis for Natural Hazards. London: Geological Society, Special Publications, pp. 133—140. DOI: https://doi.org/10.1144/GSL.SP.2006.261.01.10 69. Davy, P., Bour, O., De Dreuzy, J.-R., and Darcel, C., 2006. Flow in multiscale fractal fracture networks. In: Cello, G., and Mala- mud, B.D., eds., 2006. Fractal Analysis for Natural Hazards. London: Geological Society, Special Publications, pp. 31—45. DOI: https://doi.org/10.1144/GSL.SP.2006.261.01.03 70. Paparo, G., Gregori, G. P., Poscolieri, M., Marson, I., Angelucci, F., and Glorioso, G., 2006. Crustal stress crises and seismic activ- ity in the Italian peninsula investigated by fractal analysis of acoustic emission, soil exhalation and seismic data. In: Cello, G., and Malamud, B.D., eds., 2006. Fractal Analysis for Natural Hazards. London: Geological Society, Special Publications, pp. 47—61. DOI: https://doi.org/10.1144/GSL.SP.2006.261.01.04 71. Telesca, L., Lapenna, V., Vallianatos, F., Makris, J., and Saltas, V., 2004. Multifractal features in short-term time dynamics of ULF geomagnetic field measured in Crete, Greece. Chaos Solit. Fractals, 21(2), pp. 273—282. DOI: https://doi.org/10.1016/j.chaos.2003.10.020 72. Christensen, K., Danon, L., Scanlon, T., and Bak, P., 2002. Unified scaling law for earthquakes. Proceedings of the National Acad- emy of Sciences (PNAS), 99(suppl_1), pp. 2509—2513. DOI: https://doi.org/10.1073/pnas.012581099 73. Corral, Á., 2003. Local distributions and rate fluctuations in a unified scaling law for earthquakes. Phys. Rev. E, 68(3), 035102(R). DOI: https://doi.org/10.1103/PhysRevE.68.035102 74. Pelinovsky, E.N., 1989. Tsunami climbing a beach and Tsunami zonation. Sci. Tsunami Haz., 7, pp. 117—123. 75. Zhong, M., Long, Y., Zhang, W., Chen, Z., and Xie, Q., 2009. Multi-Fractal Analysis of the Explosion Seismic Signal Based on Seismic Exploration. In: First International Conference on Information Science and Engineering (ICISE ‘09): Proc. Nanjing, China, 26—28 Dec. 2009. IEEE: 2009. P. 600—603. DOI: https://doi.org/10.1109/ICISE.2009.766 76. Bloomfield, P., and Nychka, D., 1992. Climate spectra and detecting climate change. Clim. Change, 21(3), pp. 275—287. DOI: https://doi.org/10.1007/BF00139727 77. Mandelbrot, B.B., 1977. Fractals: Form, Chance and Dimension. San Francisco: W.H. Freeman and Company. 78. Kirichenko, L.O., and Radivilova, Т.А., 2019. Fractal analysis of self-similar and multifractal time series. Monograph. Kharkiv: KhNURE Publ. (in Ukrainian). 79. Fulleknig, M., Mareev, E., and Rycroft, M., eds., 2006. Sprites, elves and intense lightning discharges. NATO Science Series II. Dordrecht: Springer. DOI: https://doi.org/10.1007/1-4020-4629-4 80. Potapov, A., and Cerman, V., 2019. Features of multi-fractal structure of high-altitude lightning discharges in the ionosphere: elves, jets, sprites. J. Eng., 2019(20), pp. 6781—6783. DOI: https://doi.org/10.1049/joe.2019.0478 81. Kumar, S., Cuntz, M., and Musielak, Z.E., 2015. Fractal and Multifractal Analysis of the Rise of Oxygen in Earth’s Early Atmo- sphere. Chaos Solit. Fractals., 77, pp. 296—303. DOI: https://doi.org/10.1016/j.chaos.2015.06.007 82. Аlimov, V.A., Vybornov, F.I., Rakhlin, A.V., 2008. On some features of the fractal structure of developed small-scale ionospheric turbulence. Izv. Vyssh. Uchebn. Zaved. Radiofizika, LI(4), pp. 287—294 (in Russian). DOI: https://doi.org/10.1007/s11141-008-9025-7 83. Burlaga, L.F., and Klein, L.W., 1986. Fractal structure of the interplanetary magnetic field. J. Geophys. Res., 91(A1), pp. 347—350. DOI: https://doi.org/10.1029/JA091iA01p00347 84. Chernogor, L.F., and Domnin, I.F., 2014. Physics of geocosmic storms. Monograph. Kharkov: KhNU imeni V.N. Karazina Publ. (in Russian). 85. Burlaga, L.F., Wang, C., and Ness, N.F., 2003. A model and observations of the multifractal spectrum of the heliospheric magnet- ic field strength fluctuations near 40 AU. Geophys. Res. Lett., 30(10), 1543. DOI: https://doi.org/10.1029/2003GL016903 86. Ivanov, S.S., 1996. Multifractal properties and dimension of the geomagnetic field reversal attractor. Geomagnetizm i aeronomiya,36(4), pp. 149—156 (in Russian). 87. Mandelbrot, B., 1967. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, 156(3775), pp. 636—638. DOI: https://doi.org/10.1126/science.156.3775.636 88. Burton, R.K., McPherron, R.L., and Russell, C.T., 1975. An empirical relationship between interplanetary conditions and Dst. J. Geophys. Res., 80(31), pp. 4204—4214. DOI: https://doi.org/10.1029/JA080i031p04204 89. Yu, Z.G., Anh, V.V., Wanliss, J.A., and Watson, S. M., 2007. Chaos game representation of the Dst index and prediction of geo- magnetic storm events. Chaos Solit. Fractals, 31(3), pp. 736—746. DOI: https://doi.org/10.1016/j.chaos.2005.12.046 90. Wanliss, J.A., 2004. Nonlinear variability of SYM-H over two solar cycles. Earth Planets Space, 56, pp. e13—e16. DOI: https://doi.org/10.1186/BF03352507 91. Toledo, B., Medina, P., Blunier, S., Rogan, J., Stepanova, M., and Valdivia, J., 2021. Multifractal Characteristics of Geomagnetic Field Fluctuations for the Northern and Southern Hemispheres at Swarm Altitude. Entropy, 23(5), 558. DOI: https://doi.org/10.3390/e23050558 92. Ioshpa, B.A., Obridko, V.I.M., and Rudenchik, E.A., 2008. Fractal Properties of Solar Magnetic Fields. Astron. Lett., 34(3), pp. 210—216. DOI: https://doi.org/10.1134/S1063773708030080 93. Vitinskii, Yu.I., 1965. Solar Activity Forecasting. NASA TTF-289 TT65-50115. 94. Mandelbrot, B., and Wallis, J.R., 1969. Computer experiments with fractional Gaussian noises. Water Resour. Res., 5(1), pp. 228— 241. DOI: https://doi.org/10.1029/WR005i001p00228 95. Rypdal, M., and Rypdal, K., 2012. Is there long-range memory in solar activity on timescales shorter than the sunspot period? J. Geophys. Res.: Space Phys., 117(A4). DOI: https://doi.org/10.1029/2011JA017283 96. Ruzmaikin, A., Feynman, J., and Robinson, P., 1994. Long-term persistence of solar activity. Solar Phys., 149(2), pp. 395—403. DOI: https://doi.org/10.1007/BF00690625 97. Ogurtsov, M.G., 2004. New Evidence for Long-Term Persistence in the Sun’s Activity. Solar Phys., 220(1), pp. 93—105. DOI: https://doi.org/10.1023/B:sola.0000023439.59453.e5 98. Kim, R.-S., Yi, Y., Cho, K., Moon, Y.-J., and Kim, S., 2006. Fractal Dimension and Maximum Sunspot Number in Solar Cycle. J. Astron. Space Sci., 23(3), pp. 227—236. DOI: https://doi.org/10.5140/JASS.2006.23.3.227 99. Qin, Z., 1994. A fractal study on sunspot relative number. Chin. Astron. Astrophys., 18(3), pp. 313—318. DOI: https://doi.org/10.1016/0275-1062(94)90045-0 100. Weiss, N.O., and Foukal, P., 1990. Periodicity and Aperiodicity in Solar Magnetic Activity. Phil. Trans. R. Soc. Lond. Ser. A. Math. Phys. Sci., 330(1615). The Earth’s Climate and Variability of the Sun Over Recent Millennia: Geophysical, Astronomical and Archaeological Aspect, pp. 617—625. DOI: https://doi.org/10.1098/rsta.1990.0042 101. Movahed, M.S., Jafari, G.R., Ghasemi, F., Rahvar, S., and Tabar, M.R.R., 2006. Multifractal detrended fluctuation analysis of sun- spot time series. J. Stat. Mech.: Theory Exp., 02, 02003(9 p.). DOI: https://doi.org/10.1088/1742-5468/2006/02/P02003 102. Hu, J., Gao, J., and Wang, X., 2009. Multifractal analysis of sunspot time series: the effects of the 11-year cycle and Fourier trun- cation. J. Stat. Mech.: Theory Exp., 02, 02066. DOI: https://doi.org/10.1088/1742-5468/2009/02/P02066 103. Wu, N., Li, Q.-X., and Zou, P., 2015. Multifractal properties of solar filaments and sunspots numbers. New Astron., 38, pp. 1—10. DOI: https://doi.org/10.1016/j.newast.2014.12.008 104. Zelenyi, L.M., and Milovanov, A.V., 1991. Fractal properties of sunspots. Sow Astron. Lett., 17(6), pp. 425—427. 105. Zelenyi, L.M., and Milovanov, A.V., 2004. Fractal topology and strange kinetics: from percolation theory to problems of space electrodynamics. Uspekhi fizicheskikh nauk, 174(8), pp. 809—852 (in Russian). DOI: https://doi.org/10.3367/UFNr.0174.200408a.0809 106. Kozlov, V.I., 1999. Estimation of the scaling properties of the dynamics of cosmic ray fluctuations in the solar activity cycle. Geo- magnetizm i aeronomiya, 39(1), pp. 100—104 (in Russian). 107. Val’chuk, Т.Е., and Mogilevtskiy, E.I., 2009. Discreteness of space-time manifestations of solar activity and solar-terrestrial rela- tions. Geomagnetizm i aeronomiya, 49(5), pp. 579—584 (in Russian). DOI: https://doi.org/10.1134/S0016793209050016 108. Onishchenko, A., Chernogor, L., and Lazorenko, O., 2019. Dynamical Fractal Analysis of the Acoustic Ultra-Wideband Signal Caused by the Chelyabinsk Meteoroid. Eskişehir Technical Univ. J. of Sci. and Tech. A – Appl. Sci. and Eng., 20, pp. 188—192. DOI: https://doi.org/10.18038/estubtda.655702 109. Lazorenko, O.V., and Chernogor, L.F., 2009. Ultrawideband signals and processes. Monograph. Kharkov: V.N. Karazin Kharkiv National University Publ. (in Russian). 110. Chernogor, L.F. , Lazorenko, O.V., and Onishchenko, A.A., 2017. Multi-Fractal Analysis of the Gravitational Waves. Vestnik ofV.N. Karazin Kharkiv National University. Ser. Physics, 26, pp. 33—39. 111. Chernogor, L.F., Lazorenko, O.V., and Onishchenko, A.A., 2018. Fractal Analysis of the Gravitational Waves as a Unique Ul- tra-Wideband Process. In: Proc. 9th Int. Conf. on Ultrawideband and Ultrashort Impulse Signals. Odessa, Ukraine, 4—7 Sept. 2018, pp. 34—39. DOI: https://doi.org/10.1109/UWBUSIS.2018.8519979 112. Abbott, B.P. et al., 2016. Observation of Gravitational waves from a Binary Black Hole Merger. Phys. Rev. Lett., 116(6), 061102 (16 p.). DOI: 10.1103/PhysRevLett.116.061102 113. Chernogor, L.F., 2010. Nonlinear radiophysics. Textbook. Kharkov: V.N. Karazin Kharkiv National University Publ. (in Russian). 114. Turcotte, D.L., 2004. The relationship of fractals in geophysics to "the new science". Chaos Solit. Fractals, 19(2), pp. 255—258. DOI: https://doi.org/10.1016/S0960-0779(03)00039-0 115. Schulke, T., and Siemroth, P., 1996. Vacuum arc cathode spots as a self-similarity phenomenon. IEEE Trans. Plasma Sci., 24(1), pp. 63—64. DOI: https://doi.org/10.1109/27.491692 116. Potapov, A.A., 2015. Fractal Radar: Towards 1980—2015. In: The 8th CHAOS Int. Conf.: Proc. Paris, France, 26—29 May 2015. Paris: Henri Poincare Institute 117. Kagan, Y.Y., and Knopoff, L., 1980. Spatial distribution of earthquakes: the two-point correlation function. Geophys. J. Roy. Astr. Soc., 62, pp. 303—320. DOI: https://doi.org/10.1111/j.1365-246X.1980.tb04857.x 118. Sadovskiy, M.A., Golubeva, T.V., Pisarenko, V.F., Shnirman, M.G., 1984. Characteristic dimensions of rock and hierarchical properties of seismicity. Izv. Akad. Nauk SSSR. Fiz. Zemli (USSR), 2, pp. 3—15. 119. Okubo, P.G., and Aki, K., 1987. Fractal geometry in the San Andreas Fault System. J. Geophys. Res., 92, pp. 345—355. DOI: https://doi.org/10.1029/JB092iB01p00345 120. Aviles, C.A., Scholz, C.H., and Boatwright, J., 1987. Fractal analysis applied to characteristic segments of the San Andreas Fault. J. Geophys. Res., 92, pp. 331—344. DOI: https://doi.org/10.1029/JB092iB01p00331 121. D’Amico, S. ed., 2012.Earthquake Research and Analysis — Seismology, Seismotectonic and Earthquake Geology. Rijeka: InTech Publ. DOI: https://doi.org/10.5772/1117 122. Brown, S.R., and Scholz, C.H., 1985. Broad band with study of the topography of natural rock surfaces. J. Geophys. Res., 90, pp. 12575—12582. DOI: https://doi.org/10.1029/JB090iB14p12575 123. Scholz, C.H., and Aviles, C.A., 1986, The fractal geometry of faults and faulting. In: Das, S., Boatwright, J., and Scholz, C.H., eds., 1986. Earthquake Source Mechanics, Am. Gcophys. Un. Maurice Ewing Ser. 6, pp. 147—156. DOI: https://doi.org/10.1029/GM037p0147 124. Sammis, C.G., and Biegel, R.L., 1989. Fractals, Fault-gouge, and Friction. Pure Appl. Geophys., 131(1—2), pp. 255—271. DOI: https://doi.org/10.1007/BF00874490 125. Mallat, S., 1998. A Wavelet Tour of Signal Processing. San Diego, CA: Academic Press. DOI: https://doi.org/10.1016/B978-012466606-1/50008-8 126. Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.E., 2002. Multifractal detrend- ed fluctuation analysis of nonstationary time series. Phys. A: Stat. Mech. Appl., 316(1—4), pp. 87—114. DOI: https://doi.org/10.1016/S0378-4371(02)01383-3 |
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