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UFN, 2004, Volume 174, Number 8, Pages 809–852 (Mi ufn78)  

This article is cited in 171 scientific papers (total in 171 papers)

REVIEWS OF TOPICAL PROBLEMS

Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics

L. M. Zelenyi, A. V. Milovanov

Space Research Institute, Russian Academy of Sciences

Abstract: The goal of this review is to outline some unconventional ideas behind new paradigms in the modern theory of turbulence. Application of nonstandard, topological methods to describe the structural properties of the turbulent state is considered and the transition to kinetic equations in fractional derivatives for describing the microscopic behavior of a medium is examined. Central to the discussion is the concept of the percolation constant $\mathcal C\approx 1.327…$, a universal parameter describing the topology of nonequilibrium (quasi)stationary states in complex nonlinear dynamical systems allowing self-organized critical behavior. Much attention is given to the formation of power-law energy density spectra in turbulent media. A number of topical problems in modern cosmic electrodynamics, including the self-consistent fractal model of a turbulent current sheet, substorm dynamics, and the formation and dynamical evolution of large-scale magnetic fields in the solar photosphere and interplanetary space, are also discussed.

DOI: https://doi.org/10.3367/UFNr.0174.200408a.0809

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English version:
Physics–Uspekhi, 2004, 47:8, 749–788

Bibliographic databases:

PACS: 05.40.-a, 05.45.Df, 05.65.+b, 94.30.-d
Received: July 4, 2003
Revised: March 30, 2004

Citation: L. M. Zelenyi, A. V. Milovanov, “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics”, UFN, 174:8 (2004), 809–852; Phys. Usp., 47:8 (2004), 749–788

Citation in format AMSBIB
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\by L.~M.~Zelenyi, A.~V.~Milovanov
\paper Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics
\jour UFN
\yr 2004
\vol 174
\issue 8
\pages 809--852
\mathnet{http://mi.mathnet.ru/ufn78}
\crossref{https://doi.org/10.3367/UFNr.0174.200408a.0809}
\transl
\jour Phys. Usp.
\yr 2004
\vol 47
\issue 8
\pages 749--788
\crossref{https://doi.org/10.1070/PU2004v047n08ABEH001705}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000225645400001}


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    1. Bogdan Hnat, Sandra C. Chapman, George Rowlands, “Compressibility in Solar Wind Plasma Turbulence”, Phys Rev Letters, 94:20 (2005), 204502  crossref  isi  scopus
    2. Yordanova, E, “Anisotropic scaling features and complexity in magnetospheric-cusp: a case study”, Nonlinear Processes in Geophysics, 12:6 (2005), 817  crossref  adsnasa  isi  scopus
    3. Milovanov, AV, “Fractional generalization of the Ginzburg-Landau equation: an unconventional approach to critical phenomena in complex”, Physics Letters A, 337:1–2 (2005), 75  crossref  zmath  adsnasa  isi  elib  scopus
    4. Selezneva L.V., “The stochastical model of approximation of the solution of subdiffusion equation”, Korus 2005, Proceedings, 2005, 100–103  isi
    5. Giuseppe Consolini, Paola Michelis, Matthieu Kretzschmar, “A Thermodynamic Approach to the Magnetospheric Complexity: The Role of Fluctuations”, Space Sci Rev, 122:1–4 (2006), 293  crossref  isi  scopus
    6. Vasily E. Tarasov, “Magnetohydrodynamics of fractal media”, Phys Plasmas, 13:5 (2006), 052107  crossref  mathscinet  isi  scopus
    7. Francesco Chiaravalloti, Alexander V Milovanov, Gaetano Zimbardo, “Self-similar transport processes in a two-dimensional realization of multiscale magnetic field turbulence”, Phys Scr, t122 (2006), 79  crossref  isi  scopus
    8. V Naulin, O E Garcia, M Priego, J Juul Rasmussen, “The application of passive tracers for investigating transport in plasma turbulence”, Phys Scr, t122 (2006), 129  crossref  adsnasa  isi  scopus
    9. A. C.-L. Chian, Y. Kamide, E. L. Rempel, W. M. Santana, “On the chaotic nature of solar-terrestrial environment: Interplanetary Alfvén intermittency”, J Geophys Res, 111:a7 (2006), A07S03  crossref  isi  scopus
    10. Vasily E Tarasov, George M Zaslavsky, “Nonholonomic constraints with fractional derivatives”, J Phys A Math Gen, 39:31 (2006), 9797  crossref  mathscinet  zmath  isi  scopus
    11. F Zonca, S Briguglio, L Chen, G Fogaccia, T S Hahm, A V Milovanov, G Vlad, “Physics of burning plasmas in toroidal magnetic confinement devices”, Plasma Phys Control Fusion, 48:12b (2006), B15  crossref  isi  scopus
    12. E. I. Mogilevsky, N. S. Shilova, “Fractal-cluster analysis and small-scale structures of solar flares”, Geomagn Aeron, 46:3 (2006), 303  crossref  isi  elib  scopus
    13. Tarasov, VE, “Electromagnetic fields on fractals”, Modern Physics Letters A, 21:20 (2006), 1587  crossref  zmath  adsnasa  isi  elib  scopus
    14. Revnivtsev, M, “Broad band variability of SS433: accretion disk at work?”, Astronomy & Astrophysics, 447:2 (2006), 545  crossref  isi  scopus
    15. M. Kretzschmar, G. Consolini, “Complexity in the Earth's magnetotail plasma sheet”, Boundary Layers, Waves and Non-Linear Dynamical Processes \series Advances in Space Research, Advances in Space Research, 37, no. 3, 2006, 552–558  crossref  isi  scopus
    16. V. Ya. Rudyak, A. A. Belkin, D. A. Ivanov, V. V. Egorov, “On the nonclassical diffusion of molecules of liquid and dense gases”, Dokl Phys, 52:2 (2007), 115  crossref  adsnasa  isi  elib  scopus
    17. K. Kiyani, S. C. Chapman, B. Hnat, R. M. Nicol, “Self-Similar Signature of the Active Solar Corona within the Inertial Range of Solar-Wind Turbulence”, Phys Rev Letters, 98:21 (2007), 211101  crossref  adsnasa  isi  scopus
    18. S C Lim, L P Teo, “Weyl and Riemann–Liouville multifractional Ornstein–Uhlenbeck processes”, J Phys A Math Theor, 40:23 (2007), 6035  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    19. C. H. Eab, S. C. Lim, L. P. Teo, “Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions”, J Math Phys (N Y ), 48:8 (2007), 082301  crossref  mathscinet  zmath  adsnasa  isi  scopus
    20. Alexander V. Milovanov, Kristoffer Rypdal, “Stretched exponential relaxation and ac universality in disordered dielectrics”, Phys Rev B, 76:10 (2007), 104201  crossref  isi  scopus
    21. Massimo Materassi, Giuseppe Consolini, “Magnetic Reconnection Rate in Space Plasmas: A Fractal Approach”, Phys Rev Letters, 99:17 (2007), 175002  crossref  adsnasa  isi  scopus
    22. L. Zelenyi, M. Oka, H. Malova, M. Fujimoto, D. Delcourt, W. Baumjohann, “Particle Acceleration in Mercury’s Magnetosphere”, Space Sci Rev, 132:2–4 (2007), 593  crossref  adsnasa  isi  elib  scopus
    23. A. M. Bykov, I. N. Toptygin, “Instabilities of a multicomponent plasma with accelerated particles and magnetic field generation in astrophysical objects”, Phys. Usp., 50:2 (2007), 141–174  mathnet  crossref  crossref  adsnasa  isi
    24. N. G. Bandurin, V. A. Ignatev, “Paket programm dlya resheniya sistem nelineinykh integro-differentsialnykh uravnenii (odno-, dvukh- i trekhmernye nachalno-kraevye zadachi)”, Matem. modelirovanie, 19:2 (2007), 105–111  mathnet  zmath
    25. L. K. Naphadzokova, G. V. Kozlov, G. E. Zaikov, “Role of diffusion processes in a model reaction of reesterification”, J Appl Polym Sci, 105:5 (2007), 2837  crossref  isi  elib  scopus
    26. Tarasov, VE, “The fractional Chapman Kolmogorov equation”, Modern Physics Letters B, 21:4 (2007), 163  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    27. Tarasov, VE, “Liouville and Bogoliubov equations with fractional derivative”, Modern Physics Letters B, 21:5 (2007), 237  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    28. Tarasov, VE, “Fractional derivative as fractional power of derivative”, International Journal of Mathematics, 18:3 (2007), 281  crossref  mathscinet  zmath  isi  scopus
    29. Meszaros, C, “Mathematical Modeling of drying processes using methods of the nonequilibrium thermodynamics and percolation theory”, Drying Technology, 25:7–8 (2007), 1297  crossref  isi  elib  scopus
    30. I. G. Samusev, V. V. Bryukhanov, A. M. Ivanov, I. S. Labutin, B. A. Loginov, “Heterogeneous triplet-triplet annihilation of erythrosine and anthracene molecules on a fractal anodized aluminum surface”, J Appl Spectrosc, 74:2 (2007), 230  crossref  adsnasa  isi  elib  scopus
    31. S C Lim, L P Teo, “Topological symmetry breaking of self-interacting fractional Klein–Gordon field theories on toroidal spacetime”, J Phys A Math Theor, 41:14 (2008), 145403  crossref  mathscinet  zmath  adsnasa  isi  scopus
    32. E. Yordanova, Z. Vörös, “Magnetosheath Plasma Turbulence and Its Spatiotemporal Evolution as Observed by the Cluster Spacecraft”, Phys Rev Letters, 100:20 (2008), 205003  crossref  adsnasa  isi  scopus
    33. V P Budaev, S Savin, L Zelenyi, N Ohno, S Takamura, E Amata, “Intermittency and extended self-similarity in space and fusion plasma: boundary effects”, Plasma Phys Control Fusion, 50:7 (2008), 074014  crossref  adsnasa  isi  elib  scopus
    34. V. A. Zhabrev, S. V. Chuppina, V. I. Margolin, “Self-organization as the rational choice of the direction of a chemical process”, Glass Phys Chem, 34:6 (2008), 641  crossref  isi  elib  scopus
    35. Budaev, VP, “Generalized Scale Invariance and Log-Poisson Statistics for Turbulence in the Scrape-off-Layer Plasma in the T-10 Tokamak”, Plasma Physics Reports, 34:10 (2008), 799  crossref  adsnasa  isi  elib  scopus
    36. Materassi, M, “Turning the resistive MHD into a stochastic field theory”, Nonlinear Processes in Geophysics, 15:4 (2008), 701  crossref  adsnasa  isi  scopus
    37. Potapov, AA, “Systems concept and components of fractal radio electronics: Part I. Development stages and the state of the art”, Journal of Communications Technology and Electronics, 53:9 (2008), 977  crossref  isi  scopus
    38. Alekseev, AD, “Fractal analysis of the hierarchic structure of fossil coal surface”, Journal of Mining Science, 44:3 (2008), 235  crossref  isi  scopus
    39. Naphadzokova, LK, “Description of the model transesterification reaction within the framework of a strange diffusion concept”, Journal of Applied Polymer Science, 109:5 (2008), 2791  crossref  isi  scopus
    40. Efremov, A, “Multilevel modeling of the influence of surface transport peculiarities on growth, shaping, and doping of Si nanowires”, Physica E-Low-Dimensional Systems & Nanostructures, 40:7 (2008), 2446  crossref  adsnasa  isi  scopus
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    42. Budaev, VP, “Extended self-similarity of intermittent turbulence in edge magnetized plasmas”, Nuclear Fusion, 48:2 (2008), 024014  crossref  mathscinet  adsnasa  isi  elib  scopus
    43. Zonca, F, “The physics of burning plasmas in toroidal magnetic field devices”, International Journal of Modern Physics A, 23:8 (2008), 1165  crossref  adsnasa  isi  scopus
    44. Milovanov, AV, “Stretched-exponential decay functions from a self-consistent model of dielectric relaxation”, Physics Letters A, 372:13 (2008), 2148  crossref  zmath  adsnasa  isi  elib  scopus
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    46. Zonca F., Chen L., “Nonlinear Dynamics and Complex Behaviors in Magnetized Plasmas of Fusion Interest”, Frontiers in Modern Plasma Physics, AIP Conference Proceedings, 1061, 2008, 34–44  crossref  adsnasa  isi
    47. Alexander V. Milovanov, “Pseudochaos and low-frequency percolation scaling for turbulent diffusion in magnetized plasma”, Phys Rev E, 79:4 (2009), 046403  crossref  isi  scopus
    48. Alexander V Milovanov, Rehab Bitane, Gaetano Zimbardo, “Kolmogorov–Sinai entropy in field line diffusion by anisotropic magnetic turbulence”, Plasma Phys Control Fusion, 51:7 (2009), 075003  crossref  isi  scopus
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    51. Mukhamedov A.M., “Turbulence. 1. Phase manifolds of turbulent dynamics”, Russ. Phys. J., 52:3 (2009), 314–320  crossref  zmath  isi  elib  scopus
    52. T. E. Val’chuk, E. I. Mogilevsky, “Discreteness of spatial-temporal manifestations of solar activity and solar-terrestrial phenomena”, Geomagn Aeron, 49:5 (2009), 551  crossref  isi  scopus
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    55. Kirchanov V.S., “Diffusion and relaxation of fractional order in fractal media in the classical and quantum cases”, Russian Phys. J., 52:4 (2009), 343–353  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
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    58. Alexander V Milovanov, “Dynamic polarization random walk model and fishbone-like instability for self-organized critical systems”, New J. Phys, 13:4 (2011), 043034  crossref  isi  scopus
    59. M. A. Vasyutin, “Fractal dimension of structural inhomogeneities in granular YBCO superconductor in magnetic field”, Tech. Phys. Lett, 37:8 (2011), 743  crossref  adsnasa  isi  elib  scopus
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    62. B.Y. Datsko, V.V. Gafiychuk, “Chaotic dynamics in Bonhoffer–van der Pol fractional reaction–diffusion system”, Signal Processing, 91:3 (2011), 452  crossref  zmath  isi  elib  scopus
    63. A A Khamzin, R R Nigmatullin, A P Alekhin, A S Sitdikov, A S Nikitin, “The NMR line shape of magneto-active nanoclusters in moveable nano-containers with self-similar stochastic dynamics”, International Conference on Resonances in Condensed Matter: Altshuler100, J. Phys. Conf. Ser, 324, 2011, 012005  crossref  adsnasa  isi  elib  scopus
    64. Sharma A.S., Veeramani T., “Extreme events and long-range correlations in space weather”, Nonlinear Processes in Geophysics, 18:5 (2011), 719–725  crossref  adsnasa  isi  scopus
    65. Sliusarenko O.Yu., “Generalized Fokker-Planck equation and its solution for linear non-Markovian Gaussian systems”, Condensed Matter Physics, 14:2 (2011), 23002  crossref  isi  elib  scopus
    66. Rekhviashvili C.Sh., Gavasheli D.Sh., “Teploprovodnost i teploemkost tverdykh tel s fraktalnoi strukturoi”, Nelineinyi mir, 9:5 (2011), 288–293  elib
    67. L. M. Zelenyi, H. V. Malova, A. V. Artemyev, V. Yu. Popov, A. A. Petrukovich, “Thin current sheets in collisionless plasma: Equilibrium structure, plasma instabilities, and particle acceleration”, Plasma Phys. Rep, 37:2 (2011), 118  crossref  adsnasa  isi  elib  elib  scopus
    68. Meilanov R.P., Alisultanov Z.Z., “O drobno-differentsialnom analize kvantovo-statisticheskikh sistem”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 13:1 (2011), 77–82  elib
    69. Karstina S.G., “Vliyanie strukturnoi organizatsii molekulyarnoi matritsy na protsessy obrazovaniya ustoichivykh fraktalnykh klasterov adsorbirovannykh molekul”, Izvestiya Kaliningradskogo gosudarstvennogo tekhnicheskogo universiteta, 2011, no. 23, 25–32  elib
    70. Kirillov A.K., “Issledovanie uglei donetskogo ugsholnogo basseina metodom malouglovogo rentgenovskogo rasseyaniya”, Fiziko-tekhnicheskie problemy gornogo proizvodstva, 2011, no. 14, 20–32  elib
    71. E. Baskin, A. Iomin, “Fractional electrostatic equations in fractal composite structures”, Computers & Mathematics with Applications, 64:10 (2012), 3302–3309  crossref  mathscinet  zmath  isi  scopus
    72. Vasyl Gafiychuk, Bohdan Datsko, “Different Types of Instabilities and Complex Dynamics in Reaction-Diffusion Systems With Fractional Derivatives”, J. Comput. Nonlinear Dynam, 7:3 (2012), 031001  crossref  mathscinet  isi  scopus
    73. I. G. Marchenko, I. I. Marchenko, “Anomalous temperature dependence of diffusion in crystals in time-periodic external fields”, JETP Letters, 95:3 (2012), 137–142  mathnet  crossref  isi  elib  elib
    74. J. Birn, A. V. Artemyev, D. N. Baker, M. Echim, M. Hoshino, L. M. Zelenyi, “Particle Acceleration in the Magnetotail and Aurora”, Space Sci Rev, 173:1-4 (2012), 49–102  crossref  zmath  isi  elib  scopus
    75. V.N. Borodikhin, “Fractional differential kinetic equation and growth of the nuclei of a new phase at phase transitions”, Physics Letters A, 376:24-25 (2012), 1952–1954  crossref  zmath  isi  elib  scopus
    76. Alexander S. Balankin, Benjamin Espinoza Elizarraraz, “Map of fluid flow in fractal porous medium into fractal continuum flow”, Phys. Rev. E, 85:5 (2012)  crossref  isi  elib  scopus
    77. Z. Z. Alisultanov, R. P. Meylanov, “Some features of quantum statistical systems with an energy spectrum of the fractional-power type”, Theoret. and Math. Phys., 171:3 (2012), 769–779  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    78. Hélène Porchon, “Fractal topology foundations”, Topology and its Applications, 159:14 (2012), 3156–3170  crossref  mathscinet  zmath  isi  scopus
    79. G.P. Pavlos, L.P. Karakatsanis, M.N. Xenakis, “Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics”, Physica A: Statistical Mechanics and its Applications, 391:24 (2012), 6287–6319  crossref  isi  scopus
    80. A. V. Milovanov, A. Iomin, “Localization-delocalization transition on a separatrix system of nonlinear Schrödinger equation with disorder”, EPL, 100:1 (2012), 10006  crossref  isi  elib  scopus
    81. Alexander Balankin, Baltasar Mena, C. Martínez-González, Daniel Matamoros, “Random walk in chemical space of Cantor dust as a paradigm of superdiffusion”, Phys. Rev. E, 86:5 (2012)  crossref  isi  scopus
    82. Pustil'nik L.A., Ikhsanov N.R., Beskrovnaya N.G., “On the Energy Release in Solar Flares”, Waves and Instabilities in Space and Astrophysical Plasmas, AIP Conference Proceedings, 1439, eds. Sulem P., Mond M., Amer Inst Physics, 2012, 63–70  crossref  adsnasa  isi  scopus
    83. Korolev L.V., Bytev D.O., “Modelirovanie protsessov sluchainogo perenosa v usloviyakh lokalnoi neravnovesnosti”, Izvestiya vysshikh uchebnykh zavedenii. Seriya: Khimiya i khimicheskaya tekhnologiya, 55:1 (2012), 100–104  elib
    84. Polyakov S.A., Bykov V.I., Chertorylskii I.S., “Opisanie protsessov formirovaniya nanostrukturnykh materialov s ispolzovaniem nelineinykh bazovykh modelei khimicheskoi dinamiki”, Nanotekhnika, 2012, no. 3, 12–18  elib
    85. O. G. Bakunin, “Reconstruction of streamline topology, and percolation models of turbulent transport”, Phys. Usp., 56:3 (2013), 243–260  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    86. Starokurov Yu.V., Letuta S.N., Pashkevich S.N., Antropova T.V., Gordeeva Yu.A., Saletsky A.M., “Luminescence Kinetics of Two-Component Molecular Systems in Porous Glasses”, Opt. Spectrosc., 114:1 (2013), 87–90  crossref  adsnasa  isi  elib  scopus
    87. Starokurov Yu.V., Letuta S.N., Pashkevich S.N., Antropova T.V., Gordeeva Yu.A., Saletskii A.M., “Kinetika lyuminestsentsii dvukhkomponentnykh molekulyarnykh sistem v poristykh steklakh”, Optika i spektroskopiya, 114:1 (2013), 95–95  crossref  elib
    88. Xiao-Jing Ma, H. M. Srivastava, Dumitru Baleanu, Xiao-Jun Yang, “A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations”, Mathematical Problems in Engineering, 2013 (2013), 325121, 6 pp.  crossref  mathscinet  zmath  isi  scopus
    89. A. A. Chernyshov, M. M. Mogilevsky, B. V. Kozelov, “Use of fractal approach to investigate ionospheric conductivity in the auroral zone”, J. Geophys. Res. Space Physics, 118:7 (2013), 4108–4118  crossref  isi  scopus
    90. A. A. Chernyshov, M. M. Mogilevsky, B. V. Kozelov, “Fractal approach to the description of the auroral region”, Plasma Phys. Rep, 39:7 (2013), 562  crossref  adsnasa  isi  elib  scopus
    91. V. A. Stuchinsky, “Size effects in percolation of small regions on planar and cylindrical surfaces”, Tech. Phys. Lett, 39:4 (2013), 380  crossref  mathscinet  adsnasa  isi  elib  scopus
    92. L.P. Karakatsanis, G.P. Pavlos, M.N. Xenakis, “Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar flares dynamics”, Physica A: Statistical Mechanics and its Applications, 392:18 (2013), 3920–3944  crossref  mathscinet  isi  scopus
    93. V. N. Borodikhin, “Phase transitions and peculiarities of the growth of nuclei of the new phase of a substance”, Theoret. and Math. Phys., 177:1 (2013), 1390–1399  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    94. D. A. Zenyuk, N. A. Mitin, Yu. N. Orlov, “Modelirovanie sluchainogo bluzhdaniya na Kantorovom mnozhestve”, Preprinty IPM im. M. V. Keldysha, 2013, 031, 18 pp.  mathnet
    95. Devi S.P., Singh S.B., Sharma A.S., “Deterministic Dynamics of the Magnetosphere: Results of the 0-1 Test”, Nonlinear Process Geophys., 20:1 (2013), 11–18  crossref  adsnasa  isi  scopus
    96. N. S. Arkashov, V. A. Seleznev, “On a random walk model on sets with self-similar structure”, Siberian Math. J., 54:6 (2013), 968–983  mathnet  crossref  mathscinet  isi
    97. V. V. Uchaikin, “Fractional phenomenology of cosmic ray anomalous diffusion”, Phys. Usp., 56:11 (2013), 1074–1119  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    98. G.P. Pavlos, L.P. Karakatsanis, M.N. Xenakis, E.G. Pavlos, A.C. Iliopoulos, “Universality of tsallis non-extensive statistics and time series analysis: Theory and applications”, Physica A: Statistical Mechanics and its Applications, 395 (2014), 58–95  crossref  mathscinet  isi  scopus
    99. Yu. I. Yermolaev, “Where are medium-scale solar-wind variations formed?”, Geomagn. Aeron, 54:2 (2014), 162  crossref  isi  elib  scopus
    100. D. A. Zenyuk, Yu. N. Orlov, “O primenenii drobnogo ischisleniya Rimana–Liuvillya dlya opisaniya raspredelenii veroyatnostei”, Preprinty IPM im. M. V. Keldysha, 2014, 018, 21 pp.  mathnet
    101. A.V.. Milovanov, Jens Juul Rasmussen, “A mixed SOC-turbulence model for nonlocal transport and Lévy-fractional Fokker–Planck equation”, Physics Letters A, 378:21 (2014), 1492–1500  crossref  mathscinet  zmath  isi  elib  scopus
    102. L. V. Matveev, “Advection of an impurity in percolation media with a finite correlation length”, J. Exp. Theor. Phys, 118:4 (2014), 662  crossref  adsnasa  isi  elib  scopus
    103. Z. A. Nakhusheva, “The Samarskii Problem for the Fractal Diffusion Equation”, Math. Notes, 95:6 (2014), 815–819  mathnet  crossref  crossref  mathscinet  isi  elib
    104. A. A. Chernyshov, K. V. Karelsky, A. S. Petrosyan, “Subgrid-scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas”, Phys. Usp., 57:5 (2014), 421–452  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    105. A.V.. Milovanov, Alexander Iomin, “Topological approximation of the nonlinear Anderson model”, Phys. Rev. E, 89:6 (2014)  crossref  isi  elib  scopus
    106. B. A. Snopok, “Nonexponential Kinetics of Surface Chemical Reactions”, Theor Exp Chem, 50:2 (2014), 67–95  crossref  isi  elib  scopus
    107. Shakura N. Postnov K. Sidoli L. Paizis A., “Bright Flares in Supergiant Fast X-Ray Transients”, Mon. Not. Roy. Astron. Soc., 442:3 (2014), 2325–2330  crossref  isi  elib  scopus
    108. D. A. Zenyuk, “Modelirovanie sluchainykh bluzhdanii na regulyarnykh fraktalnykh mnozhestvakh”, Matem. modelirovanie, 26:11 (2014), 101–104  mathnet  mathscinet  elib
    109. Artemyev A.V. Vasko I.Y. Lutsenko V.N. Petrukovich A.A., “Formation of the High-Energy Ion Population in the Earth's Magnetotail: Spacecraft Observations and Theoretical Models”, Ann. Geophys., 32:10 (2014), 1233–1246  crossref  isi  elib  scopus
    110. Lev Zelenyi, Anton Artemyev, Anatoli Petrukovich, “Properties of Magnetic Field Fluctuations in the Earth’s Magnetotail and Implications for the General Problem of Structure Formation in Hot Plasmas”, Space Sci Rev, 2015  crossref  isi  scopus
    111. Markus J. Aschwanden, Norma B. Crosby, Michaila Dimitropoulou, Manolis K. Georgoulis, Stefan Hergarten, James McAteer, Alexander V. Milovanov, Shin Mineshige, Laura Morales, Naoto Nishizuka, Gunnar Pruessner, Raul Sanchez, A. Surja Sharma, Antoine Strugarek, Vadim Uritsky, “25 Years of Self-Organized Criticality: Solar and Astrophysics”, Space Sci Rev, 2015  crossref  isi  scopus
    112. F Zonca, L Chen, S Briguglio, G Fogaccia, A.V. Milovanov, “Energetic particles and multi-scale dynamics in fusion plasmas”, Plasma Phys. Control. Fusion, 57:1 (2015), 014024  crossref  isi  elib  scopus
    113. G.P. Pavlos, A.C. Iliopoulos, G.N. Zastenker, L.M. Zelenyi, L.P. Karakatsanis, “Tsallis non-extensive statistics and solar wind plasma complexity”, Physica A: Statistical Mechanics and its Applications, 422 (2015), 113–135  crossref  mathscinet  isi  scopus
    114. A.A. Chernyshov, M.M. Mogilevsky, B.V. Kozelov, “Application of nonlinear methods to the study of ionospheric plasma”, J. Phys.: Conf. Ser, 574 (2015), 012128  crossref  isi  scopus
    115. E. V. Yushkov, A. G. Frank, A. V. Artemyev, A. A. Petrukovich, I. Y. Vasko, “Formation of a quasi-one-dimensional current sheet in the laboratory experiment and in the Earth’s magnetotail”, Plasma Phys. Rep, 41:1 (2015), 71  crossref  isi  elib  scopus
    116. A. V. Petlenko, Yu. A. Kopytenko, “Influence of anomalous particle diffusion on the current system formation and coherence of Pi2 geomagnetic pulsation local ionospheric sources”, Geomagn. Aeron, 55:1 (2015), 24  crossref  isi  scopus
    117. A. M. Mukhamedov, “Deindividuation phenomenon: Links between mesodynamics and macroscopic phenomenology of turbulence”, Phys Mesomech, 18:1 (2015), 24  crossref  isi  elib  scopus
    118. L.M.. Zelenyi, A.M.. Bykov, Yu.A.. Uvarov, A.V.. Artemyev, “Intermittency of magnetic field turbulence: Astrophysical applications of in-situ observations”, J. Plasma Phys, 2015, 1  crossref  isi  scopus
    119. G. Consolini, S. Grandioso, E. Yordanova, M. F. Marcucci, G. Pallocchia, “STATISTICAL AND SCALING FEATURES OF FLUCTUATIONS IN THE DISSIPATION RANGE DURING A RECONNECTION EVENT”, ApJ, 804:1 (2015), 19  crossref  isi  elib  scopus
    120. A. V. Guglielmi, “On permanent and sporadic pulsations of the magnetosphere”, Izv., Phys. Solid Earth, 51:3 (2015), 331  crossref  isi  elib  scopus
    121. I. V. Dolbin, G. V. Kozlov, A. K. Mikitaev, “Fire resistance structural model of polymer–organoclay composites”, High Temperature, 53:4 (2015), 554–557  mathnet  crossref  crossref  isi  elib  elib
    122. G.P. Pavlos, L.P. Karakatsanis, A.C. Iliopoulos, E.G. Pavlos, M.N. Xenakis, “Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex”, Physica A: Statistical Mechanics and its Applications, 2015  crossref  isi  scopus
    123. N. I. Shakura, K. A. Postnov, A. Yu. Kochetkova, L. Hjalmarsdotter, L. Sidoli, “Wind accretion: Theory and observations”, Astron. Rep, 59:7 (2015), 645  crossref  isi  elib  scopus
    124. N. E. Kask, E. G. Leksina, S. V. Michurin, G. M. Fedorov, D. B. Chopornyak, “Broadening and shift of the spectral lines of hydrogen atoms and silicon ions in laser plasma”, Quantum Electron., 45:6 (2015), 527–532  mathnet  crossref  isi  elib
    125. N. S. Arkashov, V. A. Seleznev, “On one model of sub- and superdiffusion on topological spaces with a self-similar structure”, Theory Probab. Appl., 60:2 (2016), 173–186  mathnet  crossref  crossref  isi  elib
    126. Budaev V.P. Zelenyi L.M. Savin S.P., “Generalized Self-Similarity of Intermittent Plasma Turbulence in Space and Laboratory Plasmas”, J. Plasma Phys., 81:6 (2015), 395810602  crossref  isi  elib  scopus
    127. Gubchenko V.M., “Kinetic Description of the 3D Electromagnetic Structures Formation in Flows of Expanding Plasma Coronas. Part 1: General”, Geomagn. Aeron., 55:7 (2015), 831–845  crossref  isi  elib  scopus
    128. Riazantseva M.O. Budaev V.P. Zelenyi L.M. Zastenker G.N. Pavlos G.P. Safrankova J. Nemecek Z. Prech L. Nemec F., “Dynamic Properties of Small-Scale Solar Wind Plasma Fluctuations”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 373:2041 (2015), 20140146  crossref  isi  scopus
    129. Patsourakos S., Georgoulis M.K., Vourlidas A., Nindos A., Sarris T., Anagnostopoulos G., Anastasiadis A., Chintzoglou G., Daglis I.A., Gontikakis C., Hatzigeorgiu N., Iliopoulos A.C., Katsavrias C., Kouloumvakos A., Moraitis K., Nieves-Chinchilla T., Pavlos G., Sarafopoulos D., Syntelis P., Tsironis C., Tziotziou K., Vogiatzis I.I., Balasis G., Georgiou M., Karakatsanis L.P., Malandraki O.E., Papadimitriou C., Odstrcil D., Pavlos E.G., Podlachikova O., Sandberg I., Turner D.L., Xenakis M.N., Sarris E., Tsinganos K., Vlahos L., “the Major Geoeffective Solar Eruptions of 2012 March 7: Comprehensive Sun-To-Earth Analysis”, Astrophys. J., 817:1 (2016), 14  crossref  isi  scopus
    130. Sharma A.S. Aschwanden M.J. Crosby N.B. Klimas A.J. Milovanov A.V. Morales L. Sanchez R. Uritsky V., “25 Years of Self-Organized Criticality: Space and Laboratory Plasmas”, Space Sci. Rev., 198:1-4 (2016), 167–216  crossref  isi  scopus
    131. V. V. Kocharovsky, Vl. V. Kocharovsky, V. Yu. Martyanov, S. V. Tarasov, “Analytical theory of self-consistent current structures in a collisionless plasma”, Phys. Usp., 59:12 (2016), 1165–1210  mathnet  crossref  crossref  adsnasa  isi  elib
    132. Riazantseva M.O. Budaev V.P. Rakhmanova L.S. Zastenker G.N. Safrankova J. Nemecek Z. Prech L., “Comparison of properties of small-scale ion flux fluctuations in the flank magnetosheath and in the solar wind”, Adv. Space Res., 58:2 (2016), 166–174  crossref  isi  scopus
    133. Popov I., Ben Ishai P., Khamzin A., Feldman Yu., “The mechanism of the dielectric relaxation in water”, Phys. Chem. Chem. Phys., 18:20 (2016), 13941–13953  crossref  isi  scopus
    134. Pavlos G.P., Malandraki O.E., Pavlos E.G., Iliopoulos A.C., Karakatsanis L.P., “Non-extensive statistical analysis of magnetic field during the March 2012 ICME event using a multi-spacecraft approach”, Physica A, 464 (2016), 149–181  crossref  mathscinet  isi  elib  scopus
    135. Sidoli L., Paizis A., Postnov K., “INTEGRAL study of temporal properties of bright flares in Supergiant Fast X-ray Transients”, Mon. Not. Roy. Astron. Soc., 457:4 (2016), 3693–3701  crossref  isi  elib  scopus
    136. Silin V.P. Budaev V.P. Savin S.P. Rakhmanova L.S. Ryazantsev M.O. Popov V.Yu. Uryupin S.A., “On the superdiffusive scalings of transport in plasma”, Bull. Lebedev Phys. Inst., 43:4 (2016), 132–137  crossref  isi  elib  scopus
    137. Chen L., Zonca F., “Physics of Alfvén waves and energetic particles in burning plasmas”, Rev. Mod. Phys., 88:1 (2016), 015008  crossref  isi  elib  scopus
    138. Makin V.S., Pestov I Yu., Makin R.S., “Abnormal spatial nanogratings formation by long pulse laser radiation on condensed matter surfaces”, 2016 Days on Diffraction (DD) (St.Petersburg, Russia), eds. Motygin O., Kiselev A., Kapitanova P., Goray L., Kazakov A., Kirpichnikova A., IEEE, 2016, 298–303  crossref  isi  scopus
    139. Shuman V.N., “on Prognostication Ability of Active Geosystems: Metastability and Steady Transitions Instead of Attractors”, Geofiz. Zhurnal, 38:6 (2016), 3–24  crossref  isi
    140. Shuman V.N., “Fractional Dynamics and Emissive Activity of Geosystems”, Geofiz. Zhurnal, 38:3 (2016), 72–83  crossref  isi
    141. Shuman V.N., “Spontaneous Emission Activity of Lithosphere and Seismoelectromagnetic Phenomena”, Geofiz. Zhurnal, 38:2 (2016), 79–87  crossref  isi
    142. D. A. Zenyuk, L. V. Klochkova, Yu. N. Orlov, “Modelirovanie nestatsionarnykh sluchainykh protsessov kineticheskimi uravneniyami s drobnymi proizvodnymi”, Zhurnal SVMO, 18:2 (2016), 125–133  mathnet  elib
    143. Mikhael A. Vasyutin, Nikolay D. Kuzmichev, Dmitri A. Shilkin, “Fractal boundaries of vortex pinning clusters in copper-oxide superconductors in magnetic field”, Zhurn. SFU. Ser. Matem. i fiz., 10:2 (2017), 261–265  mathnet  crossref
    144. Bykov A.M., Ellison D.C., Osipov S.M., “Nonlinear Monte Carlo model of superdiffusive shock acceleration with magnetic field amplification”, Phys. Rev. E, 95:3 (2017)  crossref  isi  scopus
    145. Riazantseva M.O., Rakhmanova L.S., Zastenker G.N., Ermolaev Yu.I., “Types of spectra of ion flux fluctuations in the solar wind and magnetosheath at the interface between inertial and dissipative ranges”, Geomagn. Aeron., 57:1 (2017), 1–7  crossref  isi  scopus
    146. Naeem I. Khan M.D., “Symmetry classification of time-fractional diffusion equation”, Commun. Nonlinear Sci. Numer. Simul., 42 (2017), 560–570  crossref  isi  elib  scopus
    147. P. S. Kondratenko, “Asymptotic approach to the description of nonclassical transport processes. Fermat's principle”, JETP Letters, 106:9 (2017), 604–607  mathnet  crossref  crossref  isi  elib
    148. Mbemmo A.M.F., Kenmoe G.D., Kofane T.C., “Shape Potential Effects on Transport and Diffusion Phenomena”, Fluct. Noise Lett., 16:2 (2017), 1750011  crossref  isi  scopus
    149. Melkikh A.V. Khrennikov A., “Quantum-Like Model of Partially Directed Evolution”, Prog. Biophys. Mol. Biol., 125 (2017), 36–51  crossref  isi  elib  scopus
    150. Chernyshov A.A. Kozelov B.V. Mogilevsky M.M., “Study of Auroral Ionosphere Using Percolation Theory and Fractal Geometry”, J. Atmos. Sol.-Terr. Phys., 161 (2017), 127–133  crossref  isi  scopus
    151. Tikhomirova N.S. Samusev I.G. Slezhkin V.A. Bryukhanov V.V., “Rhodamine 6G Fluorescence Quenching By An External Heavy Atom and Silver Nanoparticles At the Nanoporous-Silica-Water Boundary”, J. Appl. Spectrosc., 84:3 (2017), 376–381  crossref  isi  scopus
    152. Popov I., Lunev I., Khamzin A., Greenbaum (Gutina) Anna, Gusev Yu., Feldman Yu., “the Low-Temperature Dynamic Crossover in the Dielectric Relaxation of Ice i-H”, Phys. Chem. Chem. Phys., 19:42 (2017), 28610–28620  crossref  isi  scopus
    153. Riazantseva M.O. Budaev V.P. Rakhmanova L.S. Borodkova N.L. Zastenker G.N. Yermolaev Yu.I. Safrankova J. Nemecek Z. Prech L. Pitna A., “Intermittency of the Solar Wind Density Near the Interplanetary Shock”, Geomagn. Aeron., 57:6 (2017), 645–654  crossref  isi  scopus
    154. Riazantseva M. Budaev V. Rakhmanova L. Zastenker G. Yermolaev Yu. Lodkina I. Safrankova J. Nemecek Z. Prech L., “Variety of Shapes of Solar Wind Ion Flux Spectra: Spektr-R Measurements”, J. Plasma Phys., 83:4 (2017), 705830401  crossref  isi
    155. M. V. Platonova, S. V. Tsykin, “Veroyatnostnaya approksimatsiya resheniya zadachi Koshi dlya uravneniya Shrëdingera s operatorom drobnogo differentsirovaniya”, Veroyatnost i statistika. 26, Zap. nauchn. sem. POMI, 466, POMI, SPb., 2017, 257–272  mathnet
    156. N. S. Arkashov, V. A. Seleznev, “On the dynamics of stationary shift processes with Cantor structure”, Siberian Math. J., 58:5 (2017), 752–764  mathnet  crossref  crossref  isi  elib  elib
    157. Vasyutin M.A., Kuz'michev N.D., Shilkin D.A., “Magnetic Field Gain in Vortex Pinning At Fractal Interfaces of Clusters of High-Temperature Superconductors”, Tech. Phys., 63:2 (2018), 307–309  crossref  isi  scopus
    158. Kurazhkovskaya N.A., Klain B.I., “Statistical Study of the Characteristics of Isolated Bursts of Midlatitude Pi2 Geomagnetic Pulsations”, Geomagn. Aeron., 58:2 (2018), 185–200  crossref  isi  scopus
    159. Milovanov V A., Rasmussen J.J., “Levy Flights on a Comb and the Plasma Staircase”, Phys. Rev. E, 98:2 (2018), 022208  crossref  isi  scopus
    160. Parkhomenko E.I., Malova H.V., Grigorenko E.E., Popov V.Yu., Petrukovich A.A., Delcourt D.C., Kronberg E.A., Daly P.W., Zelenyi L.M., ““Plasma Acceleration on Multiscale Temporal Variations of Electric and Magnetic Fields During Substorm Dipolarization in the Earth's Magnetotail””, Ann. Geophys., 61:3 (2018), GM334  crossref  isi  scopus
    161. D. I. Iudin, S. S. Davydenko, V. M. Gotlib, M. S. Dolgonosov, L. M. Zelenyi, “Physics of lightning: new model approaches and prospects of the satellite observations”, Phys. Usp., 61:8 (2018), 766–778  mathnet  crossref  crossref  adsnasa  isi  elib
    162. Sharapova T.V., Makin R.S., “Application of Fractal-Geometry Approaches to Simulating Migration Processes in Soil”, J. Surf. Ingestig., 12:6 (2018), 1248–1252  crossref  isi  scopus
    163. Herega A. Sukhanov V. Vyrovoy V. Kryvchenko Yu., “Modeling of Self-Organizing Percolation Clusters: Dependence of the Structure on History of Generation and Parameters of the Cluster System”, AIP Conference Proceedings, 2051, ed. Panin V. Psakhie S. Fomin V., Amer Inst Physics, 2018, UNSP 020105  crossref  isi
    164. Milovanov V A., Iomin A., “Subdiffusive Levy Flights in Quantum Nonlinear Schrodinger Lattices With Algebraic Power Nonlinearity”, Phys. Rev. E, 99:5 (2019), 052223  crossref  isi
    165. Mukhamedov A.M., “Developed Turbulence: New Methods For Turbulence Modeling”, Phys. Mesomech., 22:3 (2019), 181–187  crossref  isi
    166. Datsko B., Podlubny I., Povstenko Yu., “Time-Fractional Diffusion-Wave Equation With Mass Absorption in a Sphere Under Harmonic Impact”, Mathematics, 7:5 (2019), 433  crossref  isi
    167. Riazantseva M.O., Rakhmanova L.S., Zastenker G.N., Yermolaev Yu.I., Lodkina I.G., “Features of the Spectral Characteristics of Plasma Fluctuations in Different Large-Scale Streams of the Solar Wind”, Geomagn. Aeron., 59:2 (2019), 127–135  crossref  isi
    168. D. A. Zenyuk, G. G. Malinetskii, “Odnomernyi bryusselyator s drobnymi proizvodnymi po vremeni”, Preprinty IPM im. M. V. Keldysha, 2019, 098, 32 pp.  mathnet  crossref
    169. M. A. Vasyutin, N. D. Kuzmichev, D. A. Shilkin, “Matematicheskoe modelirovanie volt-ampernykh kharakteristik vysokotemperaturnykh sverkhprovodnikov s fraktalnymi granitsami klasterov normalnoi fazy”, Zhurnal SVMO, 21:4 (2019), 507–519  mathnet  crossref
    170. L. A. Bolshov, P. S. Kondratenko, L. V. Matveev, “Nonclassical transport in highly heterogeneous and sharply contrasting media”, Phys. Usp., 62:7 (2019), 649–659  mathnet  crossref  crossref  adsnasa  isi
    171. D. A. Zenyuk, G. G. Malinetskii, “Formirovanie patternov v sisteme reaktsii-diffuzii s drobnymi proizvodnymi po vremeni”, Matem. modelirovanie, 32:6 (2020), 53–65  mathnet  crossref
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