Skip to main content
Top

2016 | OriginalPaper | Chapter

5. Multifractal Analysis of Fatigue Failure

Authors : Ahad Kh. Janahmadov, Maksim Y. Javadov

Published in: Synergetics and Fractals in Tribology

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Various physical objects and signals even those with self-similarity very rarely can be described with only one value—the fractal dimension. That is why analyses based on the multifractal theory (inhomogeneous fractal objects) have received widespread. The multifractal provides vast new possibilities of fractal analysis for the complex stochastic processes.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference S.V. Bozhokin, D.A. Parshin, Fraktaly i mul’tifraktaly (NITs “Reguliarnaia i khaoticheskaia dinamika”, Izhevsk, 2001), p. 128 S.V. Bozhokin, D.A. Parshin, Fraktaly i mul’tifraktaly (NITs “Reguliarnaia i khaoticheskaia dinamika”, Izhevsk, 2001), p. 128
2.
4.
go back to reference H.G.E. Hentschel, I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors. Phys. D 8, 435–444 (1983)MathSciNetCrossRefMATH H.G.E. Hentschel, I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors. Phys. D 8, 435–444 (1983)MathSciNetCrossRefMATH
5.
go back to reference P.V. Korolenko, M.S. Maganova, A.V. Mesniankin, Novatsionnye metody analiza stokhasticheskikh protsessov i struktur v optike. Fraktal’nye i mul’tifraktal’nye metody, veivlet preobrazovaniia. Uchebnoe posobie (MGU, NII iadernoi fiziki, Moscow, 2004), p. 82 P.V. Korolenko, M.S. Maganova, A.V. Mesniankin, Novatsionnye metody analiza stokhasticheskikh protsessov i struktur v optike. Fraktal’nye i mul’tifraktal’nye metody, veivlet preobrazovaniia. Uchebnoe posobie (MGU, NII iadernoi fiziki, Moscow, 2004), p. 82
6.
go back to reference R.M. Kronover, Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii (Postmarket, Moscow, 2000), p. 352 R.M. Kronover, Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii (Postmarket, Moscow, 2000), p. 352
7.
go back to reference T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Fractal measures and their singularities of strange sets. Phys. Rev. A 33(2), 1141–1151 (1986)ADSMathSciNetCrossRefMATH T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Fractal measures and their singularities of strange sets. Phys. Rev. A 33(2), 1141–1151 (1986)ADSMathSciNetCrossRefMATH
8.
9.
go back to reference T.S. Akhromeeva, S.P. Kurdiumov, G.G. Malinetskii, A.A. Samarskii, Nestatsionarnye struktury i diffuzionnyi khaos (Nauka, Gl. red. fiz.-mat. lit, Moscow, 1992), p. 544 T.S. Akhromeeva, S.P. Kurdiumov, G.G. Malinetskii, A.A. Samarskii, Nestatsionarnye struktury i diffuzionnyi khaos (Nauka, Gl. red. fiz.-mat. lit, Moscow, 1992), p. 544
10.
go back to reference G. Shuster, Determinirovannyi khaos. Vvedenie (Mir, Moscow, 1988), p. 240 G. Shuster, Determinirovannyi khaos. Vvedenie (Mir, Moscow, 1988), p. 240
11.
go back to reference A.N. Pavlov, Metody analiza slozhnykh signalov. Ucheb. posobie dlia stud. fiz. fak. (Nauchnaia kniga, Saratov, 2008), p. 120 A.N. Pavlov, Metody analiza slozhnykh signalov. Ucheb. posobie dlia stud. fiz. fak. (Nauchnaia kniga, Saratov, 2008), p. 120
12.
go back to reference V.S. Ivanova, Razrushenie metallov (Metallurgiia, Moscow, 1979), p. 168 V.S. Ivanova, Razrushenie metallov (Metallurgiia, Moscow, 1979), p. 168
13.
go back to reference A.I. Olemskoi, V.A. Petrunin, Perestroika kondensirovannogo sostoianiia atomov v usloviiakh intensivnogo vozdeistviia. Izv. vuzov. Fizika. (1), 82–121 (1989) A.I. Olemskoi, V.A. Petrunin, Perestroika kondensirovannogo sostoianiia atomov v usloviiakh intensivnogo vozdeistviia. Izv. vuzov. Fizika. (1), 82–121 (1989)
14.
go back to reference A.I. Olemskoi, I.I. Naumov, Fraktal’naia kinetika ustalostnogo razrusheniia. V kn. Sinergetika i ustalostnoe razrushenie metallov (Nauka, Moscow, 1989), pp. 200–214 A.I. Olemskoi, I.I. Naumov, Fraktal’naia kinetika ustalostnogo razrusheniia. V kn. Sinergetika i ustalostnoe razrushenie metallov (Nauka, Moscow, 1989), pp. 200–214
15.
go back to reference A.I. Olemskoi, A.A. Katsnel’son, Sinergetika kondensirovannoi sredy. izd. 2-e. (Editorial URSS, Moscow, 2010), p. 336 A.I. Olemskoi, A.A. Katsnel’son, Sinergetika kondensirovannoi sredy. izd. 2-e. (Editorial URSS, Moscow, 2010), p. 336
16.
go back to reference Iu.B. Rumer, M.Sh. Ryvkin, Termodinamika, statisticheskaia fizika i kinetika (Izd.-vo Novosib. un-ta: Sib. univ. Izd.-vo, Novosibirsk, 2001), p. 608 Iu.B. Rumer, M.Sh. Ryvkin, Termodinamika, statisticheskaia fizika i kinetika (Izd.-vo Novosib. un-ta: Sib. univ. Izd.-vo, Novosibirsk, 2001), p. 608
17.
go back to reference B.M. Askerov, Termodinamika i staticheskaia fizika (Izd-vo Baky Universiteti, Baku, 2007), p. 512 B.M. Askerov, Termodinamika i staticheskaia fizika (Izd-vo Baky Universiteti, Baku, 2007), p. 512
18.
go back to reference V.S. Ivanova, V.F. Terent’ev, Priroda ustalosti metallov (Metallurgiia, Moscow, 1975), p. 455 V.S. Ivanova, V.F. Terent’ev, Priroda ustalosti metallov (Metallurgiia, Moscow, 1975), p. 455
19.
go back to reference A.Kh. Janahmadov, Tribotekhnicheskie problemy v neftegazovom oborudovanii (Elm, Baku, 1998), p. 216 A.Kh. Janahmadov, Tribotekhnicheskie problemy v neftegazovom oborudovanii (Elm, Baku, 1998), p. 216
20.
go back to reference O.N. Romaniv, Viazkost’ razrusheniia konstruktsionnykh stalei (Metallurgiia, Moscow, 1979), p. 176 O.N. Romaniv, Viazkost’ razrusheniia konstruktsionnykh stalei (Metallurgiia, Moscow, 1979), p. 176
21.
go back to reference O.N. Romaniv, A.S. Krys’kiv, Ispol’zovanie kriteriev mekhaniki razrusheniia dlia otsenki khladnolomkosti stalei. Fiz.-khim. mekhanika materialov. (5), 40–51 (1981) O.N. Romaniv, A.S. Krys’kiv, Ispol’zovanie kriteriev mekhaniki razrusheniia dlia otsenki khladnolomkosti stalei. Fiz.-khim. mekhanika materialov. (5), 40–51 (1981)
22.
go back to reference B.I. Medovar, L.I. Gladshtein, V.Ia. Saenko i dr. Viazkost’ razrusheniia stali 16G2AF elektroshlakovogo pereplava. Probl. spets. Elektrometallurgii. (19), 32–35 (1983) B.I. Medovar, L.I. Gladshtein, V.Ia. Saenko i dr. Viazkost’ razrusheniia stali 16G2AF elektroshlakovogo pereplava. Probl. spets. Elektrometallurgii. (19), 32–35 (1983)
23.
go back to reference O.I. Shishorina, V.I. Burba, I.Zh. Bunin, Osobennosti protsessa ustalostnogo razrusheniia konstruktsionnykh materialov v tochkakh bifurkatsii. v sb. Sinergetika i ustalostnoe razrushenie materialov (Nauka, Moscow, 1989), pp. 215–224 O.I. Shishorina, V.I. Burba, I.Zh. Bunin, Osobennosti protsessa ustalostnogo razrusheniia konstruktsionnykh materialov v tochkakh bifurkatsii. v sb. Sinergetika i ustalostnoe razrushenie materialov (Nauka, Moscow, 1989), pp. 215–224
24.
go back to reference A.Kh. Janahmadov, Termomekhanicheskaia teoriia iznosa (Elm, Baku, 1997), p. 28 A.Kh. Janahmadov, Termomekhanicheskaia teoriia iznosa (Elm, Baku, 1997), p. 28
25.
go back to reference A.Kh. Janahmadov, Neftianaia tribologiia (Elm, Baku, 2003), p. 326 A.Kh. Janahmadov, Neftianaia tribologiia (Elm, Baku, 2003), p. 326
26.
go back to reference A.I. Olemskoi, A.Ia. Flat, Ispol’zovanie kontseptsii fraktala v fizike kondensirovannoi sredy. Uspekhi fizich. nauk, Tom. 163(12), 1–50 (1993) A.I. Olemskoi, A.Ia. Flat, Ispol’zovanie kontseptsii fraktala v fizike kondensirovannoi sredy. Uspekhi fizich. nauk, Tom. 163(12), 1–50 (1993)
27.
go back to reference A.Kh. Janahmadov, O.A. Dyshin, Synergetics and fractal dimensions in tribology (reviews). J. Friction and Wear 2(1), 61–71 (2011) A.Kh. Janahmadov, O.A. Dyshin, Synergetics and fractal dimensions in tribology (reviews). J. Friction and Wear 2(1), 61–71 (2011)
28.
go back to reference L.D. Landau, E.M. Lifshits, Statisticheskaia fizika. Ch. 1 (Nauka, Moscow, 1976) L.D. Landau, E.M. Lifshits, Statisticheskaia fizika. Ch. 1 (Nauka, Moscow, 1976)
29.
go back to reference U. Frish, G. Parisi, Turbulence and predictability in geophysical fluid dynamics and climate dynamics (Proceedings of the International School of Physics “Enrico Fermi”, Cours 88, Eds M. Ghil, R. Benzi, G. Parisi) (Amsterdam, North Holland, 1985), p. 71 U. Frish, G. Parisi, Turbulence and predictability in geophysical fluid dynamics and climate dynamics (Proceedings of the International School of Physics “Enrico Fermi”, Cours 88, Eds M. Ghil, R. Benzi, G. Parisi) (Amsterdam, North Holland, 1985), p. 71
31.
go back to reference Y. Gagne, E. Hopfinger, U. Frisch, New trends in nonlinear dynamics and pattern. Forming phenomena: The geometry of nonequilibrium, NATO AST Series, Ser. B, ed. by P. Coullet, P. Huerre. vol 237 (Plemon Press, New York, 1990), p. 315 Y. Gagne, E. Hopfinger, U. Frisch, New trends in nonlinear dynamics and pattern. Forming phenomena: The geometry of nonequilibrium, NATO AST Series, Ser. B, ed. by P. Coullet, P. Huerre. vol 237 (Plemon Press, New York, 1990), p. 315
32.
go back to reference J.W. Kantelhardt, Fractal and multifractal time series, arxiv: 0804.0747, v.1, April 04 (2008) J.W. Kantelhardt, Fractal and multifractal time series, arxiv: 0804.0747, v.1, April 04 (2008)
33.
34.
38.
go back to reference A. Grossman, J. Morlet, J. Siam, Math. Anal. 15, 723 (1984) A. Grossman, J. Morlet, J. Siam, Math. Anal. 15, 723 (1984)
39.
go back to reference S. Mallat, A wavelet tour of signal processing (Academic Press, San Diego, London, Boston, New York, Sydney, Tokyo, Toronto, 1998), p. 577MATH S. Mallat, A wavelet tour of signal processing (Academic Press, San Diego, London, Boston, New York, Sydney, Tokyo, Toronto, 1998), p. 577MATH
40.
go back to reference A.A. Liubushin, Analiz dannykh sistem geofizicheskogo i ekologicheskogo monitoringa (Nauka, Moscow, 2007), p. 228 A.A. Liubushin, Analiz dannykh sistem geofizicheskogo i ekologicheskogo monitoringa (Nauka, Moscow, 2007), p. 228
41.
go back to reference J.W. Kantelhardt, S.A. Zschiegner, E. Konscienly-Bude, S. Havlin, A. Bunde, H.E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series. Phys. A 316, 87–114 (2002)CrossRefMATH J.W. Kantelhardt, S.A. Zschiegner, E. Konscienly-Bude, S. Havlin, A. Bunde, H.E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series. Phys. A 316, 87–114 (2002)CrossRefMATH
42.
go back to reference J.W. Kantelhardt, D. Rybski, S.A. Zschienger, P. Braun, E. Koscienly-Bunde, V. Livina et al., Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods. Phys. A 330, 240–245 (2003)CrossRefMATH J.W. Kantelhardt, D. Rybski, S.A. Zschienger, P. Braun, E. Koscienly-Bunde, V. Livina et al., Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods. Phys. A 330, 240–245 (2003)CrossRefMATH
43.
go back to reference A.B. Chhabra, Ch. Meneveau, R.V. Jensen, K.R. Sreenivasan, Direct determination of the () singularity spectrum and its application to fully developed turbulence. Phys. Rev. A 40(9), 40 (1989)CrossRef A.B. Chhabra, Ch. Meneveau, R.V. Jensen, K.R. Sreenivasan, Direct determination of the () singularity spectrum and its application to fully developed turbulence. Phys. Rev. A 40(9), 40 (1989)CrossRef
45.
go back to reference N.M. Astaf’eva, Veivlet-analiz, osnovy teorii i primery primeneniia. Uspekhi fizicheskikh nauk, Tom 166(11), 1145 (1996) N.M. Astaf’eva, Veivlet-analiz, osnovy teorii i primery primeneniia. Uspekhi fizicheskikh nauk, Tom 166(11), 1145 (1996)
46.
go back to reference A.N. Pavlov, V.S. Anishchenko, Mul’tfraktal’nyi analiz slozhnykh signalov. Uspekhi fizicheskikh nauk, Tom 177(8), 859–876 (2007)CrossRef A.N. Pavlov, V.S. Anishchenko, Mul’tfraktal’nyi analiz slozhnykh signalov. Uspekhi fizicheskikh nauk, Tom 177(8), 859–876 (2007)CrossRef
47.
go back to reference G. Boffetta, M. Cencini, M. Falcioni, A. Vilpiani, Predictability, a way to characterize complexity. Phys. Rp. 356, 367–474 (2002)ADSMathSciNetMATH G. Boffetta, M. Cencini, M. Falcioni, A. Vilpiani, Predictability, a way to characterize complexity. Phys. Rp. 356, 367–474 (2002)ADSMathSciNetMATH
48.
go back to reference P.J. Brockwell, R.A. Davis, Springer texts in statistics. Introduction to time series and forecasting (Springer, New York, 1988) P.J. Brockwell, R.A. Davis, Springer texts in statistics. Introduction to time series and forecasting (Springer, New York, 1988)
49.
go back to reference R.N. Mantegna, Fast accurate algorithm for numerical simulation of levy stable stochastic processes. Phys. Rev. E 49, 4677–4683 (1994)ADSCrossRef R.N. Mantegna, Fast accurate algorithm for numerical simulation of levy stable stochastic processes. Phys. Rev. E 49, 4677–4683 (1994)ADSCrossRef
50.
go back to reference M.F. Shlesinger, Comment on “stochastic process with ultraslow convergence to a Gaussian, The Truncated Levy Flight”. Phys. Rev. Lett. 74, 4959 (1995)ADSCrossRef M.F. Shlesinger, Comment on “stochastic process with ultraslow convergence to a Gaussian, The Truncated Levy Flight”. Phys. Rev. Lett. 74, 4959 (1995)ADSCrossRef
51.
go back to reference D. Sornette, Critical phenomena in natural sciences (Springer, New York, 2001)MATH D. Sornette, Critical phenomena in natural sciences (Springer, New York, 2001)MATH
52.
go back to reference A. Olemskoi, S. Kokhan, Effective temperature of self-similar time series, analytical and numerical developments. Phys. A 360, 37–58 (2006)CrossRef A. Olemskoi, S. Kokhan, Effective temperature of self-similar time series, analytical and numerical developments. Phys. A 360, 37–58 (2006)CrossRef
53.
go back to reference C.-K. Peng, S.V. Buldyrev, S. Havlin, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 49, 1685 (1994)ADSCrossRef C.-K. Peng, S.V. Buldyrev, S. Havlin, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 49, 1685 (1994)ADSCrossRef
54.
go back to reference S.M. Ossadnik, S.B. Buldgrev, A.L. Goldberger, S. Havlin, R.N. Mantegna, C.-K. Peng, M. Simons, H.E. Stanley, Biophys. J. 67, 64 (1994)ADSCrossRef S.M. Ossadnik, S.B. Buldgrev, A.L. Goldberger, S. Havlin, R.N. Mantegna, C.-K. Peng, M. Simons, H.E. Stanley, Biophys. J. 67, 64 (1994)ADSCrossRef
55.
go back to reference D. Sornette, Critical phenomena in natural Sciences (Springer, New York, 2001)MATH D. Sornette, Critical phenomena in natural Sciences (Springer, New York, 2001)MATH
56.
go back to reference A. Olemskoi, S. Kokhan, Effective temperature of self—similar time series, analytical and numerical development. Phys. A 360, 37–58 (2006)CrossRef A. Olemskoi, S. Kokhan, Effective temperature of self—similar time series, analytical and numerical development. Phys. A 360, 37–58 (2006)CrossRef
57.
go back to reference C.-K. Peng, S.V. Buldyrev, S. Havlin, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 49, 1685 (1994)ADSCrossRef C.-K. Peng, S.V. Buldyrev, S. Havlin, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 49, 1685 (1994)ADSCrossRef
58.
go back to reference S.M. Ossadnik, S.B. Buldyrev, A.L. Goldberger, S. Havlin, R.N. Mantegna, C.-K. Peng, M. Simons, H.E. Stanley, Biophys. J. 67, 64 (1994)ADSCrossRef S.M. Ossadnik, S.B. Buldyrev, A.L. Goldberger, S. Havlin, R.N. Mantegna, C.-K. Peng, M. Simons, H.E. Stanley, Biophys. J. 67, 64 (1994)ADSCrossRef
59.
60.
go back to reference J.W. Kantelhardt, E. Koscienly-Bunde, H.H.A. Rego, S. Havlin, A. Bunde, Phys. A 295, 441 (2001)CrossRef J.W. Kantelhardt, E. Koscienly-Bunde, H.H.A. Rego, S. Havlin, A. Bunde, Phys. A 295, 441 (2001)CrossRef
61.
63.
go back to reference A. Bunde, S. Havlin, J.W. Kantelhardt, T. Penzel, J.-H. Peter, K. Voight, Phys. Rev. Lett. 85, 3736 (2000)ADSCrossRef A. Bunde, S. Havlin, J.W. Kantelhardt, T. Penzel, J.-H. Peter, K. Voight, Phys. Rev. Lett. 85, 3736 (2000)ADSCrossRef
64.
go back to reference P. Oswiecimka, J. Kwapien, S. Drozdz, Wavelet versus detrended fluctuation analysis of multifractal structures. Phys. Rev. E 74, 016103 (2006)ADSCrossRef P. Oswiecimka, J. Kwapien, S. Drozdz, Wavelet versus detrended fluctuation analysis of multifractal structures. Phys. Rev. E 74, 016103 (2006)ADSCrossRef
65.
go back to reference G.-F. Gu, W.-X. Zhou, Detrended fluctuation analysis for fractal and multifractals in higher dimensions. Phys. Rev. E 74, 061104 (2006)ADSCrossRef G.-F. Gu, W.-X. Zhou, Detrended fluctuation analysis for fractal and multifractals in higher dimensions. Phys. Rev. E 74, 061104 (2006)ADSCrossRef
66.
go back to reference A. Arneodo, B. Audit, N. Decoster, J.F. Muzy, C. Vaillant, Wavelet based multifractal formalism: application to DNA sequences, satellite images of the cloud structure, and stock market data, in The science of disaster: climate disruptions, market crashes, and heart attacks, ed. by A. Bunde, J. Kropp, H.J. Schellnhuber (Springer, Berlin, 2002) A. Arneodo, B. Audit, N. Decoster, J.F. Muzy, C. Vaillant, Wavelet based multifractal formalism: application to DNA sequences, satellite images of the cloud structure, and stock market data, in The science of disaster: climate disruptions, market crashes, and heart attacks, ed. by A. Bunde, J. Kropp, H.J. Schellnhuber (Springer, Berlin, 2002)
67.
go back to reference I. Rodriguez-Iturbe, A. Rialdo, Fractal river basins—change and self-organization (Cambrige University Press, Cambrige, 1997) I. Rodriguez-Iturbe, A. Rialdo, Fractal river basins—change and self-organization (Cambrige University Press, Cambrige, 1997)
68.
go back to reference A.I. Olemskoi, V.N. Borisiuk, I.A. Shuda, Mul’tifraktal’nyi analiz vremennykh riadov. Bisnik Sum DU, Seriia “Fizika, matematika, mekhanika”, 2 (2008) A.I. Olemskoi, V.N. Borisiuk, I.A. Shuda, Mul’tifraktal’nyi analiz vremennykh riadov. Bisnik Sum DU, Seriia “Fizika, matematika, mekhanika”, 2 (2008)
69.
go back to reference E. Koscielny-Bunde, J.W. Kantelhard, P. Braun, A. Bunde, S. Havlin, Long-term persistence and multifractality of river runoff records. J. Hydrol. 332, 120 (2006)CrossRef E. Koscielny-Bunde, J.W. Kantelhard, P. Braun, A. Bunde, S. Havlin, Long-term persistence and multifractality of river runoff records. J. Hydrol. 332, 120 (2006)CrossRef
70.
go back to reference J.W. Kantelhard, E. Koscielny-Bunde, D. Rybinski, P. Braun, A. Bunde, S. Havlin, Long-term persistence and multifractality of precipitation an river runoff records. J. Geophys. Res. (Atmosph.), 111, DO1106 (2006) J.W. Kantelhard, E. Koscielny-Bunde, D. Rybinski, P. Braun, A. Bunde, S. Havlin, Long-term persistence and multifractality of precipitation an river runoff records. J. Geophys. Res. (Atmosph.), 111, DO1106 (2006)
71.
go back to reference B.B. Mandelbrot, The Fractal Geometry of Nature (W.H.Freeman, 1983), p. 537 B.B. Mandelbrot, The Fractal Geometry of Nature (W.H.Freeman, 1983), p. 537
72.
go back to reference B. Podobnik, H.E. Stanley, Detrended cross—correlation analysis, a new method for analyzing two nonstationary time series. Phys. Rev. Lett. 100, 084102 (2008)ADSCrossRef B. Podobnik, H.E. Stanley, Detrended cross—correlation analysis, a new method for analyzing two nonstationary time series. Phys. Rev. Lett. 100, 084102 (2008)ADSCrossRef
Metadata
Title
Multifractal Analysis of Fatigue Failure
Authors
Ahad Kh. Janahmadov
Maksim Y. Javadov
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-28189-6_5

Premium Partner