Abstract
Fractals are called geometric objects: line, surface, spatial body having very jagged shape, and self-similarity.
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Literatures
B.B. Mandelbrot, Fractals: forme, chance and dimension (Freeman, San Fracisko, 1977), p. 362
A.V. Korolenko, M.S. Maganova, A.V. Mesniankin, Innovatsionnye metody analiza stokhasticheskikh protsessov i struktur v optike. Fraktal’nye i mul’tifraktal’nye metody, veivlet-preobrazovaniia. Uchebnoe posobie (MGU im. M.V.Lomonosova, NII iadernoi fiziki im. D.V. Skobel’tsyna, Moscow, 2004), p. 82
B.F. Timofeev, Fraktal. Fizika tverdogo tela (Nauk. Dumka, Kiev, 1998), 2, 460–461
A.F. Bulat, V.I. Dyrda, Fraktaly v geomekhanike (Nauk. Dumka, Kiev, 2005), p. 357
J.E. Hutchinson, Fractals and self similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981)
M. Barnsley, Fractals everywhere (Academic Press, Boston, 1988)
R.M. Kronover, Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii. per. s angl (Postmarket, Moscow, 2000), pp. 0–352
V.E. Rokotian, Avtomodel’nost’. Fizicheskaia entsiklopediia, vol. 1 (SE, Moscow, 1988), pp. 19–20
Iu.M. Maksenko, Masshtabnaia invariantnost’ (skeiling). Fizicheskaia entsiklopediia, vol. 3 (BRE, Moscow, 1992), pp. 60–61
V.L. Vinetskii, Avtomodel’nost’, Fizika tverdogo tela. Entsiklopedicheskii slovar’, vol. 1 (Nauk. Dumka, Kiev, 1996), p. 16
B.B. Mandelbrot, The fractal geometry of nature (W.H. Frecman, New York, 1982)
R.F. Voss, Random fractal forgeries. in Fundamental algorithms in computer graphics, ed. by R.A. Earnshaw (Springer, Berlin, 1985), pp. 805–835
R.F. Voss, Random fractals. Characterization and measurement, in Scalling phenomena disordered systems, ed. by R. Pynn, A. Skjeltorp (Plenum Press, New York, 1985), pp. 1–11
E. Feder, Fraktaly, per. s angl (Mir, Moscow, 1991), p. 254
B.B. Mandelbrot, Self-affine fractal sets, in Fractals in Physics, ed. by L. Pietronero, E. Tosatti (North Holland, Amsterdam, 1986), pp. 3–28
A.I. Olemskoi, A.A. Katsnel’son, Sinergetika kondensirovannoi sredy, Izd 2-e (Editorial URSS, Moscow, 2010), p. 336
V.E. Egorushkin, V.E. Panin, E.V. Savushkin, Iu.A. Khon, Sil’novozbuzhdennye sostoianiia v kristallakh. Izv. vuzov. Fizika 1, 9–33 (1987)
V.E. Panin, V.E. Egorushkin, Iu.A. Khon, T.F. Elsukova, Atomnovakansionnye sostoianiia v kristallakh. Izv. vuzov., Fizika, â„–12 (1982)
V.E. Panin, Iu.V. Griniaev, V.E. Egorushkin i dr. Spektr vozbuzhdennykh sostoianii i vikhrevoe mekhanicheskoe pole v deformiruemom kristalle. Izv. vuzov., Fizika, â„–1 (1987)
V.E. Panin, V.A. Likhachev, Iu.V. Griniaev, Strukturnye urovni deformatsii tverdykh tel (Nauka, Sib.otd-nie, Novosibirsk, 1985), p. 229
V.E. Panin, Iu.V. Griniaev, V.I. Danilov i dr. Strukturnye urovni plasticheskoi deformatsii i razrusheniia. (Nauka. Sib. Otd-nie, Novosibirsk, 1990), p. 255
V.E. Panin, V.E. Egorushkin, P.V. Makarov i dr., Fizicheskaia mezomekhanika i komp’iuternoe konstruirovanie materialov. V 2t. (Nauka. Sib. Izdat. firma RAN, Novosibirsk, 1995), p. 298
Iu.V. Grinaev, N.V. Chertova, Opisanie polzuchesti v ramkakh polevoi teorii defektov. Prikladnaia mekhanika i tekhnicheskaia fizika. 41(3), 177–183 (2000)
Trenie, iznashivanie i smazka, Spravochnik v 2-kh kn., pod red. I.V.Krachel’skogo, V.V.Anisina (Mashinostroenie, Moscow, 1978), Kn. 1, p. 400
A.Kh. Janahmadov, Termomekhanicheskaia teoriia iznosa (Elm, Baku, 1997), p. 28
A.Kh. Janahmadov, Neftianaia tribologiia (Elm, Baku, 2003), p. 326
A.Kh. Janahmadov, Tribotekhnicheskie problemy v neftegazovom oborudovanii (Elm, Baku, 1998), p. 216
A.Kh. Janahmadov, M.Y. Javadov, O.A. Dyshin, Diagnosis of the contact interaction of solid bodies at friction using fractal analysis methods. J. Sci. Appl. Eng. Q. 04, 5–16 (2014)
A.I. Olemskoi, A.Ia. Flat, Ispol’zovanie kontseptsii fraktala v fizike kondensirovannoi sredy. Usp. Fiz. Nauk., 163(12), 1–50 (1993)
Sinergetika i ustalostnoe razrushenie metallov (Nauka, Moscow, 1980), p. 246
A.I. Olemskoi, E.A. Toropov, Teoriia nizkotemperaturnoi evoliutsii ortorombicheskoi fazy vysokotemperaturnykh sverkhprovodiashchikh oksidov. Fizika metallov. Metallovedenie, 7, 32–40 (1991)
D. Adelman, C.P. Burmester, L.T. Wille, P.A. Stern, R. Gronsky, J. Phys. Condens. Matter 4, 585 (1992)
R. Rammal, G. Toulouse, M.A. Virasova, Ultrametricity for physicists. Rev. Mod. Phys. 58, 765, 788 (1986)
S.L. Ginzburg, Neobratimye iavleniia v spinovykh steklakh (Nauka, Moscow, 1989)
K. Binder, A.P. Jeung, Rev. Mod. Phys. 58, 801 (1986)
V.S. Ivanova, V.F. Terent’ev, Priroda ustalosti metallov (Metallurgiia, Moscow, 1975), p. 456
A.I. Olemskoi, I.I. Naumov, Fraktal’naia kinetika ustalostnogo razrusheniia. V sb.: Sinergetika i ustalostnoe razrushenie metallov. (Nauka, Moscow, 1989), pp. 200–215
A.T. Ogielski, Phys. Rev. Let. 55, 1634 (1986)
A.I. Olemskoi, Fraktal’naia kinetika perestroiki kristallicheskoi struktury. Fizika metallov. Metallovedenie, 68(1), 56–65 (1989)
A.M. Pashaev, A.Kh. Janahmadov, O.A. Dyshin, Fraktal’naia razmernost’ i ee sviaz’ s mekhanicheskimi svoistvami metallov i splavov v usloviiakh predrazrusheniia. Vestnik Azerbaidzhanskoi Inzhenernoi Akademii 2(2), 13–24 (2010)
R.G. Palmer, D.L. Stein, E. Abrahams et al., Models of hieracheally constrained dynamics for glassy relaxation. Phys. Rev. Let. 53(10), 958–961 (1984)
V.V. Zosimov, L.M. Liamshev, Fraktaly v volnovykh protsessakh. Uspekhi fizicheskikh nauk 165(4), 361–401 (1995)
A.Kh. Janahmadov, O.A. Dyshin, Synergetic and fractal dimensions in tribology. J. Friction Wear 32(1), 61–71 (2011)
S.N. Zhurkov, Dilatonnyi mekhanizm prochnosti tverdykh tel. Fizika tverdogo tela 25(10), 3119–3123 (1983)
Dzh. Gilman, V. Dzhonston, Vozniknovenie dislokatsii v kristallakh LiF pri nizkikh napriazheniiakh. Dislokatsii i mekhanicheskie svoistva kristallov. (Inostr. lit., Moscow, 1960), pp. 393–394
V.E. Panin, V.A. Likhachev, Iu.V. Griniaev, Strukturnye urovni deformatsii tverdykh tel (Nauka, Novosibirsk, 1985), p. 163
A.I. Olemskoi, I.A. Skliar, Evoliutsiia defektnoi struktury tverdogo tela v protsesse plasticheskoi deformatsii. Uspekhi fizicheskikh nauk 162(6), 29–79 (1992)
U. Nikolis, I. Prigozhin, Samoorganizatsiia v neravnovesnykh sistemakh. (Mir, Moscow, 1979), p. 300
A.M. Pashaev, A.Sh. Mekhtiev, A.Kh. Janahmadov, O.A. Dyshin, Avtomodel’nost’ i fraktal’naia mekhanika razrusheniia. Vestnik Azerbaidzhanskoi Inzhenernoi Akademii 1(1), 93–103 (2009)
V.S. Ivanova, Sinergetika: Prochnost’ i razrushenie metallicheskikh materialov (Nauka, Moscow, 1992), p. 160
V.S. Ivanova, A.S. Balankin, I.Zh. Bunin i dr. Sinergetika i fraktaly v materialovedenii (Nauka, Moscow, 1994), p. 383
V.S. Ivanova, Problemy prochnosti. 5, 91–98 (1982)
V.S. Ivanova, S.A. Kunavin, Izv. AN SSSR. Metally 4, 148–153 (1984)
R.E. Williford, Ser. Met. 22(11), 1749–1754 (1988)
A.R. Rosenfeld, Ibid 21(11), 1339–1361 (1987)
A.S. Balankin, A.A. Liubomudrov, I.T. Sevriukov, Zhurnal tekhnicheskoi fiziki. 59(12), 102–104 (1989)
V.A. Kuz’menko, Razvitie predstavlenii o protsesse deformirovaniia materialov (UkrNIITI, Kiev, 1968), p. 47
O.D. Khlopotov, Metallovedenie i termicheskaia obrabotka materialov. №12, 12–14 (1974)
A.S. Balankin, V.S. Ivanova, V.P. Breusov, Dokl. AN SSSR. 322(6), 1080–1085 (1992)
V.E. Panin, Iu.V. Griniaev, V.I. Danilov i dr. Strukturnye urovni plasticheskoi deformatsii i razrusheniia (Nauka, Sib.otd-e, Novosibirsk, 1990), p. 255
M. Feigenbaum, Universal’nost’ v povedenii nelineinykh sistem. UFN 141(2), 343–374 (1983)
V.A. Chernomorets, S.K. Gorbunov, Printsipy identifikatsii determinirovannoi osnovy v khaoticheskom povedenii sistem. Problemy uprvleniia i informatiki, №6, 24–33 (2005)
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Janahmadov, A.K., Javadov, M.Y. (2016). Fractal Kinetics of Fracture. In: Synergetics and Fractals in Tribology. Materials Forming, Machining and Tribology. Springer, Cham. https://doi.org/10.1007/978-3-319-28189-6_4
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