Vol. 6, №1, 2014
РусскийEnglish

BRIEF REPORTS



FRACTAL LABYRINTHS
Grachev V.I., Potapov A.A., Potapov V.A.
Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, http://www.cplire.ru
11/7, Mokhovaya str., 125009 Moscow, Russian Federation
grachev@cplire.ru.

Received 04.11.2011
Is basic information about fractal labyrinths, the processes of anomalous diffusion and Levy flights. It is shown, that the mathematics of fractional operators is a necessary machine description of complex technical and natural systems with fractal structure.

Keywords: fractals, fractal labyrinths, Levy flights, anomalous diffusion, fractional operators.

UDC 537.86:519.22

Bibliography – 21 references

RENSIT, 2011, 3(2):103-109
REFERENCES
  • Golgenfeld N, Kadanoff LP. Science, 1999, 284:87.
  • Danilov YuA. Prekrasny mir nauki [The wonderful world of science]. Collection. Compiled by AG Shadtina. Sanyuk VI & Trubetskoy D (Eds.). Moscow, Progress-Traditsiya Publ., 2008, 384 p.
  • Potapov AA. Fractaly v radiofizike i radiolokatsii. [Fractals in Radiophysics and Radiolocation]. Moscow, Logos Publ., 2002, 664 p. Potapov AA. Fractaly v radiofizike i radiolokatsii: topologiya vyborki [Fractals in Radiophysics and Radiolocation: topology of sample]. Moscow, Universitetskaya kniga Publ., 2005, 848 p.
  • Potapov AA. Proc. 1th Intern. Conf. “Nanostrukturnye materialy-2008” [Nanostructured materials-2008: Belarus-Russia-Ukraina]. Minsk, Belorus. Nauka Publ., 2008, 532 p.
  • Potapov AA. Proc. 1th Conf. Nanotechnological Society of Russia (NtSR). Moscow, NIYaU-MIFI Publ., 2009. 5 pp.(http://nstr.info/nor/bulletin/seminars/index. php?ID=1601).
  • Iudin DI, Trakhtengerts VYu. Fraktalnye labirinty: strukturnaya dinamika [Fractal labyrinths: a structural dynamics]. In: Nelineynye volny [Nonlinear Waves]. N.Novgorod, IPF RAS, 2007, 360-377 pp. (in Russ.).
  • Feder E. Fractals. Moscow, Mir Publ., 1991, 254 p.
  • Hunt AG, Ewing R. Percolation Theory for Flow in Porous Media. Berlin-Heidelberg: Springer, 2009. 319 p.
  • Moran PAP. Proc.Cambridge Phylos. Soc.,1946,42:15-23.
  • Pesin Y, Weiss H. Comm.Math.Phys., 1996, 182:105-153.
  • Pesin Y, Weiss H. J.Stat.Phys., 1997, 86:233-275.
  • Cristea LL, Steinsky B. Geom Dedicata, 2009, 141:1-17.
  • Kuratovsky K. Topologiya [Topology], v.2. Moscow, Mir Publ., 1969.
  • Oldham KB, Spanier J. The Fractional Calculus. NY, Academic Press, 1974, 234 р.
  • Hilfer R. (Ed.). Applications of Fractional Calculus in Physics. Singapore, World Scientific, 1999, 472 p.
  • Uchaykin VV. Metod drobnykh proizvodnykh [The method of fractional derivatives]. Ul’yanovsk, Artishok Publ., 2008, 512 p.
  • Metzler R, Klafter J. Phys.Rep., 2000, 339, 1-77 pp.
  • Potapov AA, Chernykh VA. Drobnoe ischislenie AV Letnikova v fizike fraktalov [Letnikov Fractional Calculus in the physics of fractals]. Saarbrucken, Lambert Academic Publishing, 2012, 688 p.
  • Potapov AA. Chapter V In: Fractals and fractional operators. With a foreword. Acad. Gulyaev Yu. and Corr. Memb. RAS SA Nikitov. Ed. Gil’mutdinov AH. Kazan, «Feng,» the Academy of Sciences, 2010, p. 417-472.
  • Zaslavsky GM. Gamiltonov khaos i fraktal’naya dinamika [Hamiltonian chaos and fractal dynamics]. Moscow-Izhevsk, NIZ “RKhD”, Izhevsky institut komp’yuternykh issledovaniy Publ., 2010, 472 p.
  • Gnedenko BV, Kolmogorov AN. Predel’nye raspredeleniya dlya sum nezavisimykh sluchaynykh velichin [Limit distributions for sums of independent random variables]. Moscow-Leningrad, Gostekhizdat Publ., 1949, 264 p.


Full-text electronic version of this article - web site http://elibrary.ru