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FRACTAL STRUCTURES AND PERCOLATION IN NUCLEAR REACTOR
Cover not present FRACTAL STRUCTURES AND PERCOLATION IN NUCLEAR REACTOR
Category: Number 23
Publication: 23
Summary

Motion path of neutrons in the reactor, the division points of uranium nuclei, neutron absorption point, chain fission chain reactions are considered from the standpoint of fractal geometry and percolation theory. In a study of stationary critical mode of operation of a nuclear reactor model used Cayley trees and Laplace fractals. This approach allows to obtain an equation of the neutron multiplication and expression for the critical size of the reactor. We also consider the model of irreversible growth and high fractal dimension applied to the evolution of neutrons in the reactor. Shown prospects of development of the proposed approach to the description of the reactors, especially the kinetics and transport processes of neutrons.

Keywords: fractals, percolation, chain fission, neutrons in the reactor

References

1. Tarasevich Yu. Yu. Percolation theory, applications, algorithms. - Moskwa: URSS, 2002. - 112 p. (Rus)
2. Feder E. Fractals. - New York: Plenum Press, 1988. - 260 p.
3. Bozhokin S.V., Parshin D.A. Fractals and multifractals. - Izhevsk: NITs "Regular and Chaotic Dynamics", 2001. - 128 p. (Rus)
4. Olemskoi A.I., Flath A.Y. Using fractal concepts in condensed-matter physics // Uspehi fizicheskih nauk. - 1993. - Vol. 163, № 12. - P. 1-50. (Rus)
5. Mandelbrot B.B. Fractals: Form, Chance, and Dimension. - San Francisco: Freeman, 1977. - 752 p. Mandelbrot B. B. The Fractal Geometry of Natura. - San Francisco: Freeman, 1982. - 530 p.
6. Ryazanov V.V., Turbin A.F. Tree structures, the problem of percolation and fractal phenomena in the multiplying medium. Abstracts seminar "Fractal objects in mathematics, physics and biology", 25 - 27 April 1991, Sloviansk. - Kiev: Publishing house of Society "Knowledge" of Ukraine, 1991. - Р. 17. (Rus)
7. Efros A.L. Physics and geometry of disorder. - Moskwa: Nauka, 1982. - 176 p. (Rus)
8. Patashinskii A.Z., Pokrovskii V.L. Fluctuation theory of phase transitions. - Moskwa: Nauka, 1975. - 255 p. (Rus)
9. Ma Sh. Modern Theory of Critical Phenomena. - New York: Wiley, 1980. - 374 p.
10. de Gennes P. Scaling ideas in polymer physics. - New York: Wiley, 1982. - 368 p.
11. Zelenyi L.M., Milovanov A.B. Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics // Uspehi fizicheskih nauk. - 2004. - Vol. 174, № 8. - P. 809 - 852. (Rus)
12. Uchaikin V.V. Similar anomalous diffusion and stable laws // Uspehi fizicheskih nauk. - 2003. - Vol. 173, № 8. - P 847 - 876. (Rus)
13. Zel'dovich B., Sokolov D.D., Fractal dimension and related matters // Uspehi fizicheskih nauk. - 1985. - Vol. 146, № 3. - P. 493 - 517. (Rus)
14. Smirnov B.M. Fractal clusters // Uspehi fizicheskih nauk. - 1986. - Vol. 149, № 2. - P. 177 - 210. (Rus)
15. Sokolov I.M. Dimensions and other geometric critical exponents in percolation theory // Uspehi fizicheskih nauk. - 1986. - Vol. 150, № 2. - P. 229 - 265. (Rus)
16. Harari F., Palmer E. Enumeration of graphs. - New York: Wiley, 1977. - 324 p.
17. Havlin S. Statistical and dynamical properties of fractal aggregates that do not contain loops // Fractals in Physics. - New York: Wiley, 1986. - P. 498 - 506.
18. Turbin A.F., Pratsevity N.V. Fractal sets, functions, distribution. - Kiev: Naukova Dumka, 1992. - 207 p. (Rus)
19. Harris T. Theory of branching random processes. - New York: Wiley, 1966. - 355 p.
20. Pietronero L. Everts, K., H. Wiesmann Properties similarity growing area and the capacity of the Laplacian fractal // Fractals in Physics. - New York: Wiley, 1986. - P. 221 - 226.
21. Wiesmann H., Pietronero L. Properties of Laplace fractals in the breakdown of dielectrics in two and three dimen-sions // Fractals in Physics. - New York: Wiley, 1986. - Р. 210 - 220.
22. Margolin A. The fractal dimension of the perimeter growth. // Fractals in Physics. - New York: Wiley, 1986. - P. 507 - 512.
23. Bak P., Tang C., Wiesenfeld K. Self-organized criticality // Phys. Rev. A. - 1988. - Vol. 38, № 1. - P. 364 -374.
24. Schroeder M. Fractals, Chaos, Power Laws. Minutes from an Infinite Paradise. - Izhevsk: RHD, 2001. - 528 p. (Rus)
25. Shuda I.A. Influence of the hierarchical structure and self-similarity to self-organization of complex systems. Dis. .... Doctor. Sci. Sciences. - Sumy, 2011. (Rus)
26. Olemskoi A.I. Synergetics of complex systems. Phenomenology and statistical theory. - Moskwa: Krasand, 2009. - 379 p. (Rus)
27. Nigmatullin R. Fractional integral and its physical interpretation // Teoreticheskaya i matematicheskaya fizika. - 1992. - Vol. 90, № 3. - P. 354 - 368. (Rus)

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