American Journal of Modern Physics
Volume 6, Issue 5, September 2017, Pages: 81-87
Received: Jun. 30, 2017;
Accepted: Jul. 11, 2017;
Published: Jul. 31, 2017
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Gurami Tsitsiashvili, Institute for Applied Mathematics FEB RAS, Vladivostok, Russia
V. V. Uchaikin suggested a mathematical model of an anomalous diffusion in a space. These model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and a turbulence in a plasma. Here a coordinate of diffusing particle has stable distribution and so its density satisfies diffusion equation with partial derivatives. In this paper, the anomalous diffusion with periodic initial conditions on an interval with reflecting edges, important for example in technical mechanics, is considered and analyzed.
Characteristic Time of Diffusive Mixing in Cube with Reflecting Edges, American Journal of Modern Physics.
Vol. 6, No. 5,
2017, pp. 81-87.
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Uchaikin V. V. Multidimensional symmetric anomalous diffusion. Chemical Physics. Vol. 284, 2002, pp. 507-520.
Skvortsova N. N, Batanov G. M, Petrov A. E, Pshenichnikov A. A, Sarksyan K. A, Kharchev N. K. Non-Brownian Particle Motion in Structural Plasma Turbulence. Proceedings of the XXIII Seminar on Stability for Stochastic Models. Pamplona, Spain, 2003, p. 88.
Tsitsiashvili G. Sh, Bespalov V. M, Osipova M. A. Cooperative and decomposition effects in multielement stochastic systems. Vladivostok: Dalnauka, 2003. (In Russian).
Tsitsiashvili G. Sh. Anomalous Diffusion on Finite Interval. Journal of Mathematical Sciences. Vol. 191, issue 4, 2013, pp. 582-587.
Vladimirov V. S. Equations of mathematical physics. Moscow: Nauka, 1967. (In Russian).
Embrechts P, Maejima M. An introduction to the theory of self-similar stochastic processes. International journal of modern physics B. Vol. 12-13, 2000, pp. 1399-1420.
Chen S. et al. Self-similar Random Process and Chaotic Behavior. In Serrated Flow of High Entropy Alloys. Sci. Rep. Vol. 6, 2016. Doi 10.1038/srep 29798.
Caroll R. et al. Experiments and Model for Serration Statistics in Low-Entropy, Medium Entropy Alloys. Sci. Rep. Vol. 5, 2015. Doi 10.1038/srep 16997.
Zhang Z. J. et al. Nanoscale origins of the damage tolerance of the high-entropy alloy CrMnFeCoNi. Nat Commun. Vol. 6, 2015. PMC free article [PubMed].
Youssef K. M. et al. A novel low density, high-hardness, high entropy alloy with close packed single-phase nanocrystalline structures. Mater Res Lett. Vol. 3 (2), 2015.
Feller W. Introduction to probability theory and its applications. Moscow: Mir, T. 2, 1984. (In Russian).
Mikosch T. et al. Is network traffic approximated by stable Levy motion or fractional Brownian motion? Annals of Applied Probability. Vol. 12, no. 1, 2002, pp. 23-68.
Khokhlov Yu. S. Multivariate fractional Levi motion and its applications. Informatics and its applications. Vol. 10, no. 2, 2016, pp. 98-106. (In Russian).