Numerical Analysis of Automodel Solutions for Superdiffusive Transport

Alexander B. Kukushkin, Vladislav S. Neverov, Petr A. Sdvizhenskii, Vladimir V. Voloshinov


The distributed computing analysis of the accuracy of automodel solutions for the Green’s function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have been suggested for the 1D transport equation with a model long-tailed step-length probability distribution function (PDF) with various power-law exponents. These PDFs describe the transport dominated by the Lévy flights. Massive computing experiments were done to verify automodel solutions. The Everest distributed computing platform and the cluster at NRC ‘Kurchatov Institute’ were used. The results verify the high accuracy of automodel solutions in a wide range of space-time variables and suggest extending the developed method of automodel solutions to a wider class of stochastic phenomena.

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Shlesinger, M.; Zaslavsky, G. M.; and Frisch, U. (Eds.). “Lévy Flights and Related Topics in Physics”. New York: Springer-Verlag, 1995.

A.A. Dubkov, B. Spagnolo, and V.V. Uchaikin. “Lévy flight superdiffusion: an introduction”, Int. J. Bifurcation Chaos, vol. 18, p. 2649, 2008.

J. Klafter, I.M. Sokolov, "Anomalous diffusion spreads its wings," Physics world, vol. 18, p. 29, 2005.

I.I. Eliazar, M.F. Shlesinger. "Fractional motions," Phys. Rep., vol. 527, pp. 101-129, 2013.

Mandelbrot, B.B.. “The Fractal Geometry of Nature,” New York: W. H. Freeman, 1982.

Biberman, L. M., Sov. Phys. JETP, vol, 19, p.584, 1949.

Holstein T., Phys. Rev., v. 72, № 12, p. 1212, 1947.

Biberman L.M., Vorob'ev V.S., Yakubov I.T. “Kinetics of Nonequilibrium Low Temperature Plasmas”, (New York: Consultants Bureau), 1987.

I. B. Levinson, Zh. Eksp. Teor. Fiz., vol. 75, pp. 234-248, July 1978.

Kukushkin A.B., Lisitsa V.S., and Saveliev Yu.A., JETP Lett., vol. 46, p.448, 1987.

A.V. Subashiev, O. Semyonov, Z. Chen, S. Luryi. “Temperature controlled Lévy flights of minority carriers in photoexcited bulk n-InP”, Phys. Lett. A, vol. 378, pp. 266–269, 2014.

Kukushkin A.B. and Sdvizhenskii P.A., J. Phys. A: Math. Theor., vol. 49, paper 255002, 2016.

Kukushkin A.B. and Sdvizhenskii P.A., “Accuracy analysis of automodel solutions for Lévy flight-based transport: from resonance radiative transfer to a simple general model”, J. Phys. Conf. Series (to be published).

Sukhoroslov O., Volkov S., Afanasiev A. “A Web-Based Platform for Publication and Distributed Execution of Computing Applications” in 14th International Symposium on Parallel and Distributed Computing (ISPDC). IEEE, 2015, pp. 175-184.

Volkov S., Sukhoroslov O. “A Generic Web Service for Running Parameter Sweep Experiments in Distributed Computing Environment,” in Procedia Computer Science, Volume 66, 2015, pp. 477-486.

Abramov V.A., Kogan V.I., Lisitsa V.S., In: Reviews of Plasma Physics, 1987, Vol.12 (Leontovich M.A., Kadomtsev B.B., Eds.) New York: Consultants Bureau, p.151.


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