Discontinuity, Nonlinearity, and Complexity
On the Way to Generalized Kinetics for Multiscale Complex System
Discontinuity, Nonlinearity, and Complexity 8(2) (2019) 199210  DOI:10.5890/DNC.2019.06.007
V. V. Uchaikin
Ulyanovsk State University, Ulyanovsk, Rissia
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Abstract
Development of nanotechnology throws a new challenge to statistical physics. The classical statistical physics is underlaid by classical or quantum mechanics of closed systems, classical version of the Central Limit Theorem, the Markov model of Brownian motion, the linear approximation of the perturbation theory as a main mathematical tool. The nanotechnology has caused constructing new models: nonlocal in space and time dynamics, generalized Limit Theorem for the Levystable family as limit distributions, nonMarkovian (subordinated) Levymotion and instead of the Brownian one, selfsimilar (fractal) and nonlocal (integral and fractional differential) analysis. The article gives a short review of these concepts. The multiscale complex system is considered to exacute a selfsimilar motion obeying the Levy stable statistics, which generalized then to fractionally stable kind. The intermediate asymptotics is introduced on the base of truncated Lévy flight. This leads to the correspondence principle connecting classical and nanostatistics. Some numerical results are presented.
Acknowledgments
This work is partially supported by the Russian Foundation of Basic Research (Project 1851 53018).
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