Automodelity as a characteristic property of nonlocal anomalous diffusion
https://doi.org/10.34680/2076-8052.2021.2(123).43-46
Abstract
A brief presentation of the relationship between a non-Gaussian family of stable laws and the self-similarity of the nonlocal processes described by them. The characteristic property of self-similarity makes it possible to arrange the ballistic, Brownian, and Levy-models of motion in a logically connected chain with characteristic exponents a = 1,2 and 0 < a < 2, which determine the degrees of differential operators describing these movements. The family of models generated by fractional values of a is characterized by a specific property of nonlocality, which is reflected in the physical interpretation in terms of fractality, if we are talking about the spatial derivative, and heredity, in the case of time-differentiation.
References
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Review
For citations:
Uchaikin V.V. Automodelity as a characteristic property of nonlocal anomalous diffusion. Title in english. 2021;(2(123)):43-46. (In Russ.) https://doi.org/10.34680/2076-8052.2021.2(123).43-46
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