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Transport and relaxation properties of stochastic systems with anomalous slow evolution


Presented Institute of Applied Physics of NAS of Ukraine

Bystryk Yu.S.

A series of scientific works is devoted to the investigation of the anomalous transport behavior of stochastic systems which are characterized by Levy statistics and ultraslow evolution, to the studying of the phenomenon of anomalous relaxation in two-state systems, properties of elements of which evolve according to the dichotomous process, and to the development of methods for theoretical description and analysis of nonequilibrium systems with anomalous properties, the state parameters of which change due to influence of random fluctuations.

Using the Montroll-Weiss equation, limiting probability densities and corresponding scaling functions which describe the asymptotic in time behavior of ultraslow Levy flights were determined. Anomalous transport properties of such processes were studied. It was indicated that scaling functions belong to the class of slowly varying functions. The total classification of limiting probability densities was carried out. It was shown that limiting probability densities are heavy-tailed or exponential functions and depend on parameters describing the behavior of jump-length distributions.

On the basis of the continuous-time random walk theory the integral equation which describes relaxation in pointed two-state systems was derived. It was obtained a number of results related to exact anomalous relaxation laws. Also universal anomalous relaxation laws were derived in the case of the long-time regime when distributions of waiting times in possible states of the system characterized by heavy and/or superheavy tails.

The results obtained in the series of works are fundamental, expand the understanding of the statistical properties of systems with anomalous slow behavior and develop methods for their description. In particular, in some cases they describe the dependences observed for anomalous slow relaxation processes associated with spin dynamics in magnetic systems, compaction of granular materials and adsorption-desorption of substances by substrate surfaces, and can also be used in modeling diffusion and transport processes in construction materials, research of features of movement of defects in inhomogeneous environments, their capture by dislocations, etc. The obtained results can be used in research centers, where theoretical and experimental studies of statistical properties of systems with anomalous properties are carried out.

Number of publications: 6 articles which have been published in leading professional journals indexed by scientometric databases Scopus and Web of Science; 2 articles – in the leading professional journal indexed by the scientometric database Scopus; 1 article – in the materials of the International Scientific Conference and 9 papers have been presented as abstracts of reports at conferences. The total number of references to the author’s publications / work’s h-index according to databases is: Scopus – 52/3, Web of Science – 49/3, Google Scholar – 77/4.