Seminar by Prof. Valeriy Arkhinchee

At 2:00 p.m., June 21, 2024, the lectures from Prof. Valeriy Arkhinchee and Dr. Le Dai Nam takes place  on the 6th Floor of the Library with detailed content as follows:

Prof. Valeriy Arkhincheev presents a talk entitled "Stochastic processes in complex media and fractional calculus. Application for a living systems"

Abstract:

The report is devoted to the stochastic processes in the complex systems with fractal structure. According to the many investigations in this field the strict and rigorous approach to this problem must be based on the fractional calculus. The brief review and history of fractals was given. The deduction of the diffusions of fractional order was furthered on the basis of the microscopic model of the comb structure. The author was among the first researchers to propose the exact deduction of the fractional order diffusion equations (1991 y.) and obtain the analytic solution of this fractional order equation.

The developed approach was applied to the problem of mass transfer in living plants with finite lengths of bitches in the framework of the mathematical comb model was studied. In our paper (Scientific Reports, 2019) it was established that mass transfer processes in living plants depend on the geometric fractal structure of plants, specifically, that the mass transfer is accelerated from steam to bitches. Now this study was continued and the more real model with finite lengths of bitches was studied. From mathematical point of view the solution of fractional order equation with reflecting boundary conditions was obtained. The transition from anomalous character of mass transfer to usual diffusion due to finite length of ribs was furthered. The anomalous character of mass transfer leads to dependencies of effective diffusion coefficients, describing mass transfer, on the length of bitches. It was shown the control and self regulation of the transfer processes of water, fertilizers in plants and as a result the growth of bitches and leaves in plants was governed by the lengths of bitches. The discussion of obtained results was given.