Влияние фрактальной структуры на электрическое поле в грозовых облаках

The paper considers the degree of fractal structure impact on the electric field intensity inside thunderstorm clouds using the apparatus of fractional integrodifferentiation. We propose a mathematical model of intensity dynamics of a static electric field in the thunderstorm clouds, taking into account media with fractal dimension. The results obtained confirm the close connection of electrophysical processes in thunderclouds with the fractal medium itself. В статье с помощью аппарата дробного интегро-дифференцирования рассматривается степень влияния фрактальной структуры на напряженность электрического поля внутри грозовых облаков. Предлагается математическая модель динамики напряженности статического электрического поля в грозовых облаках с учетом сред с фрактальной размерностью. Полученные результаты подтверждают тесную связь электрофизических процессов в грозовых облаках с самой фрактальной средой В статье с помощью аппарата дробного интегро-дифференцирования рассматривается степень влияния фрактальной структуры на напряженность электрического поля внутри грозовых облаков. Предлагается математическая модель динамики напряженности статического электрического поля в грозовых облаках с учетом сред с фрактальной размерностью. Полученные результаты подтверждают тесную связь электрофизических процессов в грозовых облаках с самой фрактальной средой.

An efficient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration

An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives was obtained in Yang and Srivastava (Commun Nonlinear Sci Numer Simul 29(1–3):499–504, 2015). In this paper, we obtain the numerical solution of damped forced oscillator problems by employing the operational matrix of integration of Bernoulli orthonormal polynomials. The operational matrix of integration is determined with the help of the integral operator on Bernoulli orthonormal polynomials. Numerical examples of two different problems of spring are given to delineate the performance and perfection of this approach and compared the results with the exact solution.

Fractional Fokker-Planck equation in a fractal medium

This paper studies a fractal modification of Fokker-Planck equation for a heat conduction in a fractal medium. Fourier transform and Darboux transformation are used to solve the equation, some new results are obtained.

Charge Density Distribution Model in Self-Organizing Cloud

The paper considers a charge distribution model in a thundercloud presenting a self-organizing system in view of its fractal structure. An analytical solution to the model equation is obtained. Using numerical calculations, the distribution of charges in the fractal medium is shown and a comparative analysis of the existing models is carried out.

Numerical research of non-isothermal filtration process in fractal medium with non-locality in time

The difference scheme for the numerical solution of boundary problem for a system of equations for non-isothermal filtration with a Caputo derivative of fractional order on time is developed. Stability of the differential scheme is proved. Computational experiment in the analysis of solutions obtained has been done. Physical processes pass slowly in the fractal medium with non-locality in time. It is explained by the fact the occasionally wandering particle is being eliminated from the start place slowly, since not all directions of the movement become available for it. Values of pressure and temperature depending on the coordinate of layer radius and time calculated, and graphs of the dynamics pressure and temperature changes according to the layer radius and in depending on the time are built. Deceleration of the processes with time in the solutions for fractional derivatives which is characteristic for such medium has been established.

ON PETROPHYSICAL PARAMETERS’S RELATIONS IN FRACTAL MEDIUM

Features of influence of fractal characteristics of the environment on interrelation of petrophysical parameters in heterogeneous fluid-saturated medium on the example of the collection of core samples from the productive horizons of the Devonian and of the Carboniferous are considered. It is shown that the typical characteristics of fractal mediums, connecting physical characteristics with the impedance can be used at the prediction of petrophysical parameters at the lack of information.