Вісник № 01. Інноваційні дослідження у наукових роботах студентів
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Перегляд Вісник № 01. Інноваційні дослідження у наукових роботах студентів за Ключові слова "Hilbert space"
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Документ Application of the correlation theory of inhomogeneous random fields to the study of the statistically inhomogeneous screen model(Національний технічний університет "Харківський політехнічний інститут", 2021) Cheremskaya, Nadezhda ValentinovnaThe article considers the problem of finding a field created by a system of fluctuating sources on the screen, which is characterized by a correlation function, where 1 2, AA K r r the correlation function is separable. This image corresponds to a random field on the screen, which is the sum of a separable field and a heterogeneous random field of the first rank, which significantly changes the correlation radius at a distance l. The model studied in this paper does not assume uncorrelated sources and coincidence of laws of intensity change and therefore corresponds to a system of sources with significantly different intensities and laws of their change in the direction of wave propagation in the transverse plane. The correlation function of the sources be not assumed to be separable and the field distribution on the screen is an inhomogeneous random field of the first rank or is the sum of a separable field and a statistically inhomogeneous field of the first rank. To find a solution in the approximation of a parabolic equation, a method of immersion in the corresponding Hilbert space is proposed, which allows one to quickly and efficiently find the statistical characteristics of the solution. As an example, the influence of statistical inhomogeneity on the intensity function of a luminous screen, which has the shape of a round disk, is considered. An off-screen correlation function is obtained, which contains information on the size and nature of inhomogeneities of emitting sources on a luminous screen. A numerical analysis of the representation for the correlation function is carried out in the case when the statistical heterogeneous of the environmen is generated by the presence of a continuous spectrum or a spectrum at zero. The article obtains approximate calculation formulas for the average temperature field and its dispersion, which take into account fluctuation processes in the calculation of thermal regimes of solar panels, which allow to make appropriate corrections in theoretical calculations.