Yuldashev P.V., Konnova E.O., Karzova M.M., Khokhlova V.A. «Three-Dimensional Wide-Angle Parabolic Equations with Propagator Separation Based on Finite Fourier Series» Акустический журнал, 70, № 5, с. pp. 783-796 (2024)

A possibility of constructing wide-angle diffraction models using Fourier series decomposition of the propagation operator of one-way wave equations is investigated. The propagation operator is considered as a function of the propagation step, reference wavenumber, and transversal Laplacian operator, which appears under the square-root of the pseudodifferential operator in the theory of one-way equations. It is shown that in this operator formalism, Fourier series decomposition approximates the one-way propagator by a weighted sum of exponential propagators, whose structure is similar to the propagator of the standard or small-angle parabolic equation. The exact propagator is modified using Hermite interpolation polynomials in order to achieve two crucial properties that guarantee fast convergence of the Fourier series: propagator periodicity and continuity of its derivatives. It is demonstrated that for three-dimensional diffraction problems, contrary to the standard split-step Pade approach, the proposed wide-angle propagation model allows for using efficient numerical methods and operator splitting procedures available for the standard parabolic equation. As a result, it is possible to organize computations separately along each of the two coordinate axes that are perpendicular to the predominant direction of wave propagation.

Raghib R., Naciri I., Khalfi H., Elmaimouni L., Yu J., Benami A., Bybi A. «A Semi-Analytical Approach for Analyzing Acoustic Wave Propagation in Three-Dimensional Hexagonal FGM pipes» Акустический журнал, 70, № 6, с. pp1-24 (2024)

This study presents a semi-analytical approach for analyzing acoustic wave propagation in three-dimensional hexagonal functionally graded (FGM) pipes composed of Aluminum (Al) and silicon nitride (SN), employing the Legendre polynomial method. Two different configurations of FGM pipes, namely (SN/Al/SN) and (Al/SN/Al), are investigated by solving the governing motion equations. The characteristics of phase velocity and normalized frequency dispersion curves for various modes and frequencies are analyzed, revealing the complex wave behavior arising from the hexagonal structure. The study examines the effects of material gradients, pipe geometry, and boundary conditions, highlighting the strong influence of normal stresses on boundary conditions. Additionally, the distribution of acoustic wave energy is found to be mainly confined to the interior of the cylinder. Our results demonstrate a high level of agreement with existing research, affirming the precision and reliability of our method. The Legendre polynomial method accurately captures wave propagation in functionally graded pipes, offering a versatile approach applicable to various structures. These findings provide valuable insights into acoustic wave behavior in functionally graded pipes, with potential applications in non-destructive testing, material characterization, and structural health monitoring.

Khechoyan Kh.S. «Synthetic document generation for the task of visual document understanding» Ученые записки Ереванского государственного университета, физико-математических наук, 58, № 3, с. 79-87 (2024)

Для решения задачи анализа документов методами машинного обучения необходимо большое количество размеченных данных. Такие данные не всегда доступны, а если и доступны, то охватывают только определенные типы документов. Нами представлен метод создания синтетических данных, позволяющий создавать документы любого типа, предварительно определив компоненты документа. Изменяя расположение компонентов документов, текстовое содержание и визуальные элементы с помощью конфигураций, мы создаем разнообразные и реалистичные наборы данных, имитирующие реальные документы. Этот метод решает проблему нехватки размеченных наборов данных и предлагает гибкое решение для улучшения результатов модели машинного обучения. DOI: https://doi.org/10.46991/PYSUA.2024.58.3.079

Yuldashev P.V., Konnova E.O., Karzova M.M., Khokhlova V.A. «Three-Dimensional Wide-Angle Parabolic Equations with Propagator Separation Based on Finite Fourier Series» Акустический журнал, 70, № 5, с. pp. 783-796 (2024)

A possibility of constructing wide-angle diffraction models using Fourier series decomposition of the propagation operator of one-way wave equations is investigated. The propagation operator is considered as a function of the propagation step, reference wavenumber, and transversal Laplacian operator, which appears under the square-root of the pseudodifferential operator in the theory of one-way equations. It is shown that in this operator formalism, Fourier series decomposition approximates the one-way propagator by a weighted sum of exponential propagators, whose structure is similar to the propagator of the standard or small-angle parabolic equation. The exact propagator is modified using Hermite interpolation polynomials in order to achieve two crucial properties that guarantee fast convergence of the Fourier series: propagator periodicity and continuity of its derivatives. It is demonstrated that for three-dimensional diffraction problems, contrary to the standard split-step Pade approach, the proposed wide-angle propagation model allows for using efficient numerical methods and operator splitting procedures available for the standard parabolic equation. As a result, it is possible to organize computations separately along each of the two coordinate axes that are perpendicular to the predominant direction of wave propagation.

Yuldashev P.V., Konnova E.O., Karzova M.M., Khokhlova V.A. «Three-Dimensional Wide-Angle Parabolic Equations with Propagator Separation Based on Finite Fourier Series» Акустический журнал, 70, № 5, с. pp. 783-796 (2024)

A possibility of constructing wide-angle diffraction models using Fourier series decomposition of the propagation operator of one-way wave equations is investigated. The propagation operator is considered as a function of the propagation step, reference wavenumber, and transversal Laplacian operator, which appears under the square-root of the pseudodifferential operator in the theory of one-way equations. It is shown that in this operator formalism, Fourier series decomposition approximates the one-way propagator by a weighted sum of exponential propagators, whose structure is similar to the propagator of the standard or small-angle parabolic equation. The exact propagator is modified using Hermite interpolation polynomials in order to achieve two crucial properties that guarantee fast convergence of the Fourier series: propagator periodicity and continuity of its derivatives. It is demonstrated that for three-dimensional diffraction problems, contrary to the standard split-step Pade approach, the proposed wide-angle propagation model allows for using efficient numerical methods and operator splitting procedures available for the standard parabolic equation. As a result, it is possible to organize computations separately along each of the two coordinate axes that are perpendicular to the predominant direction of wave propagation.

Korunov A.O., Gusev V.A., Gorbovskoy V.S. «Rapid Estimation of the Sonic Boom Characteristics from Supersonic Passenger Aircraft in a Standard Atmosphere Based on Analytical Solutions: Cruise Mode» Акустический журнал, 70, № 4, с. pp718-732 (2024)

A method is proposed for quickly estimating the sonic boom characteristics from supersonic passenger aircraft under standard atmospheric conditions. The piecewise linear temperature profile and absence of atmospheric wind make it possible to completely reduce the problem of the geometry of sonic boom wave propagation to an algebraic form. For acoustic pressure, an analytical solution is formulated using the nonlinear geometrical acoustics approach. The dependence of the geometry of sonic boom wave propagation on the cruising flight parameters of a supersonic passenger aircraft is analyzed. Under the conditions of SBPW (Sonic Boom Prediction Workshop) 2020, the overpressure signatures on the ground from the X-59 demonstrator were calculated.