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Использование псевдоспектрального метода высокого порядка HOSM для моделирования нелинейных волн на поверхности воды конечной глубины
Фундаментальная и прикладная гидрофизика. 2025. Т. 18. № 4. С. 28–49.
Regimes and limitations of the numerical solution method for hydrodynamic equations using the approximation of the near-surface velocity potential by the high-order Taylor expansion (High Order Spectral Method, HOSM) are investigated. This approach is considered in the context of simulation of large ensembles of sea surface displacement fields under finite-depth conditions. The main attention is paid to the description of strongly nonlinear waves and waves with a wide frequency spectrum. The study is performed in planar geometry.
Bobkov G. A., Bobkov G. A., Bobkova I. V. et al., Journal of Superconductivity and Novel Magnetism 2025 Vol. 38 Article 239
In recent years, a number of studies have predicted the emergence of a nontrivial proximity effect in superconductor/antiferromagnet (S/AF) heterostructures. This effect is of considerable interest for the efficient integration of antiferromagnetic materials into the fields of superconducting spintronics and electronics. A key element of this proximity effect is the Néel triplet correlations, initially predicted ...
Added: July 2, 2026
Bakurskiy S. V., Skryabina O. V., Ruzhickiy V. I. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 113 P. 134509-1–134509-10
The miniaturization of superconducting electronics demands precise control over quasiparticle dynamics at the nanoscale. Understanding and controlling quasiparticle dynamics is essential for advancing superconducting electronics, particularly as device dimensions approach the nanoscale. Here we present direct experimental evidence for the quasiparticle-to-supercurrent conversion in planar SN-N-NS Josephson nanobridges with submicron electrodes. By employing a versatile measurement ...
Added: July 2, 2026
Polevoy K. B., Bakurskiy S. V., Ruzhickiy V. I. et al., Physical Review Applied 2026 Vol. 25 P. 024030-1–024030-12
We present a comprehensive study of planar Nb-Al-Nb Josephson junctions with submicrometer dimen sions (L ≈ 100 nm, active area of approximately 5 × 104 nm2), where the intrinsic superconductivity of the aluminum weak link plays a crucial role in enhancing device performance. Through a combi nation of theoretical modeling and experimental characterization, we demonstrate ...
Added: July 2, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2021 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Shestoperov A. I., Fomina E. V., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
He Y., Slunyaev A., Mori N. et al., Physica D: Nonlinear Phenomena 2026 Vol. 488 Article 135098
Extreme wave localizations in nonlinear dispersive media, arising from modulation instability in weakly nonlinear
wave interactions, can be effectively modeled by breather solutions. These breathers are exact solutions
of the nonlinear Schrödinger equation and provide accurate models for understanding and controlling unidirectional
rogue wave dynamics in numerical simulations or laboratory settings. A recent study by Y. He et ...
Added: February 12, 2026
Slunyaev A., Kokorina A., Physics of Fluids 2025 Vol. 37 No. 8 Article 087192
Nonlinear wave-induced perturbations are discussed within the framework of the second-order theory. Due to the slow attenuation of the long perturbations with depth, they modulate motions beneath surface waves down to the bottom and can strongly affect the wave statistics. The disturbance which corresponds to the second harmonic, at a sufficient depth, inverses the phase, thereby ...
Added: February 12, 2026
Shikanian A., Parfenyev V., Physics of Fluids 2025 Vol. 37 No. 9 Article 095127
We study two-dimensional turbulence in a square no-slip domain without bottom drag using direct numerical simulations. The dynamics are shown to depend strongly on the torque $M$ of the external forcing. When $M$ is relatively large, a long-lived coherent vortex forms at the domain center, establishing a persistent angular momentum. At lower torques, the angular ...
Added: September 6, 2025
Abrashkin A. A., World Scientific Publishing Co. Pte. Ltd, 2025.
This book is devoted to the problems of the analytical description of incompressible fluid flows in Lagrangian variables. Commonly, specialists in fluid dynamics prefer to use the Euler approach. For example, even classical textbooks by J. Batchelor, L.G. Loitsyansky, L.D. Landau, and E.M. Lifshitz do not provide the Lagrange equations of f luid dynamics. Exceptions ...
Added: January 28, 2025
Kolokolov I., Lebedev V., Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 109 No. 3 Article 035103
We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow fluctuations found in the linear approximation. We calculate the correction to the pair correlation function and the triple correlation function. It enables us ...
Added: March 25, 2024
Parfenyev V., Physics of Fluids 2024 Vol. 36 No. 1 Article 015148
An inverse turbulent cascade in a periodic square box produces a coherent system-sized vortex dipole. We study the statistics of its motion by carrying out direct numerical simulations performed for various bottom friction $\alpha$, pumping intensity $\varepsilon$, and fluid hyperviscosity $\nu$. In the main approximation, coherent vortices can be considered as point vortices, and within ...
Added: January 24, 2024
Dyachenko A., Studies in Applied Mathematics 2020 Vol. 144 No. 4 P. 493–503
One of the essential tasks of the theory of water waves is a construction of simplified mathematical models, which are applied to the description of complex events, such as wave breaking, appearing of freak waves in the assumption of weak nonlinearity. The Zakharov equation and its simplification, such as nonlinear Schrodinger equations and Dysthe equations, ...
Added: October 21, 2022
Dyachenko A., Fluids 2019 Vol. 4 No. 1 Article 47
The waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four-wave interactions of water waves allows to describe the evolution of the two groups as a system of two equations. The ...
Added: October 20, 2022
A. A. Abrashkin, Monatshefte fur Mathematik 2022 Vol. 199 No. 4 P. 717–732
Propagation of periodic stationaryweakly vortical gravitationalwaves on the freewater surface is considered. Similar wave motion was studied by Gouyon (Ann de la Fac des Sci de l’Université de Toulouse Sér 4(22):1–55, 1958) in linear and quadratic approximations in small parameter of the wave’s steepness ε for the deep water conditions.
In this paper this result is considered for the ...
Added: October 13, 2022
Abrashkin A. A., Pelinovsky E., Journal of Physics A: Mathematical and Theoretical 2021 Vol. 54 No. 39 Article 395701
To study stationary periodic weakly vortical waves on water (the Gouyon waves), the method of the modified Lagrangian variables is suggested. The wave vorticity Ω is specified as a series in the small steepness parameter ε in
the form: Ω =\sum( ε^n · Ω_n (b)), where Ω_n are arbitrary functions of the vertical Lagrangian coordinate b. Earlier Gouyon (1958) studied ...
Added: October 5, 2021
Ivanov S. K., Kamchatnov A.M., Physics of Fluids 2019 Vol. 31 Article 057102
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated, and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage ...
Added: February 4, 2021
Slunyaev A., Pelinovsky E., Water Waves 2020 Vol. 2 No. 1 P. 59–77
The nonlinear stage of the modulational (Benjamin–Feir) instability of unidirectional deep-water surface gravity waves is simulated numerically by the fifth-order nonlinear envelope equations. The conditions of steep and breaking waves are concerned. The results are compared with the solution of the full potential Euler equations and with the lower-order envelope models (the 3-order nonlinear Schrödinger ...
Added: April 22, 2020
Abrashkin A. A., Pelinovsky E., Physics-Uspekhi 2018 Vol. 61 P. 307–312
We discuss the properties of two-dimensional, non
linear, potential, and vortex waves on the surface of an ideal
liquid of infinite depth. It is shown that in the quadratic order in
the amplitude, the vorticity of the Gerstner wave is equal in
magnitude to and different in sign from that of the Stokes drift
current in a surface layer. This ...
Added: October 3, 2018
Abrashkin A. A., Pelinovsky E., Успехи физических наук 2018 Т. 188 С. 329–334
It is shown in the quadratic approximation that the Gerstner wave vorticity is equal and of different sign to the vorticity of Stokes drift current in deep water. That gives an opportunity to interpret the Stokes wave as a superposition of the Gerstner wave and the Stokes drift and to explain, why the nonlinearity in ...
Added: October 17, 2017