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Full classification of motions with uniform deformation on a rotating plane
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Rozanova O. S., Turtsynskiy M.
In book
Vol. 2164. , AIP Publishing LLC, 2019.
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
Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields
Ilyashenko Y., Journal of Fixed Point Theory and Applications 2024 Vol. 26 Article 24
We prove that Lyapunov stability problem demonstrates pathologies even on the set-theoretical level. Namely, there exists an analytic one-parameter family of 5-jets of vector fields that crosses the set of stable jets by a countable union of disjoint intervals. ...
Added: January 29, 2025
Springer, 2024.
This book provides a state-of-the-art review of Pilot Wave Theory at the beginning of the XXI century. It contains the best contributions of the first International Conference on Advances in Pilot Wave Theory, held in Lisbon in 2021. The event brought together physicists from the new emerging field of Hydrodynamic Quantum Analogs (HQA) and philosophers ...
Added: September 9, 2024
Papatryfonos K., Vervoort L., Nachbin A. et al., Physical Review Fluids 2024 Vol. 9 No. 8 Article 084001
Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscopic realization of wave-particle duality and concomitant classical analogs of a growing number of quantum effects. The question naturally arises as to how closely particle-particle correlations achieved with this classical system can mimic those arising on the quantum scale. We here introduce ...
Added: August 29, 2024
Rozanova O. S., Turtsynskiy M., , in: Nonlinear Analysis and Boundary Value ProblemsVol. 292.: Springer, 2019. P. 131–143.
We show that a small correction due to centrifugal force usually neglected in the l-plane model of atmosphere drastically influences on the stability of vortices. Namely, in the presence of the Coriolis force only there exists a wide range of parameter ensuring nonlinear stability of a vortex with uniform deformation. Taking into account the centrifugal force ...
Added: October 31, 2021
Chernousova E., Feng Y., Hryniv O. et al., Mathematical Population Studies 2021 Vol. 28 No. 2 P. 63–80
In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model. An ...
Added: October 31, 2021
Castillo M. A., Bonilla M., Loiseau J. J. et al., IFAC-PapersOnLine 2020 Vol. 53 No. 2 P. 6788–6793
This paper deals with the stabilization of a class of time-dependent linear autonomous systems with a switched structure. For this aim, the switched dynamic system is modeled by means of an implicit representation combined with a Linear-Quadratic (LQ) type control design. The proposed control design stabilizes the resulting system for all of the possible realizations ...
Added: October 30, 2021
Chernousova E., Feng Y., Hryniv O. et al., Mathematical Population Studies 2020
In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model. An ...
Added: October 28, 2020
Burov A. A., Guerman A., Nikonov V., Acta Astronautica 2018 Vol. 146 P. 181–184
We consider a gravitating system with triangular mass distribution that can be used as approximation of gravitational field for small irregular celestial bodies. In such system, the locations of equilibrium points, that is, the points where the gravitational forces are balanced, are analyzed. The goal is to find the mass distribution which provides equilibrium in ...
Added: October 1, 2018
Yablonskii S. V., Kurbatov N. M., Parfenyev V.M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 95 No. 1 P. 012707-1–012707-5
We study horizontal streaming excited by means of a low-frequency and low-intensity acoustic wave in 2D freely suspended films of thermotropic smectic liquid crystals. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of the vortices ...
Added: October 30, 2017
Gaydukov R. K., Borisov D. I., Mathematical notes 2016 Vol. 99 No. 5 P. 636–642
A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the ...
Added: May 18, 2016
Danilov V., Gaydukov R., Mathematical notes 2015 Vol. 98 No. 4 P. 561–571
We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure. ...
Added: September 27, 2015
Danilov V., Gaydukov R., Russian Journal of Mathematical Physics 2015 Vol. 22 No. 2 P. 161–173
A fluid flow along a plate with small irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure, i.e., both a thin boundary layer and the classical Prandtl boundary layer are present. It is proved that the solution of the boundary-value problem thus obtained exists and is unique ...
Added: September 3, 2015
Myshkis P. A., Международный журнал по теоретической и прикладной математике, классической и небесной механике, космодинамике 2013 № 2(3) С. 51–59
In the work received the necessary and sufficient condition for the existence for linear differential equation of n-th order the fundamental system of solutions expanding in Taylor series on multiple degrees of argument in the neighborhood of zero. Such condition is that coefficients of the equation have analogous decomposition. In the proof used the transition ...
Added: February 18, 2014