Interaction of a vortex ring with the free surface of ideal fluid

The interaction of a small vortex ring with the free surface of a perfect fluid is considered. In the frame of the point ring approximation the asymptotic expression for the Fourier-components of radiated surface waves is obtained in the case when the vortex ring comes from infinity and has both horizontal and vertical components of the velocity. The non-conservative corrections to the equations of motion of the ring, due to Cherenkov radiation, are derived.Comment: LaTeX, 15 pages, 1 eps figur

Dark matter-wave solitons in the dimensionality crossover

We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial Schr\"{o}dinger mean-field model, we find that the anomalous mode of the Bogoliubov spectrum has an eigenfrequency which coincides with the soliton oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that substantial deviations (of order of 10% or more) from the characteristic frequency $\omega_{z}/\sqrt{2}$ ($\omega_{z}$ being the longitudinal trap frequency) are possible even in the purely 1D regime.Comment: Phys. Rev. A, in pres

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.Comment: 14 page

Ultrashort pulses and short-pulse equations in (2+1)−(2+1)-dimensions

In this paper, we derive and study two versions of the short pulse equation (SPE) in $(2+1)-$dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab waveguides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting $(2+1)$-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort 1D breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing waveforms

The Yarkovsky effect and dynamical evolution of asteroids

В лекции дается описание эффекта Ярковского. Рассматриваются суточный и сезонный эффекты и их зависимость от наклона оси вращения астероида. Описывается влияние эффекта Ярковского О’Кифа Радзиевского Пэддэка (YORP-эффект) на угловую скорость вращения астероида. Приводятся сведения о методах обнаружения влияния эффекта Ярковского и YORP-эффекта по результатам наблюдений. Обсуждаются проявления эффекта Ярковского в наблюдаемом распределении орбит астероидов: сближение орбит астероидов в семействах, пары астероидов на близких орбитах, эволюционное расширение семейств астероидов, распределение астероидов по угловой скорости вращения и направлению оси вращения. Формулируются задачи для будущих исследований.The Yarkovsky effect is described in the lecture. Diurnal and season effects as well as their dependence on obliquity of axis of rotation of an asteroid are considered. Effect of the Yarkovsky—O’Keefe—Radzievskii—Paddack effect (YORP-effect) on rotation rate of an asteroid is described. Data about observational methods of the Yarkovsky and YORP effects detection are given. Evidences of the Yarkovsky effect in observed distribution of asteroids are discussed. These are orbital convergence in asteroid families, pairs of asteroids on close orbits, it is spreading of asteroids families, it is distribution of rotation rate and obliquity for asteroids. The goals for future works are previewed.Работа выполнена при поддержке Правительства Российской Федерации (постановление № 211, контракт № 02.A03.21.0006) и гранта РФФИ № 18-02-00015

Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier

We study possibilities to suppress the transverse modulational instability (MI) of dark-soliton stripes in two-dimensional (2D) Bose-Einstein condensates (BECs) and self-defocusing bulk optical waveguides by means of quasi-1D structures. Adding an external repulsive barrier potential (which can be induced in BEC by a laser sheet, or by an embedded plate in optics), we demonstrate that it is possible to reduce the MI wavenumber band, and even render the dark-soliton stripe completely stable. Using this method, we demonstrate the control of the number of vortex pairs nucleated by each spatial period of the modulational perturbation. By means of the perturbation theory, we predict the number of the nucleated vortices per unit length. The analytical results are corroborated by the numerical computation of eigenmodes of small perturbations, as well as by direct simulations of the underlying Gross-Pitaevskii/nonlinear Schr\"{o}dinger equation.Comment: 10 pages, 7 figures. To appear on Phys. Rev. A, 201