Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth

Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system with a relatively small density jump (the Boussinesq limit taking place in real oceanic conditions), in the presence of a background shear current of constant vorticity, and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders are derived from the exact Hamiltonian functional in a remarkably simple way, for two different parametrizations of the interface shape.Comment: revtex, 4.5 pages, minor corrections, summary added, accepted to JETP Letter

Classical model of elementary particle with Bertotti-Robinson core and extremal black holes

We discuss the question, whether the Reissner-Nordstr\"{o}m RN) metric can be glued to another solutions of Einstein-Maxwell equations in such a way that (i) the singularity at r=0 typical of the RN metric is removed (ii), matching is smooth. Such a construction could be viewed as a classical model of an elementary particle balanced by its own forces without support by an external agent. One choice is the Minkowski interior that goes back to the old Vilenkin and Fomin's idea who claimed that in this case the bare delta-like stresses at the horizon vanish if the RN metric is extremal. However, the relevant entity here is the integral of these stresses over the proper distance which is infinite in the extremal case. As a result of the competition of these two factors, the Lanczos tensor does not vanish and the extremal RN cannot be glued to the Minkowski metric smoothly, so the elementary-particle model as a ball empty inside fails. We examine the alternative possibility for the extremal RN metric - gluing to the Bertotti-Robinson (BR) metric. For a surface placed outside the horizon there always exist bare stresses but their amplitude goes to zero as the radius of the shell approaches that of the horizon. This limit realizes the Wheeler idea of "mass without mass" and "charge without charge". We generalize the model to the extremal Kerr-Newman metric glued to the rotating analog of the BR metric.Comment: 23 pages. Misprints correcte

Узагальнення впливу параметрів навантажень на характеристики НВЧ вузлів

The method of generalization of influence of parameters of loadings on the characteristics of UHF units that enables to predict changes of the characteristics at inclusion of UHF units in the radioelectronics systems is given.Приведена методика обобщения влияния параметров нагрузок на характеристики СВЧ узлов, которая даёт возможность прогнозировать изменения указанных характеристик при включении СВЧ узлов в радиоелектронные системы.Наведено методику узагальнення впливу параметрів навантаження на характеристики НВЧ вузлів, яка надає можливість прогнозувати зміни вказаних характеристик при включенні НВЧ вузлів в радіоелектронні системи

Screened Coulomb interactions in metallic alloys: II Screening beyond the single-site and atomic sphere approximations

A quantitative description of the configurational part of the total energy of metallic alloys with substantial atomic size difference cannot be achieved in the atomic sphere approximation: It needs to be corrected at least for the multipole moment interactions in the Madelung part of the one-electron potential and energy. In the case of a random alloy such interactions can be accounted for only by lifting the atomic sphere and single-site approximations, in order to include the polarization due to local environment effects. Nevertheless a simple parameterization of the screened Coulomb interactions for the ordinary single-site methods, including the generalized perturbation method, is still possible. We obtained such a parameterization for bulk and surface NiPt alloys, which allows one to obtain quantitatively accurate effective interactions in this system.Comment: 24 pages, 2 figure

On the modulation instability development in optical fiber systems

Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their interaction stage and the further propagation. Comparison between 4 different NLS-like systems was made: the classical NLS equation, NLS system plus higher dispersion terms, NLS plus higher dispersion and self-steepening and also fully generalized NLS equation with Raman scattering taken into account. For the latter case a mechanism of energy transfer from smaller quasi-solitons to the bigger ones is proposed to explain the dramatical increase of rogue waves appearance frequency in comparison to the systems when the Raman scattering is not taken into account.Comment: 9 pages, 54 figure

Gravitational Collapse of Dust with a Cosmological Constant

The recent analysis of Markovic and Shapiro on the effect of a cosmological constant on the evolution of a spherically symmetric homogeneous dust ball is extended to include the inhomogeneous and degenerate cases. The histories are shown by way of effective potential and Penrose-Carter diagrams.Comment: 2 pages, 2 figures (png), revtex. To appear in Phys. Rev.