T-spheres as a limit of Lemaitre-Tolman-Bondi solutions

In the Tolman model there exist two quite different branches of solutions - generic Lemaitre-Tolman-Bondi (LTB) ones and T-spheres as a special case. We show that, nonetheless, T-spheres can be obtained as a limit of the class of LTB solutions having no origin and extending to infinity with the areal radius approaching constant. It is shown that all singularities of T-models are inherited from those of corresponding LBT solutions. In doing so, the disc type singularity of a T-sphere is the analog of shell-crossing.Comment: 6 pages. 1 Reference added. To appear in Phys. Rev.

Redshift drift in axially symmetric quasi-spherical Szekeres models

Models of inhomogeneous universes constructed with exact solutions of Einstein's General Relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides large scale inhomogeneity models spherically symmetric around the observer, Swiss-cheese models have also been studied. Among them, Swiss-cheeses where the inhomogeneous patches are modeled by different particular Szekeres solutions have been used for reproducing the apparent dimming of the type Ia supernovae (SNIa). However, the problem of fitting such models to the SNIa data is completely degenerate and we need other constraints to fully characterize them. One of the tests which is known to be able to discriminate between different cosmological models is the redshift-drift. This drift has already been calculated by different authors for Lema\^itre-Tolman-Bondi (LTB) models. We compute it here for one particular axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese which has previously been shown to reproduce to a good accuracy the SNIa data, and we compare the results to the drift in the $\Lambda$CDM model and in some LTB models that can be found in the literature. We show that it is a good discriminator between them. Then, we discuss our model's remaining degrees of freedom and propose a recipe to fully constrain them.Comment: 15 pages, 7 figures, minor changes in title, text, figures and references; conclusions unchanged, this version matches the published versio

The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin

In this work, different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear "one-dimensional" potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in an analytical form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on a number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either appearance of tall waves, or formation of sharp crests at moderate-height waves.Comment: revtex4, 10 pages, 33 figure

The hodograph method applicability in the problem of long-scale nonlinear dynamics of a thin vortex filament near a flat boundary

Hamiltonian dynamics of a thin vortex filament in ideal incompressible fluid near a flat fixed boundary is considered at the conditions that at any point of the curve determining shape of the filament the angle between tangent vector and the boundary plane is small, also the distance from a point on the curve to the plane is small in comparison with the curvature radius. The dynamics is shown to be effectively described by a nonlinear system of two (1+1)-dimensional partial differential equations. The hodograph transformation reduces that system to a single linear differential equation of the second order with separable variables. Simple solutions of the linear equation are investigated at real values of spectral parameter $\lambda$ when the filament projection on the boundary plane has shape of a two-branch spiral or a smoothed angle, depending on the sign of $\lambda$.Comment: 9 pages, revtex4, 6 eps-figure

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

ПОРІВНЯЛЬНИЙ АНАЛІЗ МЕТОДІВ ВІДНОВЛЕННЯ ПРОПУЩЕНИХ ДАНИХ ЧАСУ ДОСТУПНОСТІ СЕРВЕРА В ІНФОРМАЦІЙНО- EКОНОМІЧНИХ ПРОСТОРАХ

In the article presents results of research of primary statistical characteristics of time of processing and data transmission are given in systems of information economic area. On the basis of the received results the analysis of methods of recovery of the passed data is made. In work methods of data processing with admissions are analyzed and the most rational are chosen. Change of the law of distribution of selection depending on a way of elimination of the passed data is investigated. Forecasting of time of availability of the server of information economic area is executed. The goal of this paper is primary statistical characteristics research of data processing and transmission time in IES. Particularly, the server availability time (SAT) was studied within this work. This time consists of Client-to-Server connection time, Server data processing time, and Server answer transfer time. The values of service time were taken for research, that were received while studying of cloud computing performance. It was established that if data loss is not over 6% distribution law of initial model selection saves. If data loss is between 9% and 15% methods primary statistical characteristics of studied selection were determined without consideration of data missing. Missed data was filled with data distributed by the same law as for initial selection with admissions.В статье приведены результаты исследования первичных статистических характеристик времени обработки и передачи данных в информационно-экономических пространствах. На основании полученных результатов выполнен  анализ методов восстановления пропущенных данных. В работе проанализированы приемы обработки данных с пропускам и выбраны наиболее рациональные. Исследовано изменение  закона распределения выборки в зависимости от способа устранения пропущенных данных. Выполнено прогнозирование времени доступности сервера в информационно-экономических пространствах. Цель работы состояла в исследование первичных статистических характеристик времени обработки и передачи данных в информационно-экономических пространствах.  В частности, в рамках данной работы изучалось время доступности сервера.У статті наведено  результати дослідження первинних статистичних характеристик часу обробки і передачі даних в інформаційно-економічних просторах. На підставі отриманих результатів виконано  аналіз методів відновлення пропущених даних. Проаналізовано прийоми обробки даних з пропускам та  обрано найбільш раціональні. Досліджена зміна  закону розподілу вибірки залежно від способу усунення пропущених  даних.  Виконано прогнозування часу доступності сервера економічних просторів. Мета роботи полягала у дослідження первинних статистичних характеристик часу обробки і передачі даних в інформаційно-економічних просторах. Зокрема, в рамках даної роботи вивчалося час доступності сервера