Variational principle for frozen-in vortex structures interacting with sound waves

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and general-relativistic fluid dynamics, and two-fluid plasma model including the Hall-magnetohydrodynamics. A variational formulation is found for motion and interaction of frozen-in localized vortex structures and acoustic waves in a special description where dynamical variables are, besides the Eulerian fields of the fluid density and the potential component of the canonical momentum, also the shapes of frozen-in lines of the generalized vorticity. This variational principle can serve as a basis for approximate dynamical models with reduced number of degrees of freedom.Comment: 7 pages, revtex4, no figure

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 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

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

Selection Of A Filler For Tablets Manufactured With Direct Compression Method Containing Dry Ginger Extract

The preliminary studies of physico-chemical and pharmaco-technological properties of the dry extract of ginger have determined the need for introduction of different groups of excipients for developing a solid dosage form for the treatment of type II diabetes mellitus.Aim. To choose the rational filler in the composition of tablets with ginger obtained by direct compression.Materials and methods. The study object was the dry extract of ginger (DEG) (producer “Megaprom”, Dnepr,Ukraine) and modern excipients for the production of tablets by direct compression: GalenIQ 721 (BENEO-Palatinit Gmb), Flowlac 100 (Meggle Co.), Tablettose 80 (Meggle Co.), Farmaxx (Merck), Microcelac 100 (Meggle Co.), Vivapur 112 and 102 (JRS Pharm), Prosolv HD 90, Prosolv SMCC 50 (JRS Pharm) manufactured in Germany. Pharmaco-technological and physico-chemical properties of the samples were studied according to conventional methods of the State Pharmacopoeia of Ukraine.Results and discussion. According to the results of the crystallographic analysis, the ability to the moisture absorption, resistance to crushing, disintegration time, fluidity indicators, angle of repose and bulk volume the effect of modern excipients on physicochemical and pharmaco-technological properties of the dry extract of ginger has been studied.Conclusions. According to the results of microscopic analysis, it has been found, that the rational fillers are GalenIQ 721, Prosolv HD 90, Prosolv SMCC 50, Vivapur 102 and Vivapur 112, as they provide a uniform system and the necessary resistance to destruction. The study of the kinetics of the moisture absorption has shown that addition of the fillers significantly reduces the increase in moisture compared to the dry extract. The mixture with GalenIQ 721 has the lowest parameters of moisture absorption at a relative air humidity of 45 %, 75 % and 100 %. In accordance with the results of the pharmaco-technological studies, it has been found that addition of GalenIQ 721 leads to improved flowability, disintegration, settling qualities; it indicates the feasibility of its inclusion into the composition of the solid dosage form

A Novel Componentless Power Quality Improvement Technique for Renewable Energy Sources

The main aim in power distribution system is to provide uninterrupted flow of energy at smooth sinusoidal voltage at the contracted magnitude level and frequency. However in wind power generation have numerous non linear loads, which significantly affect the quality of the power supplies. As the power of the non linear loads, the purity of the waveform of supplies is lost. In this proposed work, multiple port choppers is used to handle power quality issues such as voltage sags, harmonic distortion, in addition to normal wind turbine supplying to the customer during normal operation. The wind generation with micro turbine provides the flexibility of operation to the customer. The micro turbine based DVR can recover voltage sags in the supply voltage during abnormal load. On the other hand, it will operate as a separate DG when the wind power supply fails to supply the desired power

Slow flows of an relativistic perfect fluid in a static gravitational field

Relativistic hydrodynamics of an isentropic fluid in a gravitational field is considered as the particular example from the family of Lagrangian hydrodynamic-type systems which possess an infinite set of integrals of motion due to the symmetry of Lagrangian with respect to relabeling of fluid particle labels. Flows with fixed topology of the vorticity are investigated in quasi-static regime, when deviations of the space-time metric and the density of fluid from the corresponding equilibrium configuration are negligibly small. On the base of the variational principle for frozen-in vortex lines dynamics, the equation of motion for a thin relativistic vortex filament is derived in the local induction approximation.Comment: 4 pages, revtex, no figur

Cosmic String in Scalar-Tensor Gravity

The gravitational properties of a local cosmic string in the framework of scalar-tensor gravity are examined. We find the metric in the weak-field approximation and we show that, contrary to the General Relativity case, the cosmic string in scalar-tensor gravitation exerces a force on non-relativistic, neutral test particle. This force is proportional to the derivative of the conformal factor $A^{2}(\phi)$ and it is always attractive. Moreover, this force could have played an important role at the Early Universe, although nowadays it can be neglegible. It is also shown that the angular separation $\delta\varphi$ remains unaltered for scalar-tensor cosmic strings.Comment: 15 pages, LATEX, no figure