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

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

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

Finite time singularities in a class of hydrodynamic models

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form ${\cal L}\sim\int k^\alpha|{\bf v_k}|^2d^3{\bf k}$ in 3D Fourier representation, where $\alpha$ is a constant, $0<\alpha< 1$. Unlike the case $\alpha=0$ (the usual Eulerian hydrodynamics), a finite value of $\alpha$ results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of anti-parallel vortex filaments and an analog of the Crow instability is found at small wave-numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like $(t^*-t)^{1/(2-\alpha)}$, where $t^*$ is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal pape

Побудування регресійних моделей для розроблення технології отримання таблеток на основі імбиру лікувального

Scientific research in pharmacy, due to their multifactorial nature, is closely related to modeling of complex static systems. For this purpose, the so-called “input-output” mathematical models, which are built based on the results of the experiment, are widely used. Modeling of static systems based on the experimental data requires the solution of three interrelated tasks: planning of the experiment and its implementation; identification of the model structure and its parameters; approximation, if necessary, of a complex model to a simpler mathematical description.Научные исследования в фармации вследствие их многофакторности тесно связаны с моделированием сложных статических систем. Для этой цели широко применяются так называемые математические модели «вход – выход», которые строятся по результатам эксперимента. Моделирование статических систем на основе экспериментальных данных требует решения трех взаимосвязанных задач: планирование эксперимента и его реализация; идентификация структуры модели и ее параметров; приближение в случае необходимости сложной модели к более простому математическому описанию.Наукові дослідження у фармації через їх багатофакторність тісно пов’язані з моделюванням складних статичних систем. Для цього широко використовуються так звані математичні моделі «вхід – вихід», які будуються за результатами експерименту. Моделювання статичних систем на основі експериментальних даних вимагає вирішення трьох взаємопов’язаних завдань: планування експерименту та його реалізація; визначення структури моделі та її параметрів; наближення, за необхідності, складної моделі до більш простого математичного опису