The instability of hydrodynamic longitudinal oscillations in a non-uniform magnetoactive plasma

1972 ◽  
Vol 8 (3) ◽  
pp. 387-391
Author(s):  
V. V. Demchenko ◽  
I. A. El-Naggar
Keyword(s):  
Growth Rates ◽  
Plasma Oscillation ◽  
Magnetoactive Plasma ◽  
The Stability ◽  
Oscillation Frequencies ◽  
Inhomogeneous Magnetoactive Plasma

The stability of hydrodynamic longitudinal oscillations of an inhomogeneous magnetoactive plasma is analysed. If the non-uniformity of density is taken into account, it is shown to result in parametric-like instability at sub- and ultra- harmonics of natural plasma oscillation frequencies. The conditions for the development of unstable oscillations and their growth rates are determined.

Analyzing the current effectiveness of the Russian economy's design

2020 ◽  
Vol 8 (8) ◽  
pp. 1476-1496
Author(s):  
V.V. Smirnov
Keyword(s):  
Economic Growth ◽  
Sustainable Development ◽  
Growth Rates ◽  
Systems Approach ◽  
Mineral Resources ◽  
Cash Flows ◽  
Moscow Oblast ◽  
Structural Balance ◽  
Russian Economy ◽  
The Stability

Subject. The article discusses Russia’s economy and analyzes its effectiveness. Objectives. The study attempts to determine to what extent Russia’s economy is effective. Methods. The study is based on the systems approach and the statistical analysis. Results. I discovered significant fluctuations of the structural balance due to changing growth rates of the total gross national debt denominated in the national currency, and the stability of growth rates of governmental revenue. Changes in the RUB exchange rate and an additional growth in GDP are the main stabilizers of the structural balance, as they depend on hydrocarbon export. As a result of the analysis of cash flows, I found that the exports slowed down. Financial resources are strongly centralized, since Moscow and the Moscow Oblast are incrementing their share in the export of mineral resources, oil and refining products and import of electrical machines and equipment. Conclusions and Relevance. The fact that the Russian economy has been effectively organized is proved with the centralization of the economic power and the limits through the cross-regional corporation, such as Moscow and the Moscow Oblast, which is resilient to any regional difficulties ensuring the economic growth and sustainable development. The findings would be valuable for the political and economic community to outline and substantiate actions to keep rates of the economic growth and sustainable development of the Russian economy.

scholarly journals On the stability of ocean overflows

2008 ◽  
Vol 602 ◽  
pp. 241-266 ◽  
Author(s):  
LARRY J. PRATT ◽  
KARL R. HELFRICH ◽  
DAVID LEEN
Keyword(s):  
Potential Vorticity ◽  
Growth Rates ◽  
Deep Ocean ◽  
Basic Flow ◽  
Necessary Condition ◽  
Zero Energy ◽  
Coriolis Parameter ◽  
Hydraulic Behaviour ◽  
Zero Potential ◽  
The Stability

The stability of a hydraulically driven sill flow in a rotating channel with smoothly varying cross-section is considered. The smooth topography forces the thickness of the moving layer to vanish at its two edges. The basic flow is assumed to have zero potential vorticity, as is the case in elementary models of the hydraulic behaviour of deep ocean straits. Such flows are found to always satisfy Ripa's necessary condition for instability. Direct calculation of the linear growth rates and numerical simulation of finite-amplitude behaviour suggests that the flows are, in fact, always unstable. The growth rates and nonlinear evolution depend largely on the dimensionless channel curvature κ=2αg′/f2, where 2α is the dimensional curvature, g′ is the reduced gravity, and f is the Coriolis parameter. Very small positive (or negative) values of κ correspond to dynamically wide channels and are associated with strong instability and the breakup of the basic flow into a train of eddies. For moderate or large values of κ, the instability widens the flow and increases its potential vorticity but does not destroy its character as a coherent stream. Ripa's condition for stability suggests a theory for the final width and potential vorticity that works moderately well. The observed and predicted growth in these quantities are minimal for κ≥1, suggesting that the zero-potential-vorticity approximation holds when the channel is narrower than a Rossby radius based on the initial maximum depth. The instability results from a resonant interaction between two waves trapped on opposite edges of the stream. Interactions can occur between two Kelvin-like frontal waves, between two inertia–gravity waves, or between one wave of each type. The growing disturbance has zero energy and extracts zero energy from the mean. At the same time, there is an overall conversion of kinetic energy to potential energy for κ>0, with the reverse occurring for κ<0. When it acts on a hydraulically controlled basic state, the instability tends to eliminate the band of counterflow that is predicted by hydraulic theory and that confounds hydraulic-based estimates of volume fluxes in the field. Eddy generation downstream of the controlling sill occurs if the downstream value of κ is sufficiently small.

scholarly journals Non-axisymmetric Instabilities in Shocked Accretion Flows

2003 ◽  
Vol 214 ◽  
pp. 95-96
Author(s):  
Wei-Min Gu ◽  
Thierry Foglizzo
Keyword(s):  
Black Hole ◽  
Numerical Integration ◽  
Recent Work ◽  
Growth Rates ◽  
Linearized Equations ◽  
X Ray ◽  
Accretion Flows ◽  
The Stability ◽  
X Ray Binaries ◽  
Axisymmetric Perturbations

We investigate the stability of shocked inviscid isothermal accretion flows onto a black hole. Of the two possible shock positions, the outer one is known to be stable to axisymmetric perturbations, while the inner one is unstable. Our recent work, however, shows that the outer shock is generally linearly unstable to non-axisymmetric perturbations. Eigenmodes and growth rates are obtained by numerical integration of the linearized equations. These results offer new perspectives to interpret the variability of X-ray binaries.

scholarly journals Instability Through Anisotropy in Spherical Stellar Systems

1987 ◽  
Vol 127 ◽  
pp. 515-516
Author(s):  
P.L. Palmer ◽  
J. Papaloizou
Keyword(s):  
Growth Rate ◽  
Eigenvalue Problem ◽  
Growth Rates ◽  
Stellar Systems ◽  
Matrix Eigenvalue Problem ◽  
Simple Method ◽  
Anisotropic Models ◽  
Poisson Equations ◽  
Degree Of Anisotropy ◽  
The Stability

We consider the linear stability of spherical stellar systems by solving the Vlasov and Poisson equations which yield a matrix eigenvalue problem to determine the growth rate. We consider this for purely growing modes in the limit of vanishing growth rate. We show that a large class of anisotropic models are unstable and derive growth rates for the particular example of generalized polytropic models. We present a simple method for testing the stability of general anisotropic models. Our anlysis shows that instability occurs even when the degree of anisotropy is very slight.

Resistive Ballooning Modes in Three-Dimensional Configurations

1982 ◽  
Vol 37 (8) ◽  
pp. 848-858 ◽  
Author(s):  
D. Correa-Restrepo
Keyword(s):  
Growth Rates ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Coupled System ◽  
Small Constant ◽  
Ballooning Mode ◽  
The Stability ◽  
The Magnetic Field ◽  
Symmetric Systems ◽  
The Ideal

Resistive ballooning modes in general three-dimensional configurations are studied on the basis of the equations of motion of resistive MHD. Assuming small, constant resistivity and perturbations localized transversally to the magnetic field, a stability criterion is derived in the form of a coupled system of two second-order differential equations. This criterion contains several limiting cases, in particular the ideal ballooning mode criterion and criteria for the stability of symmetric systems. Assuming small growth rates, analytical results are derived by multiple-length-scale expansion techniques. Instabilities are found, their growth rates scaling as fractional powers of the resistivity

The Stability and the Intrinsic Growth Rates of Prey and Predator Populations

Ecology ◽  
1975 ◽  
Vol 56 (4) ◽  
pp. 855-867 ◽  
Author(s):  
James T. Tanner
Keyword(s):  
Growth Rates ◽  
The Stability

Overstability of a Viscoelastic Fluid Layer Oscillating in a Vertical Periodic Motion and Heated From Below

1979 ◽  
Vol 46 (2) ◽  
pp. 454-456
Author(s):  
S. O. Onyegegbu
Keyword(s):  
Natural Frequency ◽  
Viscoelastic Fluid ◽  
Periodic Motion ◽  
Oscillation Frequency ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
The Stability ◽  
Oscillation Frequencies

This Note examines the effect of vertical periodic motion on the stability characteristics of a viscoelastic fluid layer in a classical Benard geometry. Numerical solutions show that a resonant type behavior which enhances stability occurs at oscillation frequencies near the convective natural frequency of the viscoelastic fluid, while the effect of the periodic motion vanishes as the oscillation frequency gets very large.

On Estimates for Growth Rates of Unstable Azimuthal Disturbances in the Stability Problem of Swirling Flows with Radius- Dependent Density

2017 ◽  
Vol 13 (3) ◽  
pp. 1-12
Author(s):  
Halle Dattu Malai Subbiah
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Stability Problem ◽  
Variable Density ◽  
Swirling Flows ◽  
Wave Number ◽  
Two Dimensional ◽  
Azimuthal Wave Number ◽  
The Stability ◽  
Dependent Density

Estimates for the growth rate of unstable two-dimensional disturbances to swirling flows with variable density are obtained and as a consequence it is proved that the growth rate tends to zero as the azimuthal wave number tends to infinity for two classes of basic flows.

MHD instabilities of a cylindrical plasma with a realistic energy equation

1987 ◽  
Vol 37 (2) ◽  
pp. 175-184 ◽  
Author(s):  
Guidetta Torricelli-Ciamponi ◽  
Vittorio Ciampolini ◽  
Claudio Chiuderi
Keyword(s):  
Magnetic Field ◽  
Time Scales ◽  
Growth Rates ◽  
Thermal Conduction ◽  
Energy Equation ◽  
Magnetized Plasma ◽  
Line Radiation ◽  
Mhd Instabilities ◽  
Solar Plasmas ◽  
The Stability

The influence of a realistic energy equation on the stability of a cylindrical magnetized plasma in a force-free magnetic field is discussed. Thermal conduction, heating and line radiation are included in the treatment. Explicit growth rates for the m = 0 and m = 1 modes are derived and compared with the standard adiabatic or incompressible time-scales. Finally, the relevance of these results for laboratory and solar plasmas is discussed.

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