Numerical parameter study of stability against resistive axisymmetric modes for doublets

1978 ◽  
Vol 20 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Torkil H. Jensen ◽  
F. W. McClain
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Vertical Direction ◽  
Parameter Study ◽  
Numerical Parameter ◽  
Numerical Examples ◽  
Conducting Wall ◽  
The Stability ◽  
The Many

Stability and growth rates of resistive axisymmetric modes for doublets have been studied numerically. Because of the many parameters entering the problem this study has the form of a survey of features that are believed to be most important for stability. In general it is found that the most dangerous mode is one that either elongates or contracts the plasma in the vertical direction. Stability, and in the case of instability, the growth rate, depends on the proximity of a conducting wall surrounding the plasma. Numerical examples of this are given both for cases of a rectangular wall shape and an indented wall shape. Examples are also given that indicate the sensitivity to parameters characterizing the equilibrium. Finally, an example is given for the case of a wall with a finite resistivity. It is shown that such a wall does not affect the stability, but decreases the growth rate relative to a case where the wall is absent.

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.

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.

Feedback stabilization of tokamaks against slow axisymmetric MHD instabilities

1981 ◽  
Vol 26 (2) ◽  
pp. 351-357 ◽  
Author(s):  
Torkil H. Jensen
Keyword(s):  
Growth Rate ◽  
Control System ◽  
Stability Analysis ◽  
Vacuum Chamber ◽  
Feedback Stabilization ◽  
Wall Material ◽  
Growth Time ◽  
Conducting Wall ◽  
Mhd Instabilities ◽  
The Stability

Single axis tokamaks as well as doublets may be unstable toward axisymmetric MHD instabilities. Such instabilities may, for the case of a single-axis tokamak, be slow when the plasma is surrounded by a relatively close fitting conducting wall, such as a vacuum chamber; the growth rate may be proportional to the resistivity of the wall material. For the case of doublets, slowly growing instabilities with growth rates proportional to the plasma resistivity exist. Such slow instabilities can be stabilized by feedback control of the currents through coils surrounding the plasma; since it is only required that the amplifiers used in the circuits respond fast compared with the growth time of the slow instabilities, this feedback stabilization is not technologically demanding. This paper describes a formalism for the stability analysis of such a system consisting of the plasma, surrounded by a conducting wall or vacuum chamber and coils with their control system.

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

2018 ◽  
Author(s):  
Cody S. Dowd ◽  
Joseph W. Meadows
Keyword(s):  
Growth Rate ◽  
Porous Media ◽  
Stability Analysis ◽  
Frequency Shift ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Growth Rates ◽  
Thermoacoustic Instability ◽  
The Stability ◽  
The Impact

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties, and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a 1-D model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function. By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Cody S. Dowd ◽  
Joseph W. Meadows
Keyword(s):  
Growth Rate ◽  
Porous Media ◽  
Stability Analysis ◽  
Frequency Shift ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Growth Rates ◽  
Thermoacoustic Instability ◽  
The Stability ◽  
The Impact

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a one-dimensional (1D) model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function (FTF). By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

scholarly journals Effects of Homeopathic Preparations of Mercurius corrosivus on the Growth Rate of Severely Mercury-Stressed Duckweed Lemna gibba L.

Homeopathy ◽  
2019 ◽  
Vol 108 (02) ◽  
pp. 128-138 ◽  
Author(s):  
Tim Jäger ◽  
Sandra Würtenberger ◽  
Stephan Baumgartner
Keyword(s):  
Growth Rate ◽  
Stress Intensity ◽  
Growth Rates ◽  
Statistical Power ◽  
Test System ◽  
Lemna Gibba ◽  
Image Analysis System ◽  
Water Control ◽  
Time Period ◽  
The Stability

Background We developed a bioassay with mercury-stressed duckweed (Lemna gibba L.) to study potential effects of homeopathically potentised mercury(II) chloride (Mercurius corrosivus [Merc-c.]). The response of this bioassay to homeopathic treatments as a function of stress intensity was also of interest. Methods Duckweed was severely stressed with mercury(II) chloride for 48 hours. Afterwards plants grew in either Merc-c. (seven different potency levels, 24x to 30x) or water controls (unsuccussed and succussed water) for 7 days. Growth rates of the frond (leaf) area were determined using a computerised image analysis system for different time intervals between the measurements on days 0, 3 and 7. Three independent experiments with potentised Merc-c. each were evaluated. Additionally, three water control experiments were analysed to investigate the stability of the experimental set-up (systematic negative control [SNC] experiments). All experiments were randomised and blinded. Results Unsuccussed and succussed water did not significantly differ in terms of duckweed growth rate. The SNC experiments did not yield any significant effects, providing evidence for the stability of the experimental system. Data from the two control groups and the seven treatment groups (Merc-c. 24x–30x) were each pooled to increase the statistical power. Duckweed growth rates for day 0 to 3 were reduced (p < 0.05) after application of Merc-c. compared with the controls. Growth rates for day 3 to 7 were not influenced by the homeopathic preparations. Conclusions The present test system with Lemna gibba L. that was severely stressed by mercury yielded evidence for specific effects of Merc-c. 24x to 30x, namely a growth reduction in the first time period (day 0–3). This is in contrast to former experiments with slightly arsenic-stressed duckweed, where a growth increase was observed in the second time period (day 2–6). We hypothesise that the differing results are associated with the level of stress intensity (severe versus slight).

scholarly journals Stability of three-dimensional Gaussian vortices in an unbounded, rotating, vertically stratified, Boussinesq flow: linear analysis

2017 ◽  
Vol 824 ◽  
pp. 97-134 ◽  
Author(s):  
Mani Mahdinia ◽  
Pedram Hassanzadeh ◽  
Philip S. Marcus ◽  
Chung-Hsiang Jiang
Keyword(s):  
Growth Rate ◽  
Parameter Space ◽  
Accretion Disks ◽  
Growth Rates ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Small Region ◽  
Giant Planets ◽  
Ocean Eddies ◽  
The Stability

The linear stability of three-dimensional vortices in rotating, stratified flows has been studied by analysing the non-hydrostatic inviscid Boussinesq equations. We have focused on a widely used model of geophysical and astrophysical vortices, which assumes an axisymmetric Gaussian structure for pressure anomalies in the horizontal and vertical directions. For a range of Rossby numbers ($-0.5<Ro<0.5$) and Burger numbers ($0.02<Bu<2.3$) relevant to observed long-lived vortices, the growth rate and spatial structure of the most unstable eigenmodes have been numerically calculated and presented as a function of $Ro{-}Bu$. We have found neutrally stable vortices only over a small region of the $Ro{-}Bu$ parameter space: cyclones with $Ro\sim 0.02{-}0.05$ and $Bu\sim 0.85{-}0.95$. However, we have also found that anticyclones in general have slower growth rates compared to cyclones. In particular, the growth rate of the most unstable eigenmode for anticyclones in a large region of the parameter space (e.g. $Ro<0$ and $0.5\lesssim Bu\lesssim 1.3$) is slower than 50 turnaround times of the vortex (which often corresponds to several years for ocean eddies). For cyclones, the region with such slow growth rates is confined to $0<Ro<0.1$ and $0.5\lesssim Bu\lesssim 1.3$. While most calculations have been done for $f/\bar{N}=0.1$ (where $f$ and $\bar{N}$ are the Coriolis and background Brunt–Väisälä frequencies), we have numerically verified and explained analytically, using non-dimensionalized equations, the insensitivity of the results to reducing $f/\bar{N}$ to the more ocean-relevant value of 0.01. The results of our stability analysis of Gaussian vortices both support and contradict the findings of earlier studies with QG or multilayer models or with other families of vortices. The results of this paper provide a stepping stone to study the more complicated problems of the stability of geophysical (e.g. those in the atmospheres of giant planets) and astrophysical vortices (in accretion disks).

Longevity of oversized individuals: growth, parasitism, and history in an estuarine snail population

2000 ◽  
Vol 80 (5) ◽  
pp. 811-820 ◽  
Author(s):  
Lawrence A. Curtis ◽  
Jeffrey L. Kinley ◽  
Nathan L. Tanner
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Life Cycles ◽  
Snail Population ◽  
Ilyanassa Obsoleta ◽  
Large Size ◽  
The Stability ◽  
Habitat History ◽  
Trematode Infections

Ilyanassa obsoleta is mainly an eastern North American estuarine gastropod. Previous work on growth rate revealed a longevity of 30–40 y for this snail. Trematode infections retard growth, appear to be long-lived ([ges ]10 y) and can be frequent in this host. In 1995 a population made up of unusually large, trematode-parasitized individuals was located in Rehoboth Bay, Delaware. It was interesting to discover whether the oversized snails were the result of locally faster growth or greater age. Therefore in 1996 individually marked snails, uninfected and infected, were deployed to assess growth rates. Uninfected snails were tracked mostly in summer and autumn 1996; infected snails could be tracked longer, some through autumn 1999. Estimated growth rates of uninfected (1.5 mm y−1) and infected (0.2 mm y−1) snails in this habitat were similar to previous results and the large size of individuals in this population must be explained by greater age. Habitat history and growth rate evidence indicate the population includes snails as old as about 70 y. If correct, this becomes the greatest documented snail longevity. Trematodes gain long-term reproduction by their association with this host. By virtue of the enduring effects of long-lived individuals, and the wider potential effects of their long-lived infections (on the snails themselves and on other hosts in their life cycles), I. obsoleta stands to contribute more to the stability of coastal ecosystems than heretofore recognized.

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.

Comparison of copper sulphate pentahydrate growth rates determined by different methods

1990 ◽  
Vol 55 (7) ◽  
pp. 1691-1707 ◽  
Author(s):  
Miloslav Karel ◽  
Jiří Hostomský ◽  
Jaroslav Nývlt ◽  
Axel König
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Fluidized Bed ◽  
Growth Rates ◽  
Copper Sulphate ◽  
Crystal Growth Rate ◽  
Effect Of Temperature ◽  
Rotating Disc ◽  
Shape Factors ◽  
Data Treatment

Crystal growth rates of copper sulphate pentahydrate (CuSO4.5 H2O) determined by different authors and methods are compared. The methods included in this comparison are: (i) Measurement on a fixed crystal suspended in a streaming solution, (ii) measurement on a rotating disc, (iii) measurement in a fluidized bed, (iv) measurement in an agitated suspension. The comparison involves critical estimation of the supersaturation used in measurements, of shape factors used for data treatment and a correction for the effect of temperature. Conclusions are drawn for the choice of values to be specified when data of crystal growth rate measurements are published.

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