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.

Asymmetric spike patterns for the one-dimensional Gierer–Meinhardt model: equilibria and stability

2002 ◽  
Vol 13 (3) ◽  
pp. 283-320 ◽  
Author(s):  
M. J. WARD ◽  
J. WEI
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Solutions ◽  
Equilibrium Solutions ◽  
Matrix Eigenvalue Problem ◽  
One Dimensional ◽  
Matrix Eigenvalue ◽  
The Stability ◽  
The One ◽  
Spike Patterns ◽  
Small Eigenvalues

Equilibrium solutions to the one-dimensional Gierer–Meinhardt model in the form of sequences of spikes of different heights are constructed asymptotically in the limit of small activator diffusivity ε. For a pattern with k spikes, the construction yields k1 spikes that have a common small amplitude and k2 = k− k1 spikes that have a common large amplitude. A k- spike asymmetric equilibrium solution is obtained from an arbitrary ordering of the small and large spikes on the domain. It is shown that such solutions exist when the inhibitor diffusivity D is less than some critical value Dm that depends upon k1, on k2, and on other parameters associated with the Gierer–Meinhardt model. It is also shown that these asymmetric k-spike solutions bifurcate from the symmetric solution branch sk, for which k spikes have equal height. These asymmetric solutions provide connections between the branch sk and the other symmetric branches sj , for j = 1,…, k− 1. The stability of the asymmetric k-spike patterns with respect to the large O(1) eigenvalues and the small O(ε2) eigenvalues is also analyzed. It is found that the asymmetric patterns are stable with respect to the large O(1) eigenvalues when D > De, where De depends on k1 and k2, on certain parameters in the model, and on the specific ordering of the small and large spikes within a given k-spike sequence. Numerical values for De are obtained from numerical solutions of a matrix eigenvalue problem. Another matrix eigenvalue problem that determines the small eigenvalues is derived. For the examples considered, it is shown that the bifurcating asymmetric branches are all unstable with respect to these small eigenvalues.

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.

A Practical Application to Calculating Corrosion Growth Rates by Comparing Successive ILI Runs From Different ILI Vendors

2010 ◽  
Author(s):  
Kevin Spencer ◽  
Shahani Kariyawasam ◽  
Cathy Tetreault ◽  
Jon Wharf
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Management Program ◽  
Management Decision ◽  
Pipeline System ◽  
Data Sets ◽  
Simple Method ◽  
Integrity Management ◽  
Inspection Data ◽  
Over Time

Corrosion growth rates are an essential input into an Integrity Management Program but they can often be the largest source of uncertainty and error. A relatively simple method to estimate a corrosion growth rate is to compare the size of a corrosion anomaly over time and the most practical way to do this for a whole pipeline system is via the use of In-Line Inspection (ILI). However, the reported depth of the anomaly following an ILI run contains measurement uncertainties, i.e., sizing tolerances that must be accounted for in defining the uncertainty, or error associated with the measured corrosion growth rate. When the same inspection vendor performs the inspections then proven methods exist that enable this growth error to be significantly reduced but these methods include the use of raw inspection data and, specialist software and analysis. Guidelines presently exist to estimate corrosion growth rates using inspection data from different ILI vendors. Although well documented, they are often only applicable to “simple” cases, pipelines containing isolated corrosion features with low feature density counts. As the feature density or the corrosion complexity increases then different reporting specifications, interaction rules, analysis procedures, sizing models, etc can become difficult to account for, ultimately leading to incorrect estimations or larger uncertainties regarding the growth error. This paper will address these issues through the experiences of a North American pipeline operator. Accurately quantifying the reliability of pipeline assets over time requires accurate corrosion growth rates and the case study will demonstrate how the growth error was significantly reduced over existing methodologies. Historical excavation and recoat information was utilized to identify static defects and quantify systemic bias between inspections. To reduce differences in reporting and the analyst interpretation of the recorded magnetic signals, novel analysis techniques were employed to normalize the data sets against each other. The resulting uncertainty of the corrosion growth rates was then further reduced by deriving, and applying a regression model to reduce the effect of the different sizing models and the identified systemic bias. The reduced uncertainty ultimately led to a better understanding of the corrosion activity on the pipeline and facilitated a better integrity management decision process.

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).

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 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).

The Stability of Swirling Jets

1989 ◽  
Vol 8 (1) ◽  
pp. 38-40 ◽  
Author(s):  
Colin S. Coleman
Keyword(s):  
Growth Rate ◽  
Eigenvalue Problem ◽  
Normal Mode Analysis ◽  
Axial Flow ◽  
Mode Analysis ◽  
Small Component ◽  
Swirling Jets ◽  
Axisymmetric Mode ◽  
Negative Helicity ◽  
The Stability

AbstractThe stability of a swirling cylindrical jet of compressible fluid is examined by performing a normal mode analysis and numerically solving the eigenvalue problem. Perturbations of the form f(r)exp[i(ωt-mϕ-kz)] are considered, where f is any fluid variable. Instabilities which are characteristic of both a non-swirling (top-hat) jet and a Rankine vortex are investigated for a particular axial wavenumber.The vortex instabilities are weak, and are found to remain weak when axial flow is present. The jet instabilities are much stronger, but axial flow is a stabilizing influence. The positive helicity (km > 0) non-axisymmetric modes (m ≠ 0) are stabilized by a small component of azimuthal flow. The axisymmetric mode (m = 0) and the negative helicity non-axisymmetric modes persist in rapidly swirling jets, but with a greatly reduced growth rate.

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.

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