scholarly journals Damped perturbations in stellar systems: Genuine modes and Landau-damped waves

2021 ◽  
Author(s):  
E V Polyachenko ◽  
I G Shukhman ◽  
O I Borodina
Keyword(s):  
Initial Perturbation ◽  
Stability Study ◽  
Landau Damping ◽  
Complex Conjugate ◽  
Stellar Systems ◽  
Initial Value ◽  
Set Up ◽  
The Stability ◽  
The Waves ◽  
Problem Versus

Abstract This research was stimulated by the recent studies of damping solutions in dynamically stable spherical stellar systems. Using the simplest model of the homogeneous stellar medium, we discuss nontrivial features of stellar systems. Taking them into account will make it possible to correctly interpret the results obtained earlier and will help to set up decisive numerical experiments in the future. In particular, we compare the initial value problem versus the eigenvalue problem. It turns out that in the unstable regime, the Landau-damped waves can be represented as a superposition of van Kampen modes plus a discrete damped mode, usually ignored in the stability study. This mode is a solution complex conjugate to the unstable Jeans mode. In contrast, the Landau-damped waves are not genuine modes: in modes, eigenfunctions depend on time as exp ( − iωt), while the waves do not have eigenfunctions on the real v-axis at all. However, ‘eigenfunctions’ on the complex v-contours do exist. Deviations from the Landau damping are common and can be due to singularities or cut-off of the initial perturbation above some fixed value in the velocity space.

The Loess Slope Stability Study

2013 ◽  
Vol 380-384 ◽  
pp. 4827-4829 ◽  
Author(s):  
Shi Qiang Xu ◽  
Tao Zhao
Keyword(s):  
Slope Stability ◽  
Stability Study ◽  
Circular Arc ◽  
Highway Engineering ◽  
Loess Slope ◽  
Stability Of Slope ◽  
Set Up ◽  
The Stability

We often use circular arc method when calculating the stability of the slope. But this kind of method ignores how the slope rate of top influences stability of slope. In this thesis, a destruction model of loess slope is set up to study the regular rule of how the slope rate of top influences stability of slope, which will have great guiding significance in the construction of slopes in highway engineering.

scholarly journals Galloping Stability and Wind Tunnel Test of Iced Quad Bundled Conductors considering Wake Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xiaohui Liu ◽  
Ming Zou ◽  
Chuan Wu ◽  
Mengqi Cai ◽  
Guangyun Min ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Transmission Lines ◽  
Degrees Of Freedom ◽  
Wind Tunnel Test ◽  
Aerodynamic Coefficients ◽  
Wake Effect ◽  
Aerodynamic Coefficient ◽  
Set Up ◽  
The Stability ◽  
Three Degrees Of Freedom

A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines.

Study on the working state of the five hundred-meter aperture spherical telescope using step-wise assignment method

2014 ◽  
Vol 229 (2) ◽  
pp. 316-324 ◽  
Author(s):  
Yu Liu ◽  
Feng Gao
Keyword(s):  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Driving Mechanism ◽  
Initial Value ◽  
Unknown Parameters ◽  
Support Structure ◽  
Assignment Method ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model

The working state of the five hundred-meter aperture spherical telescope (FAST) is solved using the step-wise assignment method. In this paper, the mathematical model of the cable-net support structure of the FAST is set up by the catenary equation. There are a large number of nonlinear equations and unknown parameters of the model. The nonlinear equations are solved by using the step-wise assignment method. The method is using the analytical solutions of the cable-net equations of one working state as the initial value for the next working state, from which the analytical solutions of the nonlinear equations of the cable-net for each working state of the FAST and the tension and length of each driving cable can be obtained. The suggested algorithm is quite practically well suited to study the working state of the cable-net structures of the FAST. Also, the working state analysis result of the cable-net support structure of a reduced model of the cable-net structure reflector for the FAST is given to verify the reliability of the method. In order to show the validity of the method, comparisons with another algorithm to set the initial value are presented. This method has an important guiding significance to the further study on the control of the new type of flexible cable driving mechanism, especially the FAST.

The Mitigation of the French Nuclear Option: New Industrial Realism and Technical Democracy

2002 ◽  
Vol 13 (2) ◽  
pp. 263-279 ◽  
Author(s):  
Dominique Finon
Keyword(s):  
Waste Management ◽  
Electricity Markets ◽  
Social Preferences ◽  
Public Inquiry ◽  
The Future ◽  
Parliamentary Committee ◽  
Set Up ◽  
The Stability ◽  
The Cost ◽  
Phase Out

Nuclear phase-out policies and the European obligation to liberalise electricity markets could put the French nuclear option dramatically at risk by influencing social preferences or by constraining power producers' investment choices in the future. So far, the particular institutional set-up which has allowed the efficient build-up and operation of several series of standardised reactors preserves the stability of the main elements of the option. However, important adaptations to the evolving industrial and political environment occur and contribute to changing the option. Some institutional changes (such as local public inquiry, creation of a Parliamentary committee, independence of safety authorities) and divergence between industrial interests already allow debates on internal options such as reprocessing, type of waste management deposits, ordering of an advanced PWR. These changes improve the cost transparency, even if internalisation of nuclear externalities (cost of insurance, provisions for waste management) is still incomplete. However, when effective, this internalisation would not affect definitively the competitive position of the nuclear production because of the parallel internalisation of CO2 externalities from fossil fuel power generation in the official rationale. Consequently the real issue for the future of the nuclear option in France remains the preservation of social acceptability in the perception of nuclear risks.

scholarly journals Analysis of the interaction of thermoacoustic modes with a Green’s function approach

2018 ◽  
Vol 10 (4) ◽  
pp. 326-336 ◽  
Author(s):  
Alessandra Bigongiari ◽  
Maria Heckl
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Initial Perturbation ◽  
Time History ◽  
Function Approach ◽  
Stability Maps ◽  
Flame Describing Function ◽  
The Stability ◽  
Dynamics Simulations ◽  
Fast Prediction

In this paper, we will present a fast prediction tool based on a one-dimensional Green's function approach that can be used to bypass numerically expensive computational fluid dynamics simulations. The Green’s function approach has the advantage of providing a clear picture of the physics behind the generation and evolution of combustion instabilities. In addition, the method allows us to perform a modal analysis; single acoustic modes can be treated in isolation or in combination with other modes. In this article, we will investigate the role of higher-order modes in determining the stability of the system. We will initially produce the stability maps for the first and second mode separately. Then the time history of the perturbation will be computed, where both the modes are present. The flame will be modelled by a generic Flame Describing Function, i.e. by an amplitude-dependent Flame Transfer Function. The time-history calculations show the evolution of the two modes resulting from an initial perturbation; both transient and limit-cycle oscillations are revealed. Our study represents a first step towards the modelling of nonlinearity and non-normality in combustion processes.

scholarly journals Glacial lake drainage: a stability analysis

1997 ◽  
Vol 24 ◽  
pp. 175-180
Author(s):  
Krzysztof Szilder ◽  
Edward P. Lozowski ◽  
Martin J. Sharp
Keyword(s):  
Differential Equations ◽  
Water Flow ◽  
Frictional Heating ◽  
Initial Perturbation ◽  
Tunnel Wall ◽  
Cross Sectional ◽  
Linear Ordinary Differential Equations ◽  
Simplifying Assumptions ◽  
Lake Drainage ◽  
The Stability

A model has been formulated to determine the stability regimes for water flow in a Subglacial conduit draining from a reservoir. The physics of the water flow is described with a set of differential equations expressing conservation of mass, momentum and energy. Non-steady flow of water in the conduit is considered, the conduit being simultaneously enlarged by frictional heating and compressed by plastic deformation in response to the pressure difference across the tunnel wall. With the aid of simplifying assumptions, a mathematical model has been constructed from two time-dependent, non-linear, ordinary differential equations, which describe the time evolution of the conduit cross-sectional area and the water depth in the reservoir. The model has been used to study the influence of conduit area and reservoir levels on the stability of the water flow for various glacier and ice-sheet configurations. The region of the parameter space where the system can achieve equilibrium has been identified. However, in the majority of cases the equilibrium is unstable, and an initial perturbation from equilibrium may lead to a catastrophic outburst of water which empties the reservoir.

scholarly journals A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

1971 ◽  
Vol 13 (5) ◽  
pp. 330-343 ◽  
Author(s):  
D. F. Sheldon
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Recent Experience ◽  
Wind Tunnel Testing ◽  
Stability Derivatives ◽  
Direct Indication ◽  
Metric Dimensions ◽  
Set Up ◽  
The Stability ◽  
Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

The stability of elastico-viscous flow between rotating cylinders Part 3. Overstability in viscous and Maxwell fluids

1966 ◽  
Vol 24 (2) ◽  
pp. 321-334 ◽  
Author(s):  
D. W. Beard ◽  
M. H. Davies ◽  
K. Walters
Keyword(s):  
Viscous Flow ◽  
Couette Flow ◽  
Taylor Number ◽  
Linear Perturbation ◽  
Rotating Cylinders ◽  
Initial Value ◽  
Viscous Liquids ◽  
Maxwell Fluids ◽  
Newtonian Liquids ◽  
The Stability

Consideration is given to the possibility of overstability in the Couette flow of viscous and elastico-viscous liquids. The relevant linear perturbation equations are solved numerically using an initial-value technique. It is shown that over-stability is not possible in the case of Newtonian liquids for the cases considered. In contrast, overstability is to be expected in the case of moderately-elastic Maxwell liquids. The Taylor number associated with the overstable mode decreases steadily as the amount of elasticity in the liquid increases, and it is concluded that highly elastic Maxwell liquids can be very unstable indeed.

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