MHD Stability for a Class of Tokamak Equilibria with Fixed Boundaries

1978 ◽  
Vol 33 (7) ◽  
pp. 792-798
Author(s):  
W. Kerner
Keyword(s):  
Stability Analysis ◽  
Normal Mode ◽  
Cross Sections ◽  
Stability Limit ◽  
Stability Behavior ◽  
Mhd Stability ◽  
The Stability ◽  
High Beta ◽  
Fixed Boundaries ◽  
Flat Current

The stability behavior with respect to internal modes is discussed for a class of tokamak equilibria with non-circular cross-sections and essentially flat current profiles. The stability analysis is done by computer both symbolically and numerically with the help of a normal mode code, which extremizes the Lagrangian of the system . It is found that the stability limit agrees well with that of the Mercier criterion. There are stable high-beta equilibria in this model.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Stability Analysis of Plate-Cone Reticulated Shell

2011 ◽  
Vol 71-78 ◽  
pp. 3760-3763
Author(s):  
Xing Wang
Keyword(s):  
Stability Analysis ◽  
Bearing Capacity ◽  
Double Layer ◽  
Geometrical Nonlinearity ◽  
Ultimate Bearing Capacity ◽  
Arc Length ◽  
Stability Behavior ◽  
Destruction Mechanism ◽  
The Stability ◽  
Complete Process

This paper carries out stability analysis on plate-cone reticulated shell considering geometrical nonlinearity of cooperating work between plates and members. In this paper, stability behavior of different kinds of plate-cone reticulated shell considering geometrical nonlinearity is analyzed by using the software ANSYS, tracking complete process balance path for load-displacement by using arc-length method, the several problems of plate-cone reticulated shell are studied, such as destruction mechanism, structural ductility, ultimate bearing capacity and strength reserve, some important conclusions are obtained. After analyzing the stability behavior of double-layer reticulated shell by ANSYS and comparing with plate-cone reticulated shell, it is proved that plate-cone reticulated shell is more advantageous than double-layer reticulated shell in the aspect of stability behavior.

Dynamic and Stability Analysis of the Rotating Nanobeam in a Nonuniform Magnetic Field Considering the Surface Energy

2016 ◽  
Vol 08 (04) ◽  
pp. 1650048 ◽  
Author(s):  
M. Baghani ◽  
M. Mohammadi ◽  
A. Farajpour
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Angular Velocity ◽  
Surface Energy ◽  
Axial Load ◽  
Nonuniform Magnetic Field ◽  
Small Scale ◽  
Stability Behavior ◽  
Compressive Axial Load ◽  
The Stability

It is well-known that rotating nanobeams can have different dynamic and stability responses to various types of loadings. In this research, attention is focused on studying the effects of magnetic field, surface energy and compressive axial load on the dynamic and the stability behavior of the nanobeam. For this purpose, it is assumed that the rotating nanobeam is located in the nonuniform magnetic field and subjected to compressive axial load. The nonlocal elasticity theory and the Gurtin–Murdoch model are applied to consider the effects of inter atomic forces and surface energy effect on the vibration behavior of rotating nanobeam. The vibration frequencies and critical buckling loads of the nanobeam are computed by the differential quadrature method (DQM). Then, the numerical results are testified with those results are presented in the published works and a good correlation is obtained. Finally, the effects of angular velocity, magnetic field, boundary conditions, compressive axial load, small scale parameter and surface elastic constants on the dynamic and the stability behavior of the nanobeam are studied. The results show that the magnetic field, surface energy and the angular velocity have important roles in the dynamic and stability analysis of the nanobeams.

A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction

2011 ◽  
Vol 10 (2) ◽  
pp. 279-304 ◽  
Author(s):  
J. W. Banks ◽  
B. Sjögreen
Keyword(s):  
Stability Analysis ◽  
Normal Mode ◽  
Compressible Fluid ◽  
Elastic Solid ◽  
Interface Condition ◽  
Finite Difference Schemes ◽  
Interface Conditions ◽  
Characteristic Boundary ◽  
Mode Stability ◽  
The Stability

AbstractIn multi physics computations where a compressible fluid is coupled with a linearly elastic solid, it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid. In a numerical scheme, there are many ways that velocity- and stress-continuity can be enforced in the discrete approximation. This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes. The analysis shows that depending on the ratio of densities between the solid and the fluid, some numerical interface conditions are stable up to the maximal CFL-limit, while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit. The paper also presents a new interface condition, obtained as a simplified characteristic boundary condition, that is proved to not suffer from any reduction of the stable CFL-limit. Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.

Study on Design of Tunnel Section for Danba Diversion Tunnel

2014 ◽  
Vol 501-504 ◽  
pp. 1732-1735
Author(s):  
Jie Liu ◽  
Liang Tang ◽  
Ya Zuo ◽  
Jin Long Guo
Keyword(s):  
Stability Analysis ◽  
Plastic Zone ◽  
Cross Sections ◽  
Surrounding Rock ◽  
Hydropower Station ◽  
Diversion Tunnel ◽  
Rock Stability ◽  
Tunnel Section ◽  
Tunnel Design ◽  
The Stability

Analyzing and Evaluating the stability of the surrounding rock is an indispensable and important part in the tunnel design. In this paper, the surrounding rock stability of Danba hydropower station diversion tunnel is dealt with, FLAC3Dsoftware is used for stability analysis. Selecting three different cross sections for calculation models, comparing with the displacement and principal stress and the plastic zone which calculated by FLAC3D, we can evaluate their stability and get the best diversion tunnel design.

Convective instability in liquid pools heated from below

1971 ◽  
Vol 47 (4) ◽  
pp. 779-787 ◽  
Author(s):  
Harvey J. Palmer ◽  
John C. Berg
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Stability Analysis ◽  
Convective Instability ◽  
Temperature Drop ◽  
Stability Limit ◽  
Liquid Pool ◽  
Silicone Oils ◽  
Liquid Pools ◽  
The Stability

The linear hydrodynamic stability analysis of liquid pools heated from below combining surface tension and buoyancy effects as presented by Nield (1964) is confirmed by experiment for a series of silicone oils. The experimental method used is an adaptation of the Schmidt–Milverton technique, in which the stability limit is located by the change of slope in the plot of heat flux versus temperature drop across the liquid pool.

The Stability Analysis of Nantong Coal Mine Waste Dump, Chongqing and Prevention Measures

2012 ◽  
Vol 204-208 ◽  
pp. 3526-3531 ◽  
Author(s):  
Xin Tao Zhao ◽  
Xin Chun Gao ◽  
Dong Sheng Li
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Cross Sections ◽  
Coal Mine ◽  
Mine Waste ◽  
Prevention Measures ◽  
Waste Dump ◽  
Coal Mine Waste ◽  
Mine Waste Dump ◽  
The Stability

Coal mine waste dump often occur landslide and collapse disasters, the prevention measures and stability analysis of the waste dump must be studied.Firstly,the major factors that can cause landslide in Nantong coal mine waste dump,Chongqing were analyzed,secondly,the stability of four geological cross sections were analyzed by the limiting equilibrium method and FLAC numerical simulation method,the conclusions from two methods are same,and the conclusion is the safety factors of cross sections A and C are smallest and landslide and debris flow disasters will occur easily when face with a long heavy rainfall.thirdly, according to the main factors that can cause waste dump landslide easily and combine with the analysis results of limit equilibrium method and discrete element numerical simulation seven prevention measures were proposed, these measures can provide references for similar waste dump.

MHD stability analysis of high- beta JET discharges

1992 ◽  
Vol 34 (4) ◽  
pp. 487-499 ◽  
Author(s):  
G T A Huysmans ◽  
T C Hender ◽  
O J Kwon ◽  
J P Goedbloed ◽  
E Lazzaro ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Mhd Stability ◽  
High Beta
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