Nonlinear Evolution of the m = n = 1 Kink-Mode in a Periodic z-Pinch

1987 ◽  
Vol 42 (10) ◽  
pp. 1225-1236 ◽  
Author(s):  
K. A. Kratzsch ◽  
E. Rebhan
Keyword(s):  
Aspect Ratio ◽  
General Theory ◽  
Safety Factor ◽  
Nonlinear Evolution ◽  
Stability Boundary ◽  
Kink Mode ◽  
Ideal Mhd ◽  
Z Pinch ◽  
Special Case ◽  
Mode Stabilization

A previously developed general theory for the nonlinear evolution of external ideal MHD modes is applied to the special case of the m = n = 1 kink-mode in z-pinch equilibria with constant profile of the safety factor q. The Kruskal-Shafranov stability boundary q = - 1 eludes application of this theory since the kink-mode degenerates there. At the second stability boundary of the mode, stabilization as well as destabilization become possible depending on which values of the aspect ratio and the distance of a stabilizing wall are given.

Influence of aspect ratio, plasma viscosity, and radial position of the resonant surfaces on the plasmoid formation in the low resistivity plasma in Tokamak

2021 ◽  
Author(s):  
Wei Zhang ◽  
Zhiwei Ma ◽  
Haowei Zhang ◽  
Wen Jin CHEN ◽  
Xin Wang
Keyword(s):  
Aspect Ratio ◽  
Mode Coupling ◽  
Nonlinear Evolution ◽  
Plasma Viscosity ◽  
Cylindrical Geometry ◽  
Radial Position ◽  
Radial Location ◽  
Low Resistivity ◽  
Kink Mode ◽  
Strong Mode

Abstract In the present paper, we systematically investigate the nonlinear evolution of the resistive kink mode in the low resistivity plasma in Tokamak geometry. We find that the aspect ratio of the initial equilibrium can significantly influence the critical resistivity for plasmoid formation. With the aspect ratio of 3/1, the critical resistivity can be one magnitude larger than that in cylindrical geometry due to the strong mode-mode coupling. We also find that the critical resistivity for plasmoid formation decreases with increasing plasma viscosity in the moderately low resistivity regime. Due to the geometry of Tokamaks, the critical resistivity for plasmoid formation increases with the increasing radial location of the resonant surface.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Hypo-elasticity and plasticity

1956 ◽  
Vol 234 (1196) ◽  
pp. 46-59 ◽  
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Work Hardening ◽  
Strain Curve ◽  
Simple Extension ◽  
Logarithmic Strain ◽  
Elasticity Equations ◽  
Plastic Materials ◽  
Special Case

A general theory of work-hardening incompressible plastic materials is developed as a special case of Truesdell’s theory of hypo-elasticity. Equations are given in general coordinates for a single loading followed by one unloading, and attention is directed to materials for which the stress-logarithmic strain curve for unloading in simple extension is linear. Using a particular case of the corresponding constitutive equations for loading, which is a generalization of that suggested by Prager, applications are made to a number of specific problems.

The behaviour of supersonic flow past a body of revolution, far from the axis

1950 ◽  
Vol 201 (1064) ◽  
pp. 89-109 ◽  
Keyword(s):  
Supersonic Flow ◽  
General Theory ◽  
Body Of Revolution ◽  
Flow Past ◽  
Physical Importance ◽  
Special Case ◽  
Pointed Body ◽  
Asymptotic Forms

A theory is developed of the supersonic flow past a body of revolution at large distances from the axis, where a linearized approximation is valueless owing to the divergence of the characteristics at infinity. It is used to find the asymptotic forms of the equations of the shocks which are formed from the neighbourhoods of the nose and tail. In the special case of a slender pointed body, the general theory at large distances is used to modify the linearized approximation to give a theory which is uniformly valid at all distances from the axis. The results which are of physical importance are summarized in the conclusion (§ 9) and compared with the results of experimental observations.

scholarly journals The Steady Profile of an Axisymmetric Ice Sheet

1981 ◽  
Vol 27 (95) ◽  
pp. 25-37 ◽  
Author(s):  
I. R. Johnson
Keyword(s):  
Aspect Ratio ◽  
Power Law ◽  
Viscous Incompressible Fluid ◽  
Ice Sheet ◽  
Plane Flow ◽  
The Third ◽  
Basal Sliding ◽  
Steady Plane ◽  
Third Dimension ◽  
Special Case

AbstractSteady plane flow under gravity of an axisymmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding is treated according to a power law between shear traction and velocity. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, and temperature variation through the ice sheet is neglected. Illustrations are presented for Glen’s power law (including the special case of a Newtonian fluid), and the polynomial law of Colbeck and Evans. The analysis follows that of Morland and Johnson (1980) where the analogous problem for an ice sheet deforming under plane flow was considered. Comparisons are made between the two models and it is found that the effect of the third dimension is to reduce (or leave unchanged) the aspect ratio for the cases considered, although no general formula can be obtained. This reduction is seen to depend on both the surface accumulation and the sliding law.

Nonlinear Evolution of External Ideal MHD Modes Near the Boundary of Marginal Stability

1984 ◽  
Vol 39 (3) ◽  
pp. 288-308
Author(s):  
E. Rebhan
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Evolution ◽  
Nonlinear Boundary Conditions ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Marginal Stability ◽  
Amplitude Equations ◽  
Full Generality ◽  
Ideal Mhd ◽  
Higher Order Corrections

AbstractThe nonlinear evolution of external ideal MHD-modes is determined from the equations of ideal MHD by employing a reductive perturbation method which uses a driving parameter for expansion. The reduction of the plasma equations is the same as for internal modes and was treated previously [1]. A main problem arising in addition for external modes is the reduction of the nonlinear boundary conditions. The set of reduced boundary conditions is obtained on the undisplaced boundary in the marginally stable equilibrium position. Another additional problem arises from the fact that the linear MHD operator is only selfadjoint for linear eigenmodes but not for the higher order mode corrections. This complicates the determination of nonlinear amplitude equations for the marginal mode which are obtained from solubility conditions. The amplitude equations are qualitatively the same as for internal modes. Quantitatively, the calculation of the coefficients in these is different. Explicit expressions for the coefficients are derived in full generality. The effect of higher order corrections to the nonlinear amplitude equations is discussed quantitatively for one of two possible cases and qualitatively for the other.

scholarly journals Congruences induced by transitive representations of inverse semigroups

1987 ◽  
Vol 29 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Mario Petrich ◽  
Stuart Rankin
Keyword(s):  
General Theory ◽  
Inverse Semigroup ◽  
Symmetric Group ◽  
Transitive Group ◽  
Inverse Semigroups ◽  
Group Representations ◽  
Symmetric Inverse Semigroup ◽  
The Right ◽  
Special Case

Transitive group representations have their analogue for inverse semigroups as discovered by Schein [7]. The right cosets in the group case find their counterpart in the right ω-cosets and the symmetric inverse semigroup plays the role of the symmetric group. The general theory developed by Schein admits a special case discovered independently by Ponizovskiǐ [4] and Reilly [5]. For a discussion of this topic, see [1, §7.3] and [2, Chapter IV].

What Walrasian Marxism Can and Cannot Do

1992 ◽  
Vol 8 (1) ◽  
pp. 149-156 ◽  
Author(s):  
John Roemer
Keyword(s):  
General Theory ◽  
Technological Change ◽  
Scientific Method ◽  
Class Formation ◽  
Perfect Competition ◽  
Real Thing ◽  
The Real ◽  
Labor Power ◽  
Special Case ◽  
Method Strip

In their article “Roemer's ‘General’ Theory of Exploitation is a Special Case: The Limits of Walrasian Marxism,” Devine and Dymski portray me as some sort of Walrasian automaton who believes that phenomena that are not easily modelled using the Walrasian model of perfect competition do not exist. Their criticism of my theory assumes that I was attempting to model capitalism in its entirety, a task that, I agree, I failed to do. I did not propose a theory of accumulation, or of technological change, or of the methods by which capitalists maintain their ideological hegemony over workers, or of the methods by which they extract labor from labor power at the point of production. I was not, in short, trying to write an alternative to Das Kapital. My General Theory of Exploitation and Class (GTEC), as its Introduction explained, was an attempt at understanding the root causes of exploitation and class, so as to better understand how class formation and exploitation might occur in postcapitalist societies. To this end, I adopted a well-known scientific method: strip away many real aspects of the thing under study down to a minimal skeleton and see how many phenomena descriptive of the real thing one can generate. Then add more real aspects of the thing to the model, and see how much more one can generate.

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