MONOPOLE-CHARGE INSTABILITY

For monopoles with nonvanishing Higgs potential it is shown that with respect to “Brandt-Neri-Coleman type” variations (a) the stability problem reduces to that of a pure gauge theory on the 2-sphere (b) each topological sector admits one, and only one, stable monopole charge, and (c) each nonstable monopole admits 2∑2|q|−1 negative modes where the sum goes over all negative eigenvalues q of the non-Abelian charge Q. An explicit construction for (i) the unique stable charge (ii) the negative modes and (iii) the spectrum of the Hessian, on the 2-sphere, is then given. The relation to loops in the residual group is explained. The negative modes are tangent to suitable energy-reducing two-spheres. The general theory is illustrated for the little groups U (2), U (3), SU (3)/ℤ3 and O (5).

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Stability of Vlasov equilibria. Part 1. General theory

Journal of Plasma Physics ◽

10.1017/s0022377800026349 ◽

1982 ◽

Vol 27 (1) ◽

pp. 13-24 ◽

Cited By ~ 25

Author(s):

K. R. Symon ◽

C. E. Seyler ◽

H. R. Lewis

Keyword(s):

Distribution Function ◽

General Theory ◽

Linear Stability ◽

Vlasov Equation ◽

Stability Problem ◽

Dispersion Matrix ◽

Initial Value ◽

Spectral Matrix ◽

Concise Representation ◽

The Stability

We present a general formulation for treating the linear stability of inhomogeneous plasmas for which at least one species is described by the Vlasov equation. Use of Poisson bracket notation and expansion of the perturbation distribution function in terms of eigenfunctions of the unperturbed Liouville operator leads to a concise representation of the stability problem in terms of a symmetric dispersion functional. A dispersion matrix is derived which characterizes the solutions of the linearized initial-value problem. The dispersion matrix is then expressed in terms of a dynamic spectral matrix which characterizes the properties of the unperturbed orbits, in so far as they are relevant to the linear stability of the system.

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A non-abelian kink and its local stability

Revista Mexicana de Física ◽

10.31349/revmexfis.65.69 ◽

2018 ◽

Vol 65 (1) ◽

pp. 69

Author(s):

Rommel Guerrero ◽

Rafael Omar Rodriguez ◽

Rafael Alejandro Chavez

Keyword(s):

Scalar Field ◽

Fourth Order ◽

Local Stability ◽

Zero Mode ◽

Flat Space ◽

Adjoint Representation ◽

Higgs Potential ◽

Stability Of Solution ◽

Negative Eigenvalues ◽

The Stability

A non-abelian kink inducing asymptotically the breaking pattern $SU(5)\times Z_2\rightarrow SU(4)\times U(1)/Z_4$ is obtained. We consider a fourth order Higgs potential in a $1+1$ theory where the scalar field is in the adjoint representation of $SU(5)$. The perturbative stability of the kink also is evaluated. A Schr\"odinger-like equation for the excitations along each $SU(5)$ generator is determined and in none of the cases negative eigenvalues compromising the stability of solution are found. In particular, several bounded scalar states are determined among them the translational zero mode of the flat space $SU(5)\times Z_2$ kink.

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The two-dimensional hydrodynamical theory of moving aerofoils. IV

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1947.0019 ◽

1947 ◽

Vol 188 (1015) ◽

pp. 439-463

Keyword(s):

Stability Problem ◽

Two Dimensional ◽

Centre Of Gravity ◽

First Approximation ◽

Von Karman ◽

Moving Cylinder ◽

Period Equation ◽

The Stability ◽

Von Kármán ◽

Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

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Some Structural Properties of Systolic Tree Automata

Fundamenta Informaticae ◽

10.3233/fi-1989-12409 ◽

1989 ◽

Vol 12 (4) ◽

pp. 571-585

Author(s):

E. Fachini ◽

A. Maggiolo Schettini ◽

G. Resta ◽

D. Sangiorgi

Keyword(s):

Structural Properties ◽

Stability Problem ◽

Sufficient Condition ◽

Tree Automata ◽

Necessary And Sufficient Condition ◽

The Stability ◽

Necessary And Sufficient

We prove that the classes of languages accepted by systolic automata over t-ary trees (t-STA) are always either equal or incomparable if one varies t. We introduce systolic tree automata with base (T(b)-STA), a subclass of STA with interesting properties of modularity, and we give a necessary and sufficient condition for the equivalence between a T(b)-STA and a t-STA, for a given base b. Finally, we show that the stability problem for T(b)-ST A is decidible.

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Two-sided estimates in the stability problem for compressed elastic blocks

Mechanics of Solids ◽

10.3103/s0025654410010073 ◽

2010 ◽

Vol 45 (1) ◽

pp. 41-50

Author(s):

S. A. Panteleev

Keyword(s):

Stability Problem ◽

The Stability

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The stability problem for linear multistep methods: Old and new results

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2006.10.052 ◽

2007 ◽

Vol 210 (1-2) ◽

pp. 2-12 ◽

Cited By ~ 7

Author(s):

L. Aceto ◽

D. Trigiante

Keyword(s):

Stability Problem ◽

Multistep Methods ◽

Linear Multistep Methods ◽

The Stability

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A constructive method for the solution of the stability problem

Numerische Mathematik ◽

10.1007/bf02162400 ◽

1970 ◽

Vol 16 (1) ◽

pp. 1-7 ◽

Cited By ~ 10

Author(s):

James Lucien Howland ◽

John Albert Senez

Keyword(s):

Stability Problem ◽

Constructive Method ◽

The Stability

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Scaling behaviour of the deconfinement temperature for SU(2) pure gauge theory at finite temperature

Physics Letters B ◽

10.1016/0370-2693(85)91403-0 ◽

1985 ◽

Vol 151 (2) ◽

pp. 145-150 ◽

Cited By ~ 31

Author(s):

G. Curci ◽

R. Tripiccione

Keyword(s):

Gauge Theory ◽

Finite Temperature ◽

Pure Gauge ◽

Scaling Behaviour ◽

Pure Gauge Theory

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Design of Hydraulic Descaling Computer Control System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.608-609.19 ◽

2014 ◽

Vol 608-609 ◽

pp. 19-22

Author(s):

Ping Xu ◽

Jian Gang Yi

Keyword(s):

Control System ◽

Stability Problem ◽

Computer Control ◽

Control Methods ◽

Computer Control System ◽

Control Software ◽

Pressure Water ◽

Working Principle ◽

The Stability

Hydraulic descaling system is the key device to ensure the surface quality of billet. However, traditional control methods lead to the stability problem in hydraulic descaling system. To solve the problem, the construction of the hydraulic descaling computer control system is studied, the working principle of the system is analyzed, and the high pressure water bench of hydraulic descaling is designed. Based on it, the corresponding computer control software is developed. The application shows that the designed system is stable in practice, which is helpful for enterprise production.

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