The physics of a locked magnetic island chain maintained in the pedestal of an H-mode tokamak plasma by a static, externally generated, multi-harmonic, helical magnetic perturbation is investigated. The non-resonant harmonics of the external perturbation are assumed to give rise to significant toroidal flow damping in the pedestal, in addition to the naturally occurring poloidal flow damping. F...

The physics of a locked magnetic island chain maintained in the pedestal of an H-mode tokamak plasma by a static, externally generated, multi-harmonic, helical magnetic perturbation is investigated. The non-resonant harmonics of the external perturbation are assumed to give rise to significant toroidal flow damping in the pedestal, in addition to the naturally occurring poloidal flow damping. F...

‎The controlled harmonic oscillator with retarded damping‎, ‎is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems‎. ‎In this paper‎, ‎to solve this problem‎, ‎we presented an analytical method‎. ‎This approach is based on the homotopy perturbation method‎. ‎The solution procedure becomes easier‎, ‎simpler and mor...

Generalized stability theory is applied to a simple dynamical model of interannual ocean–atmosphere variability in the southern midlatitudes to determine the perturbations that create the most rapid growth of energy in the system. The model is composed of a barotropic quasigeostrophic atmosphere coupled to a 1.5-layer quasigeostrophic ocean, each linearized about a zonally invariant mean state,...

The present article investigates effects of the multi-frequency excitation on the output power of a piezomagnetoelastic energy harvester. The piezomagnetoelastic power generator is assumed to operate in the mono-stable mode. A perturbation technique based on the method of multiple scales is employed to develop an analytical solution to nonlinear differential equations governing the system dynam...

Synoptic eddy–mean flow interaction has been recognized as one of the key sources for extratropical lowfrequency variability. In this paper, the underlying dynamics of this interaction are examined from the perspective of a synoptic eddy-induced dynamic instability. To delineate this instability, a barotropic model is used that is linearized with respect to a stochastic basic flow prescribed wi...

In forced two-dimensional turbulence on a rotating sphere, it is well known that a multiple zonal-band structure, i.e. a structure with alternating eastward and westward jets, emerges in the course of time development. The multiple zonal-band structure then experiences intermittent mergers and disappearances of zonal jets, and a structure with only a few large-scale zonal jets is realised as an...

In this paper we will study the 2D-harmonic oscillator in 1:1 resonance. We add a general thirdand fourth order perturbation which is slowly time-dependent, and are interested in the resulting interaction between the unperturbed orbits (states). By treating this system quantummechanically we get a linear system (Schrödinger’s equation) on the infinite dimensional space . We show that this syste...

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense-Thirring effect with a new Earth’s artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally pr...

Coupling effects of Earth oblateness and direct solar radiation pressure on the motion of an artificial satellite are evaluated. Secular and periodic terms are retained up to order three and two respectively, where the coefficient 2 J of the second zonal harmonic of the geopotential is considered of first order. The solution revealed the existence of secular terms at order three that arises fro...