The aim of this paper is to give a result concerning the instability properties of the solutions of forced magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are highly oscillating spatially on the scale of the underlying flow but are growing on a larger scale depending on the magnetic Reynolds number. The existence of such solutions is called α-effect in the p...

Under the influences of stable density stratification and Earth’s rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamics— sometimes called the slow manifold—in the sense that there are diagnostic hydrostatic and gradient-wind momentum balances that constrain the fluid acceleration. The nonlinear Balance Equations are a widely successful, approximate model for th...

The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nyström (RKN) methods with varying step sizes is investigated. Perturbation methods are used to quantify the critical step sizes associated with parametric instability. It is shown that there is no parametric instability for linear constant coefficient ODEs integrated with ...

A set of simple low-dimensional diierential equations representing a chain of coupled oscillators is suggested as a model for explaining the instability of a rigidly rotating spiral wave that has been observed in spatially discrete and continuous models. Bifurcation to an invariant circle on a torus appears to be the mechanism responsible for this instability in the discrete case and is thus in...

the natural frequency and pull-in instability of clamped-clamped nano-actuators in the presence of a dielectric layer are analyzed. the influence of the presence of casimir force, electrostatic force, fringing field effect, axial force, stretching effects and the size effect are taken into account. the governing equation of the dynamic response of the actuator is transformed in a non-dimensiona...

Modulation equations play an essential rote in the understanding of complicated systems near the threshold of instability. For scalar parabolic equations for which instability occurs at nonzero wavelength, we show that the associated GinzburgLandau equation dominates the dynamics of the nonlinear problem locally, at least over a long timescale. We develop a method which is simpler than previous...