This paper investigates two different temporal finite element techniques, a multiple element (h-version) and single element (p-version) method, to analyze the stability of a system with a time-periodic coefficient and a time delay. The representative problem, known as the delayed damped Mathieu equation, is chosen to illustrate the combined effect of a time delay and parametric excitation on st...

We demonstrate that magnetic oscillations of a current-biased magnetic nanocontact can be parametrically excited by a microwave field applied at twice the resonant frequency of the oscillation. The threshold microwave amplitude for the onset of the oscillation decreases with increasing bias current, and vanishes at the transition to the auto-oscillation regime. Theoretical analysis shows that m...

In this paper we investigate a parametric resonance phenomenon of a Kaluza-Klein mode in a D-dimensional generalized Kaluza-Klein theory. As the origin of the parametric resonance we consider a small oscillation of a scale of the compactification around a today’s value of it. To make our arguments definite and for simplicity we consider two classes of models of the compactification: those by Sd...

This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupole mass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for bo...

It is a rule of thumb that time delay tends to destabilize any dynamical system. This is not true, however, in the case of delayed oscillators, which serve as mechanical models for several surprising physical phenomena. Parametric excitation of oscillatory systems also exhibits stability properties sometimes defying our physical sense. The combination of the two effects leads to challenging tas...

We propose and analyze a scheme for parametrically cooling bilayer cuprates based on the selective driving of a c-axis vibrational mode. The scheme exploits the vibration as a transducer making the Josephson plasma frequencies time dependent. We show how modulation at the difference frequency between the intrabilayer and interbilayer plasmon substantially suppresses interbilayer phase fluctuati...

This paper involves the dynamics of a delay limit cycle oscillator being driven by a time-varying perturbation in the delay: _ x 1⁄4 x t TðtÞ ð Þ εx3 with delay TðtÞ 1⁄4 2þεkþε cos ωt. This delay is chosen to periodically cross the stability boundary for the x1⁄40 equilibrium in the constant-delay system. For most of parameter space, the system is non-resonant, leading to quasiperiodic behavior...

We calculated Eq. (4) by using the Runge-Kutta method. The attractors obtained by the simulations are shown in Fig. 3(a). We can confirm the generation of periodic and chaotic attractors. In order to investigate the attractors in van der Pol oscillator under noisy parametric excitation in detail, we consider the Poincaré map. The result of the Poincaré map are shown in Fig. 3(b). We can see tha...