The gravitational wave equations form a parametric resonance system during oscillatory reheating after inflation, when cast in terms of the electric and magnetic parts of the Weyl tensor. This is in direct analogy with preheating. For chaotic inflation with a quadratic potential, this analogy is exact. The resulting amplification of the gravitational wave spectrum begins in the broad resonance ...

We propose a mode of dynamic scanning probe microscopy based on parametric resonance for highly sensitive nanoscale imaging and force spectroscopy. In this mode the microcantilever probe is excited by means of a closed-loop electronic circuit that modulates the microcantilever stiffness at a frequency close to twice its natural resonance frequency. Under ambient conditions this parametric pumpi...

1. ABSTRACT Novel mass sensors based on parametric resonance can achieve high sensitivity because of the sharp transition from zero to large response. Unlike harmonic resonance based mass sensors, the sensitivity of this novel class of sensors will not be affected by damping. However, the presence of nonlinearity in the spring and electrostatic force of the oscillator significantly change the b...

The variation of the perturbative 3-curvature parameter, ζ, is investigated in the period of reheating after inflation. The two-field model used has the inflaton, with an extra scalar field coupled to it, and non-linear effects of both fields are included as well as a slow decay mechanism into the hydrodynamic fluid of the radiation era. Changes in ζ occur and persist into the succeeding cosmic...

Two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated. The transport speed is assumed to be a constant mean speed with small harmonic variations. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton’s second law. The method of multiple scales...

Straight elastically supported beams of variable width under the action of a periodic axial force are considered. Two shape optimization problems for reducing parametric resonance zones are studied. In the first problem, the range of resonant frequencies is minimized for a given parametric resonance zone and a fixed amplitude of excitation. In the second problem, the minimal (critical) amplitud...

Parametric resonance underpins the physics of swings, resonant surface waves, and particle traps. There is increasing interest in its potential applications in atomic force microscopy AFM . In this paper, the dynamics of parametrically resonant microcantilevers for high sensitivity imaging and force spectroscopy applications is investigated theoretically. Detailed numerical parametric-resonance...

This work studies the practicality of using finite-time Lyapunov exponents (FTLEs) to detect the inception of parametric resonance for vessels operating in irregular longitudinal seas. Parametrically excited roll motion is modelled as a single degree-of-freedom system, with nonlinear damping and restoring terms. FTLEs are numerically calculated at every integration time step. Using this numeric...

In this paper, we experimentally demonstrate non-degenerate parametric resonance in a torsional micro electro mechanical (MEM) oscillator with two interacting mechanical modes of oscillation. The parametric oscillation results from a displacement-dependent electrostatic force generated in both the modes of oscillation. There is a decoupling of the input and the output frequencies in this mode o...

We study parametric resonance of interacting waves having the same wave vector and frequency. In addition to the well-known period-doubling instability we show that under certain conditions the instability is caused by a Hopf bifurcation leading to quasiperiodic traveling waves. It occurs, for example, if the group velocities of both waves have different signs and the damping is weak. The dynam...