For nearly a decade it has been known that coherent processes at the end of inflation can drive explosive particle production [1] via parametric resonance, leading to an era of preheating in the post-inflationary universe. Earlier assumptions about the transfer of energy from the inflaton to “regular” matter have been overturned, and the phenomenology of the post-inflationary universe is thus m...

We present a mathematical model for the dynamics of an electrostatically actuated micro-cantilever. For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular, illustrate that parametric r...

We present a mathematical model for the dynamics of an electrostatically actuated microcantilever. For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular, illustrate that parametric re...

Recently, there have been studies of parametric resonance decay of oscillating real homogeneous cosmological scalar fields, in both the narrow-band and broad-band case, primarily within the context of inflaton decay and (p)reheating. However, many realistic models of particle cosmology, such as supersymmetric ones, inherently involve complex scalar fields. In the oscillations of complex scalars...

The phenomenon of parametric resonance is explained and investigated both analytically and with the help of a computer simulation. Parametric excitation is studied for the example of the rotary oscillations of a simple linear system— mechanical torsion spring pendulum excited by periodic variations of its moment of inertia. Conditions and characteristics of parametric resonance and regeneration...

Subspace method identification (SMI) and model reduction for Multivariate Statistical Process Control has been proposed as an improvement to dynamic principal component analysis (DPCA). The linear parametric model structure captures both static and dynamic information from the system. In this paper, an analysis of the dimension reduction capabilities of the subspace approach is provided. It is ...

Coexistence The special case when all the independent solutions of a linear, T -periodic ODE are T -periodic. Hill’s equation A second order ODE of the form ẍ + p(t)x = 0, with p(t) T -periodic. Instability pockets Finite domains, usually intersections of instability tongues, where the trivial solution of linear, T -periodic ODEs is unstable. Instability tongues Domains in parameter space where...

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...

A mass sensing concept based on parametric resonance amplification is proposed and experimentally investigated using a non-interdigitated comb-finger driven micro-oscillator. Mass change can be detected by measuring frequency shift at the boundary of the first order parametric resonance ‘tongue’. Both platinum deposition using focused ion beam (FIB) and water vapor desorption and absorption are...

In inflationary cosmology, the particles constituting the Universe are created after inflation in the process of reheating due to the interaction with the oscillating inflaton field. We briefly review the basics of the slow reheating, and the stage of fast preheating, when the particles are created explosively in the regime of parametric resonance. The non-perturbative, out-of-equilibrium chara...