We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the superconducting quantum interference device (SQUID) attached to the cavity and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric thresh...

In this paper 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...

We present the first study of parametric resonance in quantum field theory from a complete next-to-leading order calculation in a 1/N expansion of the two-particle irreducible effective action, which includes scattering and memory effects. We present a complete numerical solution for an O(N)-symmetric scalar theory and provide an approximate analytic description of the nonlinear dynamics in the...

Time-periodic shear flows can give rise to Parametric Instability (PI), as in the case of the Mathieu equation (Stoker, 1950; Nayfeh and Mook, 1995). This mechanism results from a resonance between the oscillatory basic state and waves that are superimposed on it. Farrell and Ioannou (1996a, b) explain that PI occurs because the snapshots of the velocity profile are subject to transient growth....

We demonstrate that energy can be transferred very rapidly from the bulk to the brane through parametric resonance. In a simple realization, we consider a massless bulk field that interacts only with fields localized on the brane. We assume an initial field configuration that has the form of a wave-packet moving towards the brane. During the reflection of the wave-packet by the brane the locali...

Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson-junction circuit. In contrast to most optical systems, a significant part of emitted radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation. To quantify the correlations...

We consider a solution of the atmospheric neutrino problem based on oscillations of muon neutrinos to sterile neutrinos: νμ ↔ νs. The zenith angle (Θ) dependences of the neutrino and upward-going muon fluxes in presence of these oscillations are studied. The dependences have characteristic form with two dips: at cosΘ = −0.6÷−0.2 and cosΘ = −1.0÷−0.8. The latter dip is due to parametric resonanc...

In this paper, we propose an improved principal component analysis based on maximum entropy (MaxEnt) preservation, called MaxEnt-PCA, which is derived from a Parzen window estimation of Renyi’s quadratic entropy. Instead of minimizing the reconstruction error either based on L2-norm or L1-norm, the MaxEnt-PCA attempts to preserve as much as possible the uncertainty information of the data measu...

Low bit rate parametric coding of multichannel audio is mainly based on Binaural Cue Coding (BCC). Another multichannel audio processing method called upmix can also be used to deliver multichannel audio, typically 5.1 signals, at low data rates. More precisely, we focus on existing upmix method based on Principal Component Analysis (PCA). This PCA-based upmix method aims at blindly create a re...

We study preheating in DBI hybrid inflation. Preheating occurs since the matter fields are non-minimally coupled to the inflaton. Despite the coupling being small, preheating happens as a narrow parametric resonance in which matter fields and inflaton modes are exponentially created. We show that, within the approximations used, the process is very efficient at late times. The resonance stage g...