In this short note we consider wave equations with a periodic in time dissipation and discuss the effect of parametric resonance in the framework of energy estimates. The approach is based on a treatment for a generalized Mathieu equation related to the periodic dissipation term.

Abstract In this paper we examine the stability of stellar configurations in which interior solution is described by a closed Friedmann-Lemaître-Robertson-Walker (FLRW) geometry sourced with charged pressureless fluid and radiation. An interacting vacuum component conformally coupled massive scalar field are also included. Given simple factor for energy transfer between obtain bounded oscillato...

The parametric resonance of the axial vibrations of a cantilever pipe conveying harmonically perturbed two-phase flow is investigated using the method of multiple scale perturbation. The nonlinear coupled and uncoupled planar dynamics of the pipe are examined for a scenario when the axial vibration is parametrically excited by the pulsating frequencies of the two phases conveyed by the pipe. Aw...

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...

We consider a simple mesoscopic model of DNA in which the binding of the RNA polymerase enzyme molecule to the promoter sequence of the DNA is included through a substrate energy term modeling the enzymatic interaction with the DNA strands. We focus on the differential system for solitary waves and derive conditions--in terms of the model parameters--for the occurrence of the parametric resonan...

A finite-field optical magnetometer is demonstrated that suppresses spin-exchange collisions by dressing the atoms in a sequence of transverse AC-coupled 2π pulses. In the limit of short pulses, the attainable transverse polarization is unity. On resonance, the dressing field cancels the DC magnetic field, further suppressing spinexchange relaxation as compared to light-narrowed magnetometers. ...

Neutrino oscillations in matter can exhibit a specific resonance enhancement – parametric resonance, which is different from the MSW resonance. Oscillations of atmospheric and solar neutrinos inside the earth can undergo parametric enhancement when neutrino trajectories cross the core of the earth. In this paper we review the parametric resonance of neutrino oscillations in matter. In particula...