Dynamical parametric instability of carbon nanotubes under axial harmonic excitation by nonlocal continuum theory

Structures under parametric load can be induced to the parametric instability in which the excitation frequency is located the instability region. In the present work, the parametric instability of double-walled carbon nanotubes is studied. The axial harmonic excitation is considered and the nonlocal continuum theory is applied. The critical equation is derived as the Mathieu form by the Galerkin's theory and the instability condition is presented with the Bolotin's method. Numerical calculations are performed and it can be seen that the van der Waals interaction can enhance the stability of double-walled nanotubes under the parametric excitation. The parametric instability becomes more obvious with the matrix stiffness decreasing and small scale coefficient increasing. The parametric instability is going to be more significant for higher mode numbers. For the nanosystem with the soft matrix and higher mode number, the small scale coefficient and the ratio of the length to the diameter have obvious influences on the starting point of the instability region.     

Suppression and feedback control of anomalous induced backscattering by pump-frequency modulation

The possibility of induced backscattering parametric decay instability resonant suppression by harmonic pump-frequency modulation is demonstrated experimentally. It is shown that the pump anomalous reflection is strongly reduced at the modulation frequency equal to the difference of the decay instability eigenfrequencies. The parametric instability feedback control method is proposed based on this effect.     

Parametric instability of a magnetic junction under modulated spin-polarized current

The stability is analyzed of the magnetic junction collinear configurations against small fluctuations under amplitude-modulated current with current-perpendicular-to-plane mode. High spin injection is assumed. Under parametric resonance conditions, with the modulation frequency twice the precession frequency, instability is possible of one, or another, or both the collinear configurations. When the direct component of the current density exceeds the instability threshold of the antiparallel configuration, the parametric instability is suppressed by nonparametric one which is induced by the direct current. The parametric instability manifests itself as lowering the threshold of the direct current density in the presence of the high-frequency current; such an effect has been observed in experiments repeatedly.     

Parametric instability of a cantilever beam subjected to two electromagnetic excitations: Experiments and analytical validation

An electromagnetic device, acting like a spring with alternating stiffness, has been designed to parametrically excite the cantilever beam. However, only one parametric excitation (induced by one electromagnetic device) was considered in current research, and the effects of the design parameters of the device upon the instability were studied inadequately. Actually, multiple parametric excitations with various phases and amplitudes would bring significant impacts to the system instability. The electromagnetic device with various design parameters could cause the unstable regions to change evidently. Thus, the parametric instability of a cantilever beam subjected to two electromagnetic excitations is studied experimentally and analytically in the paper. The governing equations for the beam system are established utilizing the assumed mode method, and then verified through a DC current test. Based upon these, the instability experiments for the cantilever beam with one or two electromagnetic excitations are conducted in detail. Two design parameters of the device (magnet spacing and device location) are investigated, respectively, for their effects upon the instability regions. When two electromagnetic devices operate together to bring two parametric stiffness excitations with various phases and amplitudes to the cantilever beam, the variations of both simple and combination instability regions with coil current are observed and discussed. The above experimental results are all found to agree well with the analytical ones.     

Effects of three-body interactions in the parametric and modulational instabilities of Bose-Einstein condensates

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic-quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated.     

On the ponderomotive force and the effect of loss reaction on parametric instability

In this paper, the growth rate, ponderomotive force and the exciting condition for parametric instability are derived by considering the loss reaction using a new method. On the basis of the hydrodynamic equations, we take the production and loss reactions in plasma into account to derive the coupling equations for the electron plasma oscillation and ion acoustic oscillation, and obtain the growth rate for the parametric instability, the ponderomotive force and the exciting condition. The result shows that (a) the production reaction has no effect on the parametric instability, and the effect of loss reaction on the parametric instability is a damping one, (b) the more intensive the external field or pump is, the larger the growth rate is, (c) there exist two modes of the ponderomotive force, i.e.\ the high frequency mode and the low frequency mode, and (d) when ponderomotive force counteracts the damping force, the oscillations become non-damping and non-driving. The ratio of the electron plasma oscillation to ion acoustic oscillation is independent of the loss reaction and the external field.     

Numerical Modeling of the Process of Parametric Generation of the Cyclotron Radiation in a Reactive Medium

We present the results of numerical modeling of the effect of amplification of coherent bichromatic radiation due to its cyclotron parametric interaction with a modulated ensemble of electrons in the absence of partial synchronism of waves and particles. The numerical results agree with the analytical conclusions. We find that under certain conditions, the developing parametric instability is accompanied by “driving” of the wave frequencies to the resonance with the particles, which results in significant “peaking” of the instability.     

离子束-等离子体系统中的参量不稳定性

本文研究了外pump电场E_0在离子束-等离子体系统中所激发的静电低频参量不稳定性。导出了这种低频波的一般色散关系,并用数值方法分析了一维质子束-等离子体系统的参量不稳定性的激发过程。结果表明:离子束对等离子体中参量不稳定性的激发有极重要的影响。当没有离子束时,只能激发一种模式的波;一旦将离子束引入等离子体中,就可以在系统中激发两个波长较长的低频波。     

Analytical investigation on unstable vibrations of single-mesh gear systems with velocity-modulated time-varying stiffness

Time-varying mesh stiffness parametrically excites gear systems and causes severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and more complex instabilities might arise. Considering two different speed fluctuation models, parametric instability associated with velocity-modulated time-varying stiffness is analytically investigated using a typical single-mesh gear system model. Closed-form approximations are obtained by perturbation analysis, and verified by numerical analysis. The effects of the amplitude of the mesh stiffness variation, the characteristics of speed fluctuations and damping on parametric instability are systematically examined.     

PLANETARY GEAR PARAMETRIC INSTABILITY CAUSED BY MESH STIFFNESS VARIATION

Parametric instability is investigated for planetary gears where fluctuating stiffness results from the changing contact conditions at the multiple tooth meshes. The time-varying mesh stiffnesses of the sun-planet and ring-planet meshes are modelled as rectangular waveforms with different contact ratios and mesh phasing. The operating conditions leading to parametric instability are analytically identified. Using the well-defined properties of planetary gear vibration modes, the boundaries separating stable and unstable conditions are obtained as simple expressions in terms of mesh parameters. These expressions allow one to suppress particular instabilities by adjusting the contact ratios and mesh phasing. Tooth separation from parametric instability is numerically simulated to show the strong impact of this non-linearity on the response.     

Cyclotron mechanism of free-electron lasing without inversion

We consider one of the “paradoxical” effects of the theory of radiation and matter interaction: stimulated emission in the absence of inversion. The theory of simultaneous inversionless emission of two high-frequency waves due to their parametric interaction with ensemble of free electrons in magnetic field is developed. The analytical investigation and numerical simulation of the most interesting scheme of this two-photon interaction are presented. New effects are revealed; namely they are self-induced parametric instability of sufficiently strong waves and enhanced parametric instability in sufficiently dense electron medium.     

Observation of a backward ion-cyclotron wave parametrically excited by a modulated electron beam

The lower-hybrid parametric resonant decay instability (decay into electrostatic lower-hybrid waves and backward ioncyclotron waves) driven by a modulated electron beam is investigated experimentally. Plasma heating and the possibility of wave-enhanced particle loss associated with this instability are discussed.     

Numerical calculations of elastic modes frequencies for parametric oscillatory instability in Advanced LIGO interferometer

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors of Advanced LIGO to enable precise predictions of the problem of parametric oscillatory instability. We propose accuracy estimations through use of analytical solutions based on Chree-Lamb modes. Small deviations from cylindrical test mass shape may produce splitting of non-axial symmetric elastic modes into doublets. This splitting may increase the possibility of parametric oscillatory instability.     

50 dB parametric on-chip gain in silicon photonic wires

A pulsed mid-infrared pump at λ=2173 nm is used to demonstrate wideband optical parametric gain in a low-loss 2 cm long silicon photonic wire. Using dispersion engineering to obtain negative second-order (β2) and positive fourth-order (β4) dispersion, we generate broadband modulation instability and parametric fluorescence extending from 1911 nm-2486 nm. Using a cw probe signal to interrogate the modulation instability spectrum, we demonstrate parametric amplification >40 dB with an on-chip gain bandwidth wider than 580 nm, as well as narrowband Raman-assisted peak gain >50 dB.     

Parametric instability of dust lattice waves in a turbulent plasma sheath

It is shown that dust lattice waves (DLWs) become parametrically unstable in a turbulent dusty plasma sheath that contains random-phase ion plasma waves. Physically, the parametric instability arises because of the nonlinear coupling between ion plasma waves and DLWs. The parametric instability is identified as the possible reason for the observed "sublimation" transition of the plasma crystal from a solid to a gaslike state.     

Instability of the motion of a beam of periodically varying length

The parametric instability of the motion of a cantilever beam of periodically varying length is investigated. The boundaries of the instability regions are found and plotted.     

Instability of a periodically moving plate

The parametric instability of the in-plane motion of a rectangular plate of periodically varying length is investigated. The boundaries of the instability regions are found and plotted.     

Four-magnon decay of magnetostatic surface waves in yttrium iron garnet films

The four-magnon instability of magnetostatic surface waves (MSSWs) in yttrium iron garnet epitaxial films is investigated experimentally. It is shown that four-magnon instability for MSSWs with wave numbers 30–600 cm⁻¹ is a decay instability and develops for values of the wave magnetization close to the threshold level for second-order parametric instability of a homogeneous transverse pump wave. When the supercriticality of the MSSW power is 15–20 dB, the generated parametric spin waves themselves become unstable with respect to the four-magnon interaction, so that kinetic instability develops in the film. It is shown that the pump signal transmitted through the signal and the length of the “nonlinear” part of the film, where a MSSW is capable of exciting parametric spin waves, increase as the pump power is increased. Fiz. Tverd. Tela (St. Petersburg) 38, 330–338 (February 1997)     

The effect of a laser beam displacement on parametric oscillatory instabilities for Advanced LIGO

The arm cavities of real gravitational wave detectors can show small deviations like a tilt or a spatial shift between the cavity mirrors. These deviations lead to a separation of the optical mode centres with respect to the mirror?s centre. In this Letter we perform the computation of parametric instable modes considering the described displacement. We further analyse the possibility of parametric oscillatory instability in the Advanced LIGO interferometer for the case of a displaced arm cavity. Our results reveal an additional number of optical and elastic mode combinations due to a displacement that can give rise to the undesirable effect of parametric oscillatory instability.     

Stability in parametric resonance of axially accelerating beams constituted by Boltzmann's superposition principle

Stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated. The governing equation is derived from Newton's second law, Boltzmann's superposition principle, and the geometrical relation. When the axial speed is a constant mean speed with small harmonic variations, the governing equation can be treated as a continuous gyroscopic system with small periodically parametric excitations and a damping term. The method of multiple scales is applied directly to the governing equation without discretization. The stability conditions are obtained for combination and principal parametric resonance. Numerical examples demonstrate that the increase of the viscosity coefficient causes the lager instability threshold of speed fluctuation amplitude for given detuning parameter and smaller instability range of the detuning parameter for given speed fluctuation amplitude. The instability region is much bigger in lower order principal resonance than that in the higher order.