Interaction of electromagnetic oscillations with charged particle flows in nonuniform plasma-like structures

A hydrodynamic theory is developed of the interaction of electromagnetic oscillations with a monoenergetic charged particle beam propagating through a structure consisting of plasma and dielectric layers bounded by perfectly conducting planes. It is shown that, in such a system, plasma oscillations are excited due to the transformation of space charge oscillations of the particle flow into plasma oscillations at the layer boundaries. The regions of generation and decay of plasma oscillations are determined.     

Neutrinos in electromagnetic fields and moving media

The history of the development of the theory of neutrino-flavor and neutrino-spin oscillations in electromagnetic fields and in a medium is briefly surveyed. A new Lorentz-invariant approach to describing neutrino oscillations in a medium is formulated in such a way that it makes it possible to consider the motion of a medium at an arbitrary velocity, including relativistic ones. This approach permits studying neutrinospin oscillations under the effect of an arbitrary external electromagnetic field. In particular, it is predicted that, in the field of an electromagnetic wave, new resonances may exist in neutrino oscillations. In the case of spin oscillations in various electromagnetic fields, the concept of a critical magnetic-field-component strength is introduced above which the oscillations become sizable. In considering neutrino oscillations in moving matter, it is shown within the Lorentz-invariant formalism that the relativistic motion of matter significantly affects the character of neutrino oscillations and can radically change the conditions under which the oscillations are resonantly enhanced. Possible new effects in neutrino oscillations are discussed for the case of neutrino propagation in relativistic fluxes of matter.     

Chaotic oscillations in a coupled system of bistable oscillators

The influence of the asymmetry of the nonlinear element characteristic on the chaotic oscillations of Chua’s bistable oscillator is studied. It is shown that such asymmetry causes asymmetry of a chaotic attractor that maps the switching of motions between two basins of attraction up to the concentration of oscillations in one basin. Oscillation control in a bistable chaotic self-oscillating system (two coupled Chua’s oscillators) is considered. It is demonstrated that oscillations excited in two basins of attraction may pass to one of them and that oscillations may build up in two basins when they are autonomously excited in different basins. It is also found that chaotic oscillations in a coupled system may be excited at parameter values for which the autonomous chaotic oscillations of partial oscillators are absent. The influence of external noiselike oscillations is investigated.     

Space charge dynamics in a semiconductor superlattice affected by titled magnetic field and heating

The transition between different modes of current oscillations in a semiconductor superlattice, from close-to-harmonic (near the generation onset) to relaxation oscillations, has been investigated. The transition type is shown to change with an increase in temperature. A period-doubling bifurcation is observed at low temperatures. With an increase in temperature, the period-doubling bifurcation is observed at increasingly larger values of the voltage across the superlattice. The doubling bifurcation ceases to be observed at voltages at which the generation of oscillations of the current through the semiconductor superlattice is suppressed.     

Deformation of a fresh-water ice cover due to the capillary oscillations of underlying water

Full-scale measurements indicate that the frequencies of ice bending oscillations fall mostly into the range of 1–5 Hz. However, rarely bending oscillations may take place at about 13 Hz. Such oscillations are viewed as an intermediate between the ice bending oscillations and capillary wave oscillations on water. It is found theoretically that frequency f of the ice bending oscillations and interfacial tension coefficient α at the water-ice interface obey the relationship f ～ α^?1/4. The proportionality factor omitted here depends on the physical properties of water and ice. Putting f = 13 Hz, we, substituting the respective known quantities into this relationship, find that interfacial tension coefficient α equals α = 3.3 N/m. Thus, the interfacial tension coefficient at the water-ice interface can be estimated in this way.     

NON-LINEAR BEAM OSCILLATIONS EXCITED BY LATERAL FORCE AT COMBINATION RESONANCE

Non-linear oscillations of a beam subjected to a periodic force at a combination resonance are considered. Using the Galerkin method, a partial differential equation of oscillations is reduced to a system of ordinary differential equations with a small parameter. A system of three autonomous differential equations is derived, the multiple scales method being used. Qualitative properties of trajectories are analyzed. The Naimark-Sacker bifurcations at the combination resonance are analyzed by the center manifold method. Almost-periodic oscillations of a beam arise due to these bifurcations. These oscillations are investigated qualitatively and numerically.     

Electron motion in a Holstein molecular chain in an electric field

A charge motion in an electric field in a Holstein molecular chain is modeled in the absence of dissipation. It is shown that in a weak electric field a Holstein polaron moves uniformly experiencing small oscillations of its shape. These oscillations are associated with the chain’s discreteness and caused by the presence of Peierls-Nabarro potential there. The critical value of the electric field intensity at which the moving polaron starts oscillating at Bloch frequency is found. It is shown that the polaron can demonstrate Bloch oscillations retaining its shape. It is also shown that a breathing mode of Bloch oscillations can arise. In all cases the polaron motion along the chain is infinite.     

Nonlinear gas oscillations in an open tube under anharmonic excitation

Nonlinear gas oscillations excited in a tube with an open end by a piston driven by a crank mechanism are investigated. For the open end of the tube, a nonlinear boundary condition is formulated with allowance for oscillations at the subharmonic resonance frequency. Both first- and second-order approximations to the oscillations at the fundamental frequency and at half this frequency are calculated. The results of theoretical calculations are compared with experimental data.     

Layer-by-layer growth of PbSe studied by glancing angle scattering of 500-keV protons

Homoepitaxial growth of PbSe(111) is observed at 220°C by glancing angle scattering of 500-keV protons. The intensity of the specularly reflected ions shows oscillations during the growth. The period of the oscillations corresponds to the growth time for one mono-molecular layer. The oscillations are due to the oscillatory change in the surface step density during layer-by-layer growth. A simple model calculation reproduces the characteristic features of the observed oscillations reasonably well. Comparing the observed oscillations with the calculated ones, the density of the two-dimensional islands during growth is estimated.     

On the instability of longitudinal oscillations in an inhomogeneous isotropic plasma

The stability of forced nonlinear longitudinal oscillations in isotropic plasma is investigated. It is demonstrated that at certain ratio between the parameters of the plasma and the external force there arise parametric-like instabilities, and both harmonics and subharmonic oscillations of the order of 1/3 become unstable. The growth rate of the unstable oscillations and conditions under which they occur are defined.     

Quantum capacitance of the armchair-edge graphene nanoribbon

The quantum capacitance, an important parameter in the design of nanoscale devices, is derived for armchair-edge single-layer graphene nanoribbon with semiconducting property. The quantum capacitance oscillations are found and these capacitance oscillations originate from the lateral quantum confinement in graphene nanoribbon. Detailed studies of the capacitance oscillations demonstrate that the local channel electrostatic potential at the capacitance peak, the height and the number of the capacitance peak strongly depend on the width, especially a few nanometres, of the armchair-edge graphene nanoribbon. It implies that the capacitance oscillations observed in the experiments can be utilized to measure the width of graphene nanoribbon. The results also show that the capacitance oscillations are not seen when the width is larger than 30 nm.     

The role of auditory feedback in sustaining vocal vibrato

Vocal vibrato and tremor are characterized by oscillations in voice fundamental frequency (F0). These oscillations may be sustained by a control loop within the auditory system. One component of the control loop is the pitch-shift reflex (PSR). The PSR is a closed loop negative feedback reflex that is triggered in response to discrepancies between intended and perceived pitch with a latency of approximately 100 ms. Consecutive compensatory reflexive responses lead to oscillations in pitch every approximately 200 ms, resulting in approximately 5-Hz modulation of F0. Pitch-shift reflexes were elicited experimentally in six subjects while they sustained /u/ vowels at a comfortable pitch and loudness. Auditory feedback was sinusoidally modulated at discrete integer frequencies (1 to 10 Hz) with +/- 25 cents amplitude. Modulated auditory feedback induced oscillations in voice F0 output of all subjects at rates consistent with vocal vibrato and tremor. Transfer functions revealed peak gains at 4 to 7 Hz in all subjects, with an average peak gain at 5 Hz. These gains occurred in the modulation frequency region where the voice output and auditory feedback signals were in phase. A control loop in the auditory system may sustain vocal vibrato and tremorlike oscillations in voice F0.     

The Evolution of Acoustic Radiation by an Ensemble of Vortex Rings in Air

The evolution of acoustic radiation emitted by an ensemble of vortex rings in air is studied on the basis of nonstationary Navier–Stokes equations. We use the expansions of required functions into a power series of the initial vorticity which is a small value. The Navier–Stokes equation system reduces to a parabolic system with constant coefficients for the higher derivatives. The problem is posed as follows. The vorticity is defined inside the toroid at t = 0. The other parameters of the gas are assumed to be constant throughout the space at the initial instant of time. The solution is expressed in terms of multiple integrals, which are calculated using Korobov grids. The density oscillations were investigated. The results show that the frequency spectrum depends on time; high-frequency oscillations are observed at small times and low-frequency oscillations then occur. At the same time, the amplitude of high-frequency oscillations decreases in comparison with low-frequency oscillations. Thus, a transition of energy from the high-frequency spectrum to the lowfrequency spectrum occurs. These results can be useful for modeling decaying grid turbulence.     

Current to frequency conversion in a Josephson circuit

The voltage oscillations which occur in an ideally current-biased Josephson junction were proposed to make a current standard for metrology. We demonstrate similar oscillations in a more complex Josephson circuit derived from the Cooper pair box: the quantronium. When a constant current I is injected in the gate capacitor of this device, oscillations develop at the frequency f(B)=I/2e, with e the electron charge. We detect these oscillations through the sidebands induced at multiples of f(B) in the spectrum of a microwave signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss the potential interest of this current-to-frequency conversion experiment for metrology.     

Tamm oscillations in semi-infinite nonlinear waveguide arrays

We demonstrate the existence of nonlinear Tamm oscillations at the interface between a substrate and a one-dimensional waveguide array with either cubic or saturable, self-focusing or self-defocusing nonlinearity. Light is trapped in the vicinity of the array boundary due to the interplay between the repulsive edge potential and Bragg reflection inside the array. In the special case when this potential is linear these oscillations reduce themselves to surface Bloch oscillations.     

Nonlinear phenomena accompanying the development of oscillations excited in a layer of a linear dissipative medium by finite displacements of its boundary

A method of describing oscillations in resonators on the basis of evolution equations is proposed. The latter are obtained by simplifying the functional equations under the assumption that the distortions of travelling waves within the resonator length are small, that the Mach number for the moving boundary oscillations is small, and that the frequency is close to one of the natural frequencies of the resonator. The problems of nonstationary oscillations of a layer with a moving boundary are solved. The law that should govern the wall oscillations to provide the development of steady-state linear resonance oscillations is determined. The shape of the resonance curve formed in the presence of a boundary nonlinearity is calculated. The method of matching of asymptotics is applied to the singularly perturbed problem with small dissipation. It is shown that a boundary nonlinearity leads to a distortion of the temporal profile of the standing wave and to the generation of higher harmonics in the process of the development of steady-state oscillations. In contrast to the classical linear problems where the resonance occurs at the coincidence of the external force frequency with one of the natural frequencies, in the case under study the resonance behavior is observed in frequency bands, which are wider the higher the amplitude of the boundary oscillations is.     

Bloch oscillations in a homogeneous nucleotide chain

It is shown that, at zero temperature, a hole placed in a homogeneous synthetic nucleotide chain with applied electric field demonstrates Bloch oscillations. The oscillations of the hole placed initially on one of the base pairs arise in response to disruption of the initial charge distribution caused by nucleotide vibrations. The finite temperature fluctuations result in degradation of coherent oscillations. The maximum permissible temperature for DNA “Bloch oscillator” occurrence is estimated.     

X-ray topography analysis of bulk acoustic wave resonators

X-ray topography is first used to totally examine the fundamental modes of acoustic oscillations in the bulk-acoustic-wave (BAW) resonator on the base of an AT-cut quartz crystal at the first and third harmonics. As is evident from the experiments, the anharmonic longitudinal oscillations of the resonator can be visualized, just as the fundamental transverse acoustic oscillations can be. The amplitude-frequency response (AFR) is related to the frequency dependence of diffracted x-ray intensity.     

Aharonov-Bohm oscillations in the presence of strong spin-orbit interactions

We have measured highly visible Aharonov-Bohm (AB) oscillations in a ring structure defined by local anodic oxidation on a p-type GaAs heterostructure with strong spin-orbit interactions. Clear beating patterns observed in the raw data can be interpreted in terms of a spin geometric phase. Besides h/e oscillations, we resolve the contributions from the second harmonic of AB oscillations and also find a beating in these h/2e oscillations. A resistance minimum at B=0 T, present in all gate configurations, is the signature of destructive interference of the spins propagating along time-reversed paths.     

Homopolar oscillating-disc dynamo driven by parametric resonance

We use a simple model of Bullard-type disc dynamo, in which the disc rotation rate is subject to harmonic oscillations, to analyze the generation of magnetic field by the parametric resonance mechanism. The problem is governed by a damped Mathieu equation. The Floquet exponents, which define the magnetic field growth rates, are calculated depending on the amplitude and frequency of the oscillations. Firstly, we show that the dynamo can be excited at significantly subcritical disc rotation rate when the latter is subject to harmonic oscillations with a certain frequency. Secondly, at supercritical mean rotation rates, the dynamo can also be suppressed but only in narrow frequency bands and at sufficiently large oscillation amplitudes.