Amplitude Beating Research Articles

Evolution of coupled weakly driven waves in a dissipative plasma

The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved and time delays become unimportant. The system is then shown to be governed by two first-order coupled autonomous differential equations of cubic order for the wave amplitudes and two complementary first-order equations for the evolution of their phases. That system of equations can be decoupled and further simplified to a single second-order differential equation of Liénard's type for each amplitude. Numerical solutions for this equation are obtained in the general case, while analytic solutions are obtained for special cases in terms of parameters related to the spacing of the resonances of the two waves in frequency space, e.g., wave lengths and oscillation frequencies. These parameters are further analyzed to find classes of quasi-steady saturation and pulsating scenarios. To classify equilibrium points, local stability analysis is applied, and bifurcation conditions are determined. When the two waves saturate at similar amplitude levels, their combined signal is shown to invariably exhibit amplitude beating and phase jumps of nearly π. The obtained analytical results can be used to benchmark simulations and to interpret eigenmode amplitude measurements in fusion experiments.

Characterization of the ultrafast spectral diffusion and vibronic coherence of TIPS-pentacene using 2D electronic spectroscopy.

TIPS-pentacene is a small-molecule organic semiconductor that is widely used in optoelectronic devices. It has been studied intensely owing to its ability to undergo singlet fission. In this study, we aim to develop further understanding of the coupling between the electronic and nuclear degrees of freedom of TIPS-pentacene (TIPS-Pn). We measured and analyzed the 2D electronic spectra of TIPS-Pn in solutions. Using center line slope (CLS) analysis, we characterized the frequency-fluctuation correlation function of the 0-0 vibronic transition. Strong oscillations in the CLS values were observed for up to 5ps with a frequency of 264cm-1, which are attributable to a large vibronic coupling with the TIPS-Pn ring-breathing vibrational mode. In addition, detailed analysis of the CLS values allowed us to retrieve two spectral diffusion lifetimes, which are attributed to the inertial and diffusive dynamics of solvent molecules. Amplitude beating analysis also uncovered couplings with another vibrational mode at 1173cm-1. The experimental results can be described using the displaced harmonic oscillator model. By comparing the CLS values of the simulated data with the experimental CLS values, we estimated a Huang-Rhys factor of 0.1 for the ring-breathing vibrational mode. The results demonstrated how CLS analysis can be a useful method for characterizing the strength of vibronic coupling.

Phonons, Q -dependent Kondo spin fluctuations, and 4f phonon resonance in YbAl3

The intermediate valence (IV) compound YbAl$_3$ exhibits nonintegral valence (Yb 4$f^{14-n_f}$ (5d6s)$^z$ where z = 2+n$_f$ = 2.75) in a moderately heavy (m* = 20-30me) ground state with a large Kondo temperature (T$_K$ ~ 500-600K). We have measured the magnetic fluctuations and the phonon spectra on single crystals of this material by time-of-flight inelastic neutron scattering (INS) and inelastic x-ray scattering (IXS). We find that at low temperature, the Kondo-scale spin fluctuations have a momentum (Q) dependence similar to that seen recently in the IV compound CePd$_3$ and which can be attributed to particle-hole excitations in a coherent itinerant 4$f$ correlated ground state. The Q-dependence disappears as the temperature is raised towards room temperature and the 4$f$ electron band states become increasingly incoherent. The measured phonons can be described adequately by a calculation based on standard DFT+$U$ density functional theory, without recourse to considering 4$f$ correlations dynamically. A low temperature magnetic peak observed in the neutron scattering at ~ 30meV shows dispersion identical to an optic phonon branch. This 4$f$/phonon resonance disappears for T > 150K. The phonons appear to remain unaffected by the resonance. We discuss several possibilities for the origin of this unusual excitation, including the idea that it arises from the large amplitude beating of the light Al atoms against the heavy Yb atoms, resulting in a dynamic 4$f$/3$p$ hybridization.

Tidal oscillations in shallow bays and sediment movement

The present study seeks to understand the interaction of a directly forced, large amplitude, tidal mode with non-directly forced resonant or nearly resonant tidal modes in a coastal bay or basin despite frictional effects. It is shown that in shallow basins a non-directly forced resonant mode may be indirectly activated with a response that may be time dependent, with the amplitude of this mode increasing and then decreasing before increasing again in a cyclical manner associated with amplitude beats. A laboratory experiment and theoretical arguments are used to support these conclusions and to study the effect when the amplitude of the tidal disturbances is comparable to the depth of the basin. It is noted that the presence of such modes, whether directly or indirectly forced, and whether resonant or non-resonant, may be able to move sediment and thereby change the resonance behaviour of the basin by changing its geometry. The changes in the geometry may then change the resonant frequencies of the basin, possibly causing the decay of the mode that caused the sediment motion. The implications of the mechanism for the modelling of the tidal behaviour in other bays with more complicated geometry are considered.

Amplitude-Dependent Internal Friction and Harmonic Generation in Media with Hysteresis Nonlinearity and Linear Dissipation

Based on generalization and integration of models for dislocation mechanisms of the hysteresis nonlinearity, we propose a hysteresis equation of state of polycrystalline solids with saturated amplitude-dependent losses. Using the perturbation method, we study, both theoretically and numerically, the nonlinear effects during propagation of acoustic waves in the media with hysteresis nonlinearity and linear viscous dissipation. Nonlinear damping rate and propagation velocity of the wave at the fundamental frequency, as well as regularities for the amplitudes and phase velocities at its second and third harmonics, are determined. It is shown that the media described by such hysteresis equations of state have a nonlinear dispersion, which leads to a nonmonotonic rise and amplitude beats of the higher harmonics as the wave amplitude increases at the fundamental frequency.

Breathing dynamics of an asymmetric Gaussian beam propagating in a saturable absorbing medium

Propagation of an asymmetric Gaussian beam in a medium with saturated nonlinear refractive index is analyzed using a ``collective variable approach'' to solve the general nonlinear Schr\odinger equation and compared with that of a symmetric beam in both lossless and lossy media. For a lossless medium, we construct a diagram which defines regions of oscillatory and diffractive propagation of an asymmetric beam and compare it with that of a symmetric beam. We detect breathing dynamics of the widths and amplitude of the asymmetric beam in the oscillatory regime of propagation and identify two different types of width and amplitude beating, Type $1$ and $2$, depending on the initial beam energy and saturation constant of the medium. This is in contrast to a cubic-quintic medium where only one type of beating is obtained.

Bridge vibration logarithmic decrement estimation at the presence of amplitude beat

Logarithmic decrement is one of the key dynamic parameters characterizing bridge status. It is usually estimated from vibration records applying digital signal processing. Among the processing procedures band-pass filtering is commonly used to extract spectral components of interest. We analyze the case when two very close spectral components are present in the acceleration records. We show that construction of the filter is non-trivial in such a situation and failing to choose optimal filter’s parameters leads to significant logarithmic decrement estimation errors. Therefore we propose a method that does not require band-pass filtering but utilizes knowledge of amplitude beat presence. Simulation of the method indicated errors by an order less than using filtering.

Analysis and modeling of piano sustain-pedal effects

This paper describes the main features of the sustain-pedal effect in the piano through signal analysis and presents an algorithm for simulating the effect. The sustain pedal is found to increase the decay time of partials in the middle range of the keyboard, but this effect is not observed in the case of the bass and treble tones. The amplitude beating characteristics of piano tones are measured with and without the sustain pedal engaged, and amplitude envelopes of partial overtone decay are estimated and displayed. It is found that the usage of the sustain pedal introduces interesting distortions of the two-stage decay. The string register response was investigated by removing partials from recorded tones; it was observed that as the string register is free to vibrate, the amount of sympathetic vibrations is increased. The synthesis algorithm, which simulates the string register, is based on 12 string models that correspond to the lowest tones of the piano. The algorithm has been tested with recorded piano tones without the sustain pedal. The objective and subjective results show that the algorithm is able to approximately reproduce the main features of the sustain-pedal effect.

Distributed two-dimensional boundary-layer receptivity to non-stationary vortical disturbances in the presence of surface roughness

The distributed (over the longitudinal coordinate) excitation of two-dimensional (2D) Tollmien — Schlichting (TS) waves by weak non-stationary free-stream vortices propagating along the edge of the laminar boundary layer developing over a surface with small-amplitude 2D roughness is examined. The vorticity vector of the free-stream vortices was oriented over the span of the model, i. e., did not depend on the transverse coordinate. The theoretical analysis of the excitation mechanism reported in [1] was refined to develop, around it, a procedure making it possible to experimentally determine the coefficients of distributed vortical receptivity of the flow and the coefficients of “vortex-roughness” receptivity by fitting the experimental distributions with analytical solutions. Under conditions with controllable excitation of disturbances, a detailed hot-wire study of free-stream disturbances and boundary-layer disturbances at several vortex frequencies and at several surface-roughness periods was performed, and the shape of the controllable surface roughness was measured. The point-source method was employed to experimentally examine the characteristics of linear three-dimensional (3D) stability of the flow to TS waves, necessary for determination of the coefficients of distributed receptivity. It was found that the free-stream vortices with transverse orientation of the vorticity vector excited boundary-layer TS waves via two receptivity mechanisms: (a) on the smooth surface (due to natural non-uniformity of the flow) and (b) during interaction of the vortices with the surface roughness. The developed approach was used to experimentally estimate the amplitudes and phases of the coefficients of both types of distributed vortical receptivity as dependent on problem parameters. The absolute values of both types of receptivity coefficients were found to rapidly grow in value with increasing vortex frequency. It is shown that the most efficient excitation of TS waves is observed in the situation with satisfied resonance conditions for streamwise vortex, surface-roughness, and TS-wave streamwise wavenumbers, resulting in strong deviation of the increments of the TS waves from the linear-stability increments. Under no-resonance conditions, only amplitude beats of boundary-layer disturbances were observed.

Birefringent filter with amplitude beats

In this work, we show a very simple birefringent filter useful to modulate a broadband light spectrum. We first show the generation of various oscillating spectra using two identical multiple-order waveplates. In particular a sinusoidal broadband spectrum with a rapid oscillation is obtained. This spectrum is amplitude modulated by adding another waveplate to the system. This waveplate has a small phase shift, and with the proper orientation generates amplitude beats on the broadband spectrum. Finally, we show how this system can be voltage controlled by means of a ferroelectric liquid crystal modulator. We experimentally demonstrate this behavior with the aid of a portable spectrophotometer, and we provide a theoretical explanation on the basis of the Jones matrix formalism.

Amplitude beating of coherent phonon in graphite under high intensity photo-excitation

Femtosecond dynamics of coherent E 2g1 phonon of graphite under high density photo-excitation is investigated by time-resolved reflectivity measurements. Both at low and room temperatures we found the amplitude beating of the coherent phonon, which appears similar to the amplitude collapse and revival of the coherent A 1g phonon of bismuth. Our analysis indicates that the amplitude beating in graphite originates from two (or three) almost classical oscillators, which is in contrast to the more quantum collapse–revival in bismuth. Possible mechanisms for the amplitude beating in graphite are discussed.

Computer processing of audio signals by exclusion filters

A common task in computer music and electroacoustic signal processing is additive mixing of two audio signals. If the two input signals contain discrete spectral components, their sum will typically contain amplitude beating and other interactions between pairs of components with similar frequencies. A new method is described that suppresses spectral interactions during mixing by deriving a time variant “exclusion filter” from the short‐time spectrum of one of the signals in order to prefilter the other signal. This technique allows one of the signals (dominant) to pass through the mixing process with little modification, while the other signal (secondary) is prevented from interaction by attenuation of its conflicting spectral components. The exclusion filter is specified in a flexible manner, which can include such psychoacoustic criteria as critical bands. Audio examples will be presented.

Influence of an intracavity medium on the gain of modes generated in a wide-band laser

An analysis is made of the influence of amplitude beats of laser modes on the dynamics of operation of a wide-band laser. It is shown that an allowance for these beats in a transversely inhomogeneous intracavity medium is equivalent to an allowance for its lens-like properties. The lens-like nature of the active medium shifts the lasing band. An inhomogeneity of the absorbing medium can result in a major redistribution of the intensity of lasing in the vicinity of absorption lines. It is shown that the gain of laser modes changes negligibly due to an inhomogeneous saturation of an absorbing medium.

Optical signal with high-frequency amplitude beats formed in a frequency-modulated injection laser and an interferometer

A generator of an optical signal with amplitude beats tunable within the frequency range 0.1– 6.0 GHz was constructed on the basis of a homodyne system containing a single-frequency injection laser frequency-modulated by a regular sequence of rectangular current pulses and a Mach-Zehnder interferometer with an optical difference between the arms ensuring a delay of the modulating signal by half a period.

A quantitative description of flagellar movement in golden hamster spermatozoa.

Flagellar movement of golden hamster spermatozoa obtained from the testis and the caput and cauda epididymides was observed by a light microscope while holding them at their heads with a micropipette. Flagellar movement of capacitated spermatozoa and of reactivated spermatozoa demembranated with Triton X-100 was also observed. Testicular and caput epididymal spermatozoa showed weak movement in Tyrode's solution, whereas cauda epididymal spermatozoa showed vigorous movement. The flagellar bends of the cauda epididymal spermatozoa were almost planar. Capacitated spermatozoa moved with waves of a large amplitude. Demembranated spermatozoa reactivated with ATP only had a latent period before the initiation of flagellar movement, and beat at low frequency, whereas demembranated spermatozoa reactivated with both ATP and cAMP began to move immediately at high frequency. Thrust and hydrodynamic power output were calculated using the parameters for the typical waveforms of cauda epididymal spermatozoa before and after capacitation. The possible role of the large amplitude beat in capacitated spermatozoa is discussed. A comparison of the 'principal' and 'reverse' bends in golden hamster sperm flagella as defined by Woolley (1977) with those in sea urchin sperm flagella suggests that the so-called 'principal' bend in golden hamster sperm flagella corresponds to the reverse bend in sea urchin sperm flagella and vice versa.

Phase measurements of whistler mode signals from the Siple VLF transmitter

A digital signal processing program has been developed to measure the phases of coherent VLF signals from analog tape recordings made in the field. The program uses a constant frequency pilot tone recorded with the VLF data to correct tape speed errors and reconstruct the signal phases. We analyze several examples of whistler mode signals from the VLF transmitter at Siple Station, Antarctica, as received at Roberval, Quebec. Pulses with temporal growth show a relative phase advance with time, and thus a positive frequency offset from the transmitted signal, often from the beginning of the pulse. Amplitude beating is often seen toward the end of a pulse, sometimes with phase cycle‐skipping as the emission becomes unlocked from the input signal. Current theories of wave‐particle interaction are reviewed and found to explain some of the observed signal features, though no theory predicts the initial frequency offset of a growing pulse.