Amplitudes Of Individual Modes Research Articles

Wave mode extraction from multimodal wave signals in an orthotropic composite plate

In this paper the post-processing procedure based on the mode orthogonality is applied to extract individual waveforms at a composite plate edge from multimodal signals. To obtain the amplitudes of individual modes, numerically predicted modal through-thickness stress and displacement field values are used in the orthogonality relation. The performance of the mode extraction technique is evaluated by processing signals obtained from Finite Element (FE) modeling and experimental measurements. The propagation of the overlapping wave packets of Lamb modes S0 and A0 is considered along the fiber direction and perpendicular to that direction. The required experimental two-dimensional displacement components at the plate edge are measured by 3D Scanning Laser Doppler Vibrometer (3D SLDV). It is demonstrated that S0 mode can be extracted very well from the signal but A0 mode with slightly poorer accordance with the original waveforms and numerical predictions.

Non-adiabatic study of theKeplersubgiant KIC 6442183

Thanks to the precision of Kepler observations, [3] were able to measure the linewidth and amplitude of individual modes (including mixed modes) in several subgiant power spectra. We perform a forward modelling of a Kepler subgiant based on surface properties and observed frequencies. Non-adiabatic computations including a time- dependent treatment of convection give the lifetimes of radial and non-radial modes. Next, combining the lifetimes and inertias with a stochastic excitation model gives the amplitudes of the modes. We can now directly compare theoretical and observed linewidths and amplitudes of mixed-modes to obtain new constraints on our theoretical models.

A Numerical Determination of Acoustic Emission Sensor Response in Plates Using Dispersion Curves

This paper reports on a method for numerically modelling acoustic emission signals in simple plate geometries using dispersion curves. It is demonstrated how, by using a known source to sensor distance, it is possible to determine the arrival of the frequencies of the individual AE modes at the sensor face. Assumptions based on sensor frequency response and the amplitude of individual modes allow for an approximation of each mode arriving at the sensor face. These modes are then summed to provide a numerical model of the expected signal. Results of the model are compared with a recorded signal and show good correlation, this is further demonstrated by comparing the wavelet transforms of the modelled and recorded signal.

Compressional mode softening and Euler buckling patterns in mesoscopic beams

We describe a sequence of Euler buckling instabilities associated with the transverse modes of a mesoscopic beam subjected to compressional strain. As the strain is increased, successively higher normal mode frequencies are driven to zero; each zero signals an instability in the corresponding normal mode that can be realized if all lower instabilities are suppressed by constraints. When expressed in terms of the critical buckling modes, the potential energy functional takes the form of a multimode Ginzburg–Landau system that describes static equilibria in the presence of symmetry breaking forces. This model is used to analyse the complex equilibrium shapes that have been observed experimentally in strained mesoscopic beams. Theoretically predicted critical strain values agree with the appearances of higher order mode structures as the length-to-width aspect ratio increases. The theory also predicts upper bounds on the individual mode amplitudes that are consistent with the data. Based on insights from the theory, we suggest possible origins of the buckling patterns.

Attenuation in the sediment layers in East China Sea

Compressional wave attenuation in the frequency range 50 to 350 Hz is estimated using broadband data collected in the East China Sea. A time-frequency analysis provides amplitudes of individual modes which are used to estimate the modal attenuation coefficients. Different modes are sensitive to sediment properties at different depths and this mode-depth sensitivity is explored in a sensitivity study. Based on this sensitivity study attenuation in different layers of the sediments will be estimated using different modes which are sensitive at these depths. This is a variation of previous studies where different frequencies have been used to invert for different sediment parameters using sub-space approaches. This approach focuses the inversion to various layers (provided by the geophysical surveys at the site) of the sediment and hence presents a tool to describe the depth variations in the sediment. The attenuation versus frequency behavior of the different sediment layers will be discussed. [Work supported by ONR.]

Predictive transport modelling of type I ELMy H-mode dynamics using a theory-motivated combined ballooning–peeling model

This paper discusses predictive transport simulations of the type I ELMy high confinement mode (H-mode) with a theory-motivated edge localized mode (ELM) model based on linear ballooning and peeling mode stability theory. In the model, a total mode amplitude is calculated as a sum of the individual mode amplitudes given by two separate linear differential equations for the ballooning and peeling mode amplitudes. The ballooning and peeling mode growth rates are represented by mutually analogous terms, which differ from zero upon the violation of a critical pressure gradient and an analytical peeling mode stability criterion, respectively. The damping of the modes due to non-ideal magnetohydrodynamic effects is controlled by a term driving the mode amplitude towards the level of background fluctuations. Coupled to simulations with the JETTO transport code, the model qualitatively reproduces the experimental dynamics of type I ELMy H-mode, including an ELM frequency that increases with the external heating power. The dynamics of individual ELM cycles is studied. Each ELM is usually triggered by a ballooning mode instability. The ballooning phase of the ELM reduces the pressure gradient enough to make the plasma peeling unstable, whereby the ELM continues driven by the peeling mode instability, until the edge current density has been depleted to a stable level. Simulations with current ramp-up and ramp-down are studied as examples of situations in which pure peeling and pure ballooning mode ELMs, respectively, can be obtained. The sensitivity with respect to the ballooning and peeling mode growth rates is investigated. Some consideration is also given to an alternative formulation of the model as well as to a pure peeling model.

Role of Coincidental Nonlinear Events in the Saturation of Moderately Damped Modes

Both the level of broadband microturbulence and the behavior of driven waves can be strongly affected by local coincidences that produce nonlinear levels of the total fluctuation amplitude. We evaluate the rate at which such coincidences occur, for moderately damped modes which frequently reset their phases. They can produce significant nonlinear effects and can limit the amplitude of individual modes to low levels. These effects, which involve very many modes, are inherently difficult to observe using standard Fourier space or particle simulation techniques.

Parameters of global thunderstorm activity deduced from the long-term Schumann resonance records

Abstract Parameters of global thunderstorm activity are deduced from long-term frequency and amplitude records of the first three Schumann resonance (SR) modes performed at the Nagycennk Observatory (47.6°N, 16.7°E), Hungary, from May 1993 to May 1996. The variations of the daily frequency range of each mode, which are characteristic of the changes of the effective source width, exhibit annual and semiannual variations. Annual and semiannual variations are present in both the recorded data and the parameters of global thunderstorm activity. The effective source width varies over 3–4 h at solstices to 5–6 h during the equinox conditions. A period of about four months also appeared in the spectra of the recorded data. A similarity was found between the patterns of the annual and semiannual variations of the daily frequency range, and the changes in median solar time, apart from a three-month phase lead of the astronomical data. The similarity might be due to an unknown solar-terrestrial link. Two approaches were used for the parameterisation of the global thunderstorm activity. One of these employs the preliminary evaluation of the source-observer distance (SOD) using the ratio of individual mode amplitudes. Variations of the source intensity are obtained after dividing the amplitude recorded by that calculated for the established SOD. The second approach applies a direct summation of the individual mode intensities. Numerical simulations showed that such cumulative intensity depends on the level of the global thunderstorms rather than on the SOD. The two estimates were compared and the conclusion was made that these coincide to within ±30%. The maximum of the global thunderstorm activity occurs in summer, in the Northern hemisphere, and the minimum is observed in winter with a two-fold characteristic variance.

Quantum and classical statistics of the electromagnetic zero-point field.

A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED) wherein quantum measurements are imitated by the introduction of a stochastic classical background EM field. Random EM fluctuations are assumed to provide perturbations which can mimic some quantum phenomena while retaining a purely classical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb shift, spontaneous emission, the RMS radius of the harmonic oscillator, and the radius of the Bohr atom. This classical ZPF is represented as a homogeneous, isotropic ensemble of plane waves with fixed amplitudes and random phases. Averaging over the random phases is assumed to be equivalent to taking the ground-state expectation values of the corresponding quantum operator. We demonstrate that this is not precisely correct by examining the statistics of the classical ZPF in contrast to that of the EM quantum vacuum. We derive the distribution for the individual mode amplitudes in the ground-state as predicted by quantum field theory (QFT) and then carry out the same calculation for the classical ZPF analogue, showing that the distributions are only in approximate agreement, diverging as the density of k states decreases. We introduce an alternative classical ZPF with a different stochastic character, and demonstrate that it can exactly reproduce the statistics of the EM vacuum of QED. Incorporated into SED, this new field is shown to give the correct (QM) distribution for the amplitude of the ground-state of a harmonic oscillator, suggesting the possibility of developing further successful correspondences between SED and QED.

Bistatic cross sections of thin spherical elastic shells at resonance, and the resonance order

The acoustic scattering amplitude of elastic objects separates into specular‐reflection terms, and elastic‐resonance terms [L. Flax et al., J. Acoust. Soc. Am. 63, 723 (1978)]. For separable geometry, this holds for the individual mode amplitudes separately, and the problem arises how to classify the oberved resonances as to their mode order. For cylindrical scatterers at normal incidence, where the modal amplitudes contain cos nφ, the experimental solution is provided by observing the corresponding “daisy” pattern of the resonant bistatic cross section after isolating it by the MIIR method [G. Maze and J. Ripoche, J. Acoust. Soc. Am. 73, 41 (1983)]. We demonstrate here, for the case of spherical aluminum shells of thickness 0.1%, that mathematically, the order of a resonating mode is determined by coherent subtraction of the soft‐sphere nonresonant background, and observation of the remaining bistatic resonant cross section whose pattern is determined by Pn, (cos θ). [H. Überall was supported by the Office of Naval Research.]

Resonance Anomalies in the Lamellar Grating

The problem of diffraction by a perfectly conducting lamellar grating is examined numerically and analytically by use of a modal expansion technique. At various complex wavelengths, with a positive imaginary part, individual mode amplitudes have poles which give rise to resonance effects in the orders at nearby real wavelengths. These are the well-known resonance anomalies. We determine the trajectories of these poles as functions of groove depth, finding that as this parameter increases they move in the complex wavelength plane to a mode threshold, or cut-off wavelength—from a Rayleigh wavelength in the case of S -polarization and from zero wavelength in the case of P -polarization. It is emphasized that the modal expansion technique is particularly valuable in gaining an understanding of the dynamics of diffraction gratings, and that the resonance poles are perhaps the basic dynamical objects determining their behaviour.

An analysis of optical waveguide tapers

The characteristics of slab waveguide tapers with finite-thickness cladding are investigated by approximating the tapered section as a series of uniform five-layer waveguides with successive changes in the core and cladding thickness. The behaviour of multimode coupling and transmission characteristics for typical tapers are studied in detail by computer simulation, employing parameter values appropriate for practical systems. Strong coupling and efficient conversion between core and cladding modes are demonstrated. In addition, it is shown that for tapers of moderate slopes, the nearest-neighbour coupling approximation is quite adequate for the calculation of the individual mode amplitudes. For steeper tapers, however, additional neighbouring modes have to be taken into account, and the modal energy tends to spread further towards the higher-order modes. It is also demonstrated that relatively large step-size can be used in the iterative numerical calculations. This, in conjunction with the choice of an appropriate coupling scheme (e.g., the nearest-neighbour approximation for mild tapers), makes it possible to reduce the cost of computer simulation. The relevance of the present analysis to fiber tapers is also discussed.