Trapped Modes Research Articles

Review of Flow-Excited Resonance of Acoustic Trapped Modes in Ducted Shallow Cavities

Flow-excited resonances of acoustic trapped modes in ducted shallow cavities are reviewed in this paper. The main components of the feedback mechanism which sustains the acoustic resonance are discussed with particular emphasis on the complexity of the trapped mode shapes and the strong three-dimensionality of the cavity flow oscillations during the resonance. Due to these complexities of the flow and sound fields, it is still difficult to theoretically or numerically model the interaction mechanism which sustains the acoustic resonance. Strouhal number and resonance amplitude charts are therefore included to help designers avoid the occurrence of resonance in new installations, and effective countermeasures are provided which can be implemented to suppress trapped mode resonances in operating plants.

In-situ trapping arsenic hydride on tungsten coil and comparing interference effect of some hydride forming elements using different types of atomizers

Hydride generation atomic absorption spectrometry (HGAAS) with different types of atomizers (flame heated quartz T-tube and W-coil) was evaluated for comparison of interference effects of some hydride forming elements for arsenic determination. W-coil was used as an on-line atomizer or as a trapping surface. Mutual interferences of Sb(III), Se (IV), Sn (II) and Te(IV) on arsenic signal were compared with flame heated quartz T-tube atomizer and W-coil; on-line atomization and in-situ trapping modes. When W-coil was operated at on-line atomization mode the interference magnitudes could not be improved as much as expected with respect to quartz T-tube atomizer. However, decent improvements were achieved for interference magnitudes of each interferent species with in-situ trapping on iridium coated W-coil. Under optimized conditions and using 60s trapping period (sample volume 6ml), the limit of detection was found as 0.03ngml−1 and the calibration was linear in between 0.25–4.0ngml−1 As. The precision of the analytical method was less than 2.5% in terms of RSD (n=11) for 1.0ngml−1 arsenic concentration. The accuracy of the method was tested with certified reference materials; fortified water TMDA 61 (NWRI) and waste water EU-L-1 (SCP). The results were in a good agreement with the certified values at 95% confidence level.

Positron annihilation lifetime study of atomic imperfections in nanostructurized solids: On the parameterized trapping in wet‐milled arsenic sulfides As4S4

The phenomenon of positron–electron annihilation in lifetime measuring mode is considered as a tool to study nanostructurization in solids possessing mixed positron and positronium (Ps) trapping. Structural inhomogeneities due to guest nanoparticles in such solids are described in terms of substitution trapping in positron‐ and Ps‐related sites within the same host matrix. The developed approach allows estimation of interfacial free‐volume voids as being responsible for positron trapping and defect‐free bulk positron lifetimes of nanoparticle‐modified solids. For the example of arsenic sulfide, As4S4 nanoparticles embedded in polyvinylpyrrolidone (PVP) environment under high‐energy ball milling, an alternative algorithm to parameterize these structural imperfections is justified. Interfacial free‐volume voids between neighboring nanoparticles filled with loosely packed As4S4 crystallites are considered as the most probable positron trapping sites. The observed variations in mixed positron–Ps trapping modes under nanostructurization are adequately defined with respect to the chemistry of guest nanoparticles. Direct evidence for this algorithm is provided as the basis of experimental three‐term decomposed positron lifetime spectra for As4S4–PVP nanocomposites parameterized with respect to different fitting protocols.

A Rigorous Interpretation of Approximate Computations of Embedded Eigenfrequencies of Water Waves

In this paper, we will investigate embedded eigenvalues in the framework of the linearized theory of water waves. We assume that an approximation of an embedded eigenvalue is provided. To the question, whether there is a trapped mode near the computed solution, we provide an affirmative answer. We will prove that, under certain assumptions on the data for a water wave problem in an infinite channel \Omega^0 , the result \lambda^{0} of the numerical computation can be justified as follows: if the computational error \varepsilon is sufficiently small, there exists a water domain \Omega^\varepsilon which is a local regular perturbation of \Omega^0 and has an eigenvalue \lambda^\varepsilon \in [\lambda^0 - c \varepsilon,\, \lambda^0 + c\varepsilon] embedded in the continuous spectrum. This conclusion is made by means of an asymptotic analysis of the augmented scattering matrix, whose properties guarantee a sufficient condition for the existence of trapped mode.

Weakly nonlinear ion waves in striated electron temperatures.

The existence of low-frequency waveguide modes of electrostatic ion acoustic waves is demonstrated in magnetized plasmas for cases where the electron temperature is striated along magnetic field lines. For low frequencies, the temperature striation acts as waveguide that supports a trapped mode. For conditions where the ion cyclotron frequency is below the ion plasma frequency we find a dispersion relation having also a radiative frequency band, where waves can escape from the striation. Arguments for the formation and propagation of an equivalent of electrostatic shocks are presented and demonstrated numerically for these conditions. The shock represents here a balance between an external energy input maintained by ion injection and a dissipation mechanism in the form of energy leakage of the harmonics generated by nonlinear wave steepening. This is a reversible form for energy loss that can replace the time-irreversible losses in a standard Burgers equation.

Energy trapping of thickness-shear modes in inverted-mesa AT-cut quartz piezoelectric resonators

abstractWe studied thickness-shear vibration frequencies and modes in an inverted-mesa AT-cut quartz plate piezoelectric resonator thinner in the center and thicker near the edges. It is electroded in the central part and unelectroded near the edges. A theoretical analysis was performed using the scalar differential equations by Stevens and Tiersten for thickness-shear vibrations of electroded and unelectroded quartz plates. Based on the variational formulation of the scalar differential equations established in a previous paper and the variation-based Ritz method with trigonometric functions as basis functions, free vibration resonant frequencies and the corresponding thickness-shear modes were obtained. It was found that the electrodes tend to trap the vibration in the central part of the resonator (energy trapping) but the curvature of the resonator surface has an opposite effect. The trapping is sensitive to the electrode thickness, the electrode length, and the curvature of the resonator surface. Hence accurate design is needed to achieve proper energy trapping in inverted-mesa resonators.

Effects of transition particles on plasma instabilities in a quasi-isodynamic stellarator

We consider the impact of transition particles on the Alfvén waves and electrostatic trapped ion modes in a stellarator with closed contours of the second adiabatic invariant, which do not perfectly coincide with magnetic surfaces (a so-called quasi-isodynamic (QI) stellarator). Due to orbit transitions, the damping rate of Alfvén eigenmodes on localized electrons becomes independent of the collision frequency in the broad range of low-collision rates. Dissipative trapped ion modes (Kadomtsev–Pogutse (KP) modes) induced by the ion temperature gradient (ITG) are strongly stabilized by collisionless orbit transitions.

Graphene-based plasmonic tweezers

Conventional plasmonic tweezers with the ability to attract and immobilize nearby sub-diffraction limit sized particles can only enhance the trapping efficiency by changing the shape of the metal nanostructures. There are several problems with conventional plasmonic tweezers. First, trapped particles can easily escape from the trap by disturbances coming from the heat absorption of the metallic surfaces. These disturbances prevent prolonged observation of the trapped particles. Second, observation of the particles becomes a challenge because the opaqueness of the metal blocks the illumination pathways. These problems can be solved by using graphene, which has high transmittance and thermal conductivity. The carrier density of the graphene is tuned by externally controlling the Fermi level through the gate voltage. Tuning the carrier density alters the local field enhancement factor far beyond the capabilities provided by other metal-based plasmonic structures. In this paper, we have shown that particles can be trapped by graphene nanoholes with larger forces than gold nanoholes. The trapping forces on gold and graphene nanoholes were compared to illustrate the benefit of graphene nanoholes. Furthermore, various trapping modes of a particle under various geometries and configurations of graphene nanoholes is discussed.

Flow-Excited Acoustic Resonance of Trapped Modes of a Ducted Rectangular Cavity

Flow over ducted cavities can lead to strong resonances of the trapped acoustic modes due to the presence of the cavity within the duct. Aly and Ziada (2010, “Flow-Excited Resonance of Trapped Modes of Ducted Shallow Cavities,” J. Fluids Struct., 26(1), pp. 92–120; 2011, “Azimuthal Behaviour of Flow-Excited Diametral Modes of Internal Shallow Cavities,” J. Sound Vib., 330(15), pp. 3666–3683; and 2012, “Effect of Mean Flow on the Trapped Modes of Internal Cavities,” J. Fluids Struct., 33, pp. 70–84) investigated the excitation mechanism of acoustic trapped modes in axisymmetric cavities. These trapped modes in axisymmetric cavities tend to spin because they do not have preferred orientation. The present paper investigates rectangular cross-sectional cavities as this cavity geometry introduces an orientation preference to the excited acoustic mode. Three cavities are investigated, one of which is square while the other two are rectangular. In each case, numerical simulations are performed to characterize the acoustic mode shapes and the associated acoustic particle velocity fields. The test results show the existence of stationary modes, being excited either consecutively or simultaneously, and a particular spinning mode for the cavity with square cross section. The computed acoustic pressure and particle velocity fields of the excited modes suggest complex oscillation patterns of the cavity shear layer because it is excited, at the upstream corner, by periodic distributions of the particle velocity along the shear layer circumference.

Properties of low‐frequency trapped mode in viscous‐fluid waveguides

ABSTRACTWe derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10−3 Hz to 103 Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity.

“Caging” and resonant trapping for flexural waves in constrained elastic plates

The paper presents a model of a vibrating constrained Kirchhoff plate, which includes a region “caged” by one or two rings of rigid pins. It is tempting to assume that the “caged” region will see no vibrations and hence it is protected from an incident wave. It is demonstrated in this paper that this assumption is not correct. In particular, we identify resonant regimes for which localised trapped vibration modes, whose amplitudes exceed the amplitude of the incident wave, may occur inside the “caged” region.

Energy trapping of thickness-extensional modes in thin film bulk acoustic wave filters

This paper presents the thickness-extensional vibration of a rectangular piezoelectric thin film bulk acoustic wave filter with two pairs of electrodes symmetrically deposited on the center of the zinc oxide film. The two-dimensional scalar differential equations which were first derived to describe in-plane vibration distribution by Tiersten and Stevens are employed. The Ritz method with trigonometric functions as basis functions is used based on a variational formulation developed in our previous paper. Free vibration resonant frequencies and corresponding modes are obtained. The modes may separate into symmetric and antisymmetric ones for such a structurally symmetric filter. Trapped modes with vibrations mainly under the driving electrodes are exhibited. The six corner-type regions of the filter neglected by Tiersten and Stevens for an approximation are taken into account in our analysis. Results show that their approximation can lead to an inaccuracy on the order of dozens of ppm for the fundamental mode, which is quite significant in filter operation and application.

A stability-indicating QTRAP LC-MS/MS method for identification and structural characterization of degradation products of indapamide

A selective and sensitive stability-indicating LC-MS/MS method, operated in ESI and quadrupole linear ion trap (QTRAP) modes, has been developed for the identification and structural characterization of stressed degradation products of indapamide.

Trapped modes supported by localized potentials in the zigzag graphene ribbon

Localized potentials in the Dirac equation for the electron dynamics in a zigzag graphene ribbon are constructed to support trapped modes while the corresponding eigenvalues are embedded into the continuous spectrum.

Distinct turbulence sources and confinement features in the spherical tokamak plasma regime

New turbulence contributions to plasma transport and confinement in the spherical tokamak (ST) regime are identified through nonlinear gyrokinetic simulations. The drift wave Kelvin–Helmholtz (KH) mode characterized by intrinsic mode asymmetry is shown to drive significant ion thermal transport in strongly rotating national spherical torus experiment (NSTX) L-modes. The long wavelength, quasi-coherent dissipative trapped electron mode (TEM) is destabilized in NSTX H-modes despite the presence of strong shear, providing a robust turbulence source dominant over collisionless TEM. Dissipative trapped electron mode (DTEM)-driven transport in the NSTX parametric regime is shown to increase with electron collision frequency, offering one possible source for the confinement scaling observed in experiments. There exists a turbulence-free regime in the collision-induced collisionless trapped electron mode to DTEM transition for ST plasmas. This predicts a natural access to a minimum transport state in the low collisionality regime that future advanced STs may cover.

Ultra-high-performance liquid chromatography—Time-of-flight high resolution mass spectrometry to quantify acidic drugs in wastewater

A novel analytical approach involving an improved rotating-disk sorptive extraction (RDSE) procedure and ultra-high-performance liquid chromatography (UHPLC) coupled to an ultraspray electrospray ionization source (UESI) and time-of-flight mass spectrometry (TOF/MS), in trap mode, was developed to identify and quantify four non-steroidal anti-inflammatory drugs (NSAIDs) (naproxen, ibuprofen, ketoprofen and diclofenac) and two anti-cholesterol drugs (ACDs) (clofibric acid and gemfibrozil) that are widely used and typically found in water samples. The method reduced the amount of both sample and reagents used and also the time required for the whole analysis, resulting in a reliable and green analytical strategy. The analytical eco-scale was calculated, showing that this methodology is an excellent green analysis, increasing its ecological worth. The detection limits (LOD) and precision (%RSD) were lower than 90ng/L and 10%, respectively. Matrix effects and recoveries were studied using samples from the influent of a wastewater treatment plant (WWTP). All the compounds exhibited suppression of their signals due to matrix effects, and the recoveries were approximately 100%. The applicability and reliability of this methodology were confirmed through the analysis of influent and effluent samples from a WWTP in Santiago, Chile, obtaining concentrations ranging from 1.1 to 20.5μg/L and from 0.5 to 8.6μg/L, respectively.

Identification of new turbulence contributions to plasma transport and confinement in spherical tokamak regime

Highly distinct features of spherical tokamaks (ST), such as National Spherical Torus eXperiment (NSTX) and NSTX-U, result in a different fusion plasma regime with unique physics properties compared to conventional tokamaks. Nonlinear global gyrokinetic simulations critical for addressing turbulence and transport physics in the ST regime have led to new insights. The drift wave Kelvin-Helmholtz (KH) instability characterized by intrinsic mode asymmetry is identified in strongly rotating NSTX L-mode plasmas. While the strong E×B shear associated with the rotation leads to a reduction in KH/ion temperature gradient turbulence, the remaining fluctuations can produce a significant ion thermal transport that is comparable to the experimental level in the outer core region (with no “transport shortfall”). The other new, important turbulence source identified in NSTX is the dissipative trapped electron mode (DTEM), which is believed to play little role in conventional tokamak regime. Due to the high fraction of trapped electrons, long wavelength DTEMs peaking around kθρs∼0.1 are destabilized in NSTX collisionality regime by electron density and temperature gradients achieved there. Surprisingly, the E×B shear stabilization effect on DTEM is remarkably weak, which makes it a major turbulence source in the ST regime dominant over collisionless TEM (CTEM). The latter, on the other hand, is subject to strong collisional and E×B shear suppression in NSTX. DTEM is shown to produce significant particle, energy and toroidal momentum transport, in agreement with experimental levels in NSTX H-modes. Moreover, DTEM-driven transport in NSTX parametric regime is found to increase with electron collision frequency, providing one possible source for the scaling of confinement time observed in NSTX H-modes. Most interestingly, the existence of a turbulence-free regime in the collision-induced CTEM to DTEM transition, corresponding to a minimum plasma transport in advanced ST collisionality regime, is predicted.

Design of metaporous supercells by genetic algorithm for absorption optimization on a wide frequency band

The optimization of acoustic absorption by metaporous materials made of complex unit cells with 2D resonant inclusions is realized using genetic algorithm. A nearly total absorption over a wide frequency band can be obtained for thin structures, even for frequencies below the quarter wavelength resonances i.e., in a sub-wavelength regime. The high absorption performances of this material are due to the interplay of usual visco-thermal losses, local resonances and trapped modes. The density of resonant and trapped modes in this dissipative porous layer, is a key parameter for broadband absorption. The best configurations and critical coupling conditions are found by genetic algorithm optimization. Several types of resonators are included gradually in the studied configurations (split-rings, Helmholtz resonators, back cavities) with increasing complexity. The optimization leads to a metaporous structure with a 2-cm sub-wavelength layer thickness, exhibiting a nearly total absorption between 1800Hz and 7000Hz. The influence of the incidence angle on the absorption properties is also shown.

Bound states in the continuum in open acoustic resonators

We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct–cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich–Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

Source depth discrimination: An evaluation and comparison of several classifiers

Source depth estimation with a vertical linear array generally involves mode filtering, followed by matched-mode processing. However, this method has two main limitations: the problem of mode filtering is ill-posed in the case of partially spanning arrays; matched-mode processing is sensitive to environmental mismatch. Therefore, concerns for robustness motivate a simpler approach. The problem of depth estimation is reduced to a binary classification problem: source depth discrimination. Its aim is to evaluate whether the source is near the surface or submerged. These two hypotheses are formulated in terms of normal modes, using the concept of trapped and free modes. Several classification rules, based on modal filtering or on subspace projections, are studied. Monte-Carlo methods are used to evaluate their performance and compute receiver operating characteristics. This allows the choice of a discrimination threshold according to some expected performance. The benefits of considering a source depth discrimination problem rather than a source localization one are highlighted. The influence of noise and environmental mismatch are investigated, as well as the choice of the discrimination depth and the choice of the limit between trapped and free modes.