Low-frequency Regime Research Articles

Design and optimization of acoustic liners with a shear grazing flow: OPAL software platform applications

In the context of noise reduction in diverse applications where a shear grazing flow is present (i.e., engine nacelle, jet pump, landing gear), improved acoustic liner solutions are being sought. This is particularly true in the low-frequency regime, where space constraints currently limit the efficiency of classic liner technology. To perform the required multi-objective optimization of complex meta-surface liner candidates, a software platform called OPAL was developed. Its first goal is to allow the user to assemble a large panel of parallel/serial assembly of unit acoustic elements, including the recent concept of LEONAR materials. Then, the physical properties of this liner can be optimized, relatively to given weighted objectives (noise reduction, total size of the sample, weight), for a given configuration. Alternatively, properties such as the different impedances of liner unit surfaces can be optimized. To accelerate the process, different nested levels of optimization are considered, from 0D analytical coarse designs in order to reduce the parameter space, up to 2D plan or axisymmetric high-order Discontinuous Galerkin resolution of the Linearized Euler Equations. The presentation will focus on the different aspects of liner design considered in OPAL, and present an application on different samples made for a small scale aeroacoustic bench.

Thermally-driven flows and turbulence in vibrated liquids

Within the vast array of variants encompassed by thermal (buoyancy) convection, the particular interest of the present work is on the specific dynamics which are enabled when standard steady gravity is replaced by a time-periodic body force induced by vibrations. The study is designed as a set of separate problems, where each exemplar aims to unravel the implications of the fundamental properties of this type of flow. These include the symmetry of the emerging pattern as perceived by a real observer and as seen in a “time-averaged space”, the synchronous or non-synchronous response of the velocity field to the applied forcing, the magnitude of the so-called Thermofluid-dynamic (TFD) distortions and the peculiar route of evolution towards chaos. A kaleidoscope of previously unknown solutions is reported giving emphasis to some still poorly known aspects such as the complex nature of the textural transitions that take place in the flow as the Gershuni number is increased (from 3.30 × 102 to 5.00 × 107 for Pr = 15). It is shown that the low-frequency regime is relatively stable over this range. In addition to the standard quadrupolar pattern, in such a case peculiar convective structures emerge where the time-averaged rolls display a very regular columnar arrangement, which has been rarely observed in earlier studies. Chaotic states are enabled when larger frequencies of vibration are considered. While for intermediate frequencies concurrent aspects of the Feigenbaum and Manneville and Pomeau mechanisms can be recognized, the hallmark of the high frequency regime is its adherence to the standard Ruelle-Takens scenario.

Resonance ultrasonic spectroscopy applied to normal and tangential contact modes investigation of a constrained metallic sphere

This article reports on the analysis of the vibration modes (central eigenfrequencies) observed on a dry steel sphere clamped between two planes, under static compression and subjected to an acoustic excitation. The experimental technique is based on the analysis of the ultrasonic resonance spectrum (RUS); compression or transverse excitations are used. Two types of vibrations are observed. The first occurring in the low frequency range corresponds to modes of movement conditioned by the contacts; the second corresponds to the internal, toroidal and spheroidal deformation modes. In this article we limit our research to the modes observed in the low frequency regime and our objective is to study the influence of the static force on the position of the peaks observed in the frequency spectra. In the case of a longitudinal excitation, only one mode is observed; the transverse excitation makes it possible to detect two modes. The experimental results are compared to theoretical calculations based on theoretical models of Hertz and Hertz-Mindlin, on a development of the JKR model based on adhesion due to Van der Waals forces. In this work, the mechanical coefficients are considered to be independent of time and we do not study the phenomena of hysteresis of these coefficients.

The use of the transfer matrix method to predict the effective fluid properties of acoustical systems

The transfer matrix method (TMM) is a common method for the modelling of acoustical systems. Traditionally, this method requires each unique layer within a system to be defined by a transfer matrix and then for each matrix to be multiplied together in the sequential order of the system. Whilst the resulting matrix can be used to find the effective material properties of the modelled system, the resulting analytical expressions of these properties are often unwieldy for use. Here, a simplified approach is proposed to obtain simple analytical expressions in the low frequency regime for the effective properties of acoustical systems based on the components of the TMM and inspired by the Champoux and Stinson model. It was shown that the proposed approximation of TMM matches the effective fluid properties of a cylindrical rigid tortuous pore derived with the Champoux and Stinson model. Using this approach, analytical expressions for the effective fluid properties of a waveguide of constant cross section, side-loaded by an arbitrary number of Helmholtz resonators, were derived. These expressions were validated against the traditional transfer matrix method and with numerical computation. The result of this work offers a validated general approach that provides simple analytical low frequency approximations of the acoustical properties of media which consist of complicated networks of pores or side-branches.

Investigation of novel 3D-printed diatomic and local resonant metamaterials with impact mitigation capacity

A novel dual local resonance metamaterial chain, at a low frequency regime (<200 Hz), is designed and fabricated using selective laser sintering technology for characterization of wave attenuation and impact mitigation, consisting of a main structure and cantilever-in-mass resonators as a periodic sub-structure. The dispersion characteristics and mode polarization of metamaterial chains with various resonators are studied using a mass-spring model and finite element modelling simulation. The results clearly demonstrate the bandgap of the dual resonance system is extended by both the local resonance and diatomic resonance mechanisms. A parametric study is established to optimize the bandgap ratio, revealing that the bandgap of the design can be shifted by changing the stiffness ratio between two resonators in the sub-structure. The wave attenuation in the frequency domain obtained from impact modal tests exhibits a good agreement with computational results. In particular, the dynamic load attenuation capacities of the metamaterial chains under different impact durations are studied using impact mitigation tests, which show that the dual resonance design has the best attenuation performance under impact force, where the transmission rate is driven down to 0.2, compared with 0.48 for the design without resonators.

Stability of an oscillatory Taylor–Couette flow in an upper convected Maxwell fluid

The stability of pulsed bi-dimensional flow between two co-oscillating cylinders in a linear Maxwell fluid was studied by Riahi et al. [J. Soc. Rheol. 42, 321–327 (2014)]. In the present paper, we revisit this flow configuration with emphasis on the effect of the non-linear terms in the constitutive equation of the model, measured by the Weissenberg number, on the dynamics of the system. Under these assumptions and using the upper convected Maxwell derivative, we examine this model to large amplitude oscillatory shear giving rise to the appearance, in comparison to the linear Maxwell model, of the azimuthal normal stress in the basic state. Using the spectral method and the Floquet theory for the spatiotemporal resolution of the obtained eigenvalue problem, numerical results exhibit numerous classes of Taylor vortex flows depending on the order of magnitude of the fluid elasticity. The resulting stability diagram consists of several branches intersecting at specific frequencies where two different Taylor vortex flows simultaneously branch off from the basic state. This feature is accompanied by the occurrence of several co-dimension two bifurcation points besides jumps/drops in the corresponding critical wave number. In addition, it turns out that the elasticity produces strong destabilizing and stabilizing effects in the limit of high and low frequency regimes, respectively, attributed solely to the non-linearities considered by the rheological model.

Minimal length, maximal momentum and stochastic gravitational waves spectrum generated from cosmological QCD phase transition

We investigate thoroughly the temporal evolution of the universe temperature as a function of the Hubble parameter associated with the Stochastic Gravitational Wave (SGW), that formed at the cosmological QCD phase transition epoch to the current epoch, within the Generalized Uncertainty Principle (GUP) framework. Here we use GUP version which provide constraints on the minimum measurable length and the maximum observable momentum, that characterized by a free parameter α. We study the effect of this parameter on the SGW background. We show that the effect can slightly enhance the SGW frequency in the lower frequency regime which might be important in the detection of SGW in the future GW detection facilities.

Three-dimensional acoustic lensing with a bubbly diamond metamaterial

A sound wave travelling in water is scattered by a periodic assembly of air bubbles. The local structure matters even in the low frequency regime. If the bubbles are arranged in a face-centered cubic (fcc) lattice, a total bandgap opens near the Minnaert resonance frequency. If they are arranged in the diamond structure, which one obtains by simply adding a second bubble to the unit cell, one finds an additional branch with a negative slope (optical branch). For a single specific frequency, the medium behaves as if its refractive index (relative to water) is exactly n=−1. We show that a slab of this material can be used to design a three-dimensional flat lens. We also report super-resolution focusing in the near field of the slab and illustrate its potential for imaging in three dimensions.

Semimicroscopic Theory for Underscreening-Induced Anomalous Migration–Diffusion Coupling

We develop a novel theory for the impedance response of reversible electron transfer reactions under the influence of migration–diffusion coupling. Theory accounts for the influence of the supporting electrolyte, electroactive species, solvent, metal, and the interfacial electric field accounting underscreening. This semimicroscopic formalism is based on a modified electrode surface boundary constraint, which circumvents the essential nonlinearity in the Nernst–Planck equation. The interfacial electric field determines the kinetics of formation of compact electric double layer (C-EDL) embedded with electroactive species and influence the mass transport. This kinetics is governed by an intrinsic C-EDL formation resistance (RH), solution resistance (RΩ), and the extent of ion packing dependent on electrolyte composition. Theory unravels a characteristic ohmic-migration frequency, ω* = D/LMΩ2, a prerequisite for the outer sphere electron transfer step. A dimensionless migration–diffusion coupling number δM is unriddled, which quantifies the extent of migration contribution dependent on the potentials at IHP (ϕ1), OHP (ϕ2), diffuse layer (ϕDL), ion size-corrected screening length, charge on electroactive species, interfacial diffusivity, and RH. The magnitude of impedance (in low-frequency regime) evinces an anomalous nonmonotonic variation with ionic strength. Finally, theory accredits us to understand the underscreening-induced anomalies in migration–diffusion-controlled impedance response.

Stochastic analysis of locally resonant linear and hysteretic metamaterials for seismic isolation of process equipment

Periodic metafoundations have proven to inherit valuable properties from wave propagating in phononic periodic structures in the very low-frequency regime. Therefore, finite locally resonant metafoundations (LRMs) represent a novel type of seismic isolation for ultralow-frequency applications. In this context, it is still unknown the impact that massive resonators with varying frequencies or devices with hysteretic behavior can entail on the whole system performance. For this purpose, we develop and optimize two finite locally resonant multiple degrees of freedom (MDoF) metafoundations in this paper: i) a foundation endowed with resonators, linear springs and linear viscous dampers tuned to multiple frequencies; and ii) a foundation equipped with fully nonlinear hysteretic dampers. Both are optimized considering the stochastic nature of ground motion, modelled with a modified Kanai-Tajimi filter in the stationary frequency domain, and a massive MDoF superstructure, chosen to be a fuel storage tank. In order to take all of the above-mentioned effects into account, we establish a procedure based on nonlinear programming that is able to optimize any number of parameters. More precisely, to optimize the nonlinear behavior of damper devices we employ a Bouc-Wen hysteretic model. Therefore, we reduce the nonlinear differential equations of Bouc-Wen models to a system of linear equations through the stochastic (equivalent) linearization technique. Moreover, we test the optimized systems against natural seismic records both with linear and nonlinear time history analyses. To investigate the role of hysteresis on the nonlinear band structure, we derive linearized and nonlinear dispersion relationships for the uncoupled periodic metafoundation. Finally, we obtain further detailed information on the nonlinear wave propagation by means of a spectro-spatial analysis.

Modal approximation for plasmonic resonators in the time domain: the scalar case

We study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the non-Hermitian problem as perturbations of electro-static modes, and obtain a modal approximation of the scattered field in the frequency domain. The poles of the expansion correspond to the eigenvalues of a singular boundary integral operator and are shown to lie in a bounded region near the origin of the lower-half complex plane. Finally, we show that this modal representation gives a very good approximation of the field in the time domain. We present numerical simulations in two dimensions to corroborate our results.

Magnetic Field Dynamic Strategies for the Improved Control of the Angiogenic Effect of Mesenchymal Stromal Cells.

This work shows the ability to remotely control the paracrine performance of mesenchymal stromal cells (MSCs) in producing an angiogenesis key molecule, vascular endothelial growth factor (VEGF-A), by modulation of an external magnetic field. This work compares for the first time the application of static and dynamic magnetic fields in angiogenesis in vitro model, exploring the effect of magnetic field intensity and dynamic regimes on the VEGF-A secretion potential of MSCs. Tissue scaffolds of gelatin doped with iron oxide nanoparticles (MNPs) were used as a platform for MSC proliferation. Dynamic magnetic field regimes were imposed by cyclic variation of the magnetic field intensity in different frequencies. The effect of the magnetic field intensity on cell behavior showed that higher intensity of 0.45 T was associated with increased cell death and a poor angiogenic effect. It was observed that static and dynamic magnetic stimulation with higher frequencies led to improved angiogenic performance on endothelial cells in comparison with a lower frequency regime. This work showed the possibility to control VEGF-A secretion by MSCs through modulation of the magnetic field, offering attractive perspectives of a non-invasive therapeutic option for several diseases by revascularizing damaged tissues or inhibiting metastasis formation during cancer progression.

Simplified Evaluation of Ground Motion Amplification in the Vicinity of a Topographic Feature

ABSTRACT A two-parameter expression for the quantification of topographic effects in ground response analysis at sites located in the vicinity of a topographic feature is presented. The expression is derived from parametric analysis of convex and concave canonical shapes after identifying that the diffracted field in these geometries remains relatively stable in the low dimensionless frequency regime. The proposed expression is used in the estimation of topographic effects at two sites located in realistic topographic scenarios over a given period range. To show the quality of the approximate formula results are compared with numerical simulation values.

Accuracy of parameter estimations with a spaceborne gravitational wave observatory

Employing the Fisher information matrix analysis, we estimate parameter errors of TianQin and Laser Interferometer Space Antenna (LISA) for monochromatic gravitational waves. With the long-wavelength approximation, we derive analytical formulas for the parameter estimation errors. We separately analyze the effects of the amplitude modulation due to the changing orientation of the detector plane and the Doppler modulation due to the translational motion of the center of the detector around the Sun. We disclose that in the low-frequency regime there exist different patterns in angular resolutions and estimation errors of sources' parameters between LISA and TianQin, the angular resolution falls off as ${S}_{n}(f)/{f}^{2}$ for TianQin but ${S}_{n}(f)$ for LISA, and the estimation errors of the other parameters fall off as $\sqrt{{S}_{n}(f)}/f$ for TianQin but $\sqrt{{S}_{n}(f)}$ for LISA. In the medium-frequency regime, we observe the same pattern where the angular resolution falls off as ${S}_{n}(f)/{f}^{2}$ and the estimation errors of the other parameters fall off as $\sqrt{{S}_{n}(f)}$ for both TianQin and LISA. In the high-frequency regime, the long-wavelength approximation fails; we numerically calculate the parameter estimation errors for LISA and TianQin and find that the parameter estimation errors measured by TianQin are smaller than those by LISA.

Photoacoustic characteristics of carbon-based infrared absorbers

We present an experimental comparison of photoacoustic responsivities of common highly absorbing carbon-based materials. The comparison was carried out with parameters relevant for photoacoustic power detectors and Fourier-transform infrared (FTIR) spectroscopy: we covered a broad wavelength range from the visible red to far infrared (633 nm to 25 μm) and the regime of low acoustic frequencies (< 1 kHz). The investigated materials include a candle soot-based coating, a black paint coating and two different carbon nanotube coatings. Of these, the low-cost soot absorber produced clearly the highest photoacoustic response over the entire measurement range.

Macroscopic behavior of materials composed of two elastic media

In the present paper we investigate macroscopic two-fluid effects in systems composed of two elastic media. Using two strain tensors as macroscopic variables, we present a nonlinear analysis in the regime of long wavelengths and low frequencies. We also discuss the description in terms of relative strains and total strains. Generalizing earlier work on relative rotations for systems such as nematic elastomers or uniaxial magnetic gels, we investigate how this concept can be applied to the case of two elastic media in the linear domain. For the two strain fields and relative rotations between the two elastic media, we find a number of reversible and dissipative cross-coupling terms that couple velocity differences, mean velocities, strain fields, and relative rotations to each other as well as to temperature and concentration gradients. The question of relative translations is also analyzed. A linearized description using relative translations is physically meaningful as well as technically consistent with using strain fields and relative rotations. Finally, we apply this description to the swinging of two coupled homogeneous elastic media relative to each other, and to the oscillating actuation or active stress introduced through one of the elastic compounds.

Theory for influence of uncompensated solution resistance on EIS of diffusion limited adsorption at rough electrode

Theory is developed for the electrochemical impedance spectroscopy (EIS) of the diffusion-limited adsorption process coupled with reversible charge transfer at rough electrodes under the influence of ubiquitous uncompensated solution resistance. This study quantitatively relates the impedance response of rough electrode to its phenomenological components, viz., diffusion limited adsorption, reversible charge transfer and uncompensated solution resistance. The random roughness of electrode is expressed by the surface statistical property, i.e., power spectrum of roughness. The fractal nature of roughness is characterized in terms of fractal dimension, lower cut-off length and topothesy length. The high-frequency regime is controlled by the uncompensated solution resistance whereas the low-frequency regime is governed by the adsorption process. The magnitude of impedance as well as phase decreases with rise in adsorption isotherm (length) parameter. The intermediate frequency regime is controlled by the coupling of adsorption and uncompensated solution resistance with the diffusion process. The fractal roughness parameters has quantitative influence on the magnitude of impedance over whole frequency regime while the phase plot shows qualitative difference in the intermediate frequency regime. The governing length scales which controls the characteristic crossover frequencies are: diffusion length, adsorption-ohmic coupling length and topothesy length (or width of interface). The three emergent crossover frequencies are: (i) ohmic reduced inner crossover frequency (ii) adsorption roughness topothesy dependent pseudo-quasireversibility characteristic frequency (iii) outer crossover frequency. Synopsis: This study quantitatively relates the impedance response of rough electrode to its phenomenological components, viz., diffusion limited adsorption, reversible charge transfer and uncompensated solution resistance. The random roughness of electrode is expressed by the surface statistical property, i.e., power spectrum of roughness.

Vibration mitigation of an MDoF system subjected to stochastic loading by means of hysteretic nonlinear locally resonant metamaterials

In this paper, we intend to mitigate absolute accelerations and displacements in the low-frequency regime of multiple-degrees-of-freedom fuel storage tanks subjected to stochastic seismic excitations. Therefore, we propose to optimize a finite locally resonant metafoundation equipped with massive resonators and fully nonlinear hysteretic devices. The optimization process takes into account the stochastic nature of seismic records in the stationary frequency domain; the records are modelled with the power spectral density S0 and modified with a Kanai–Tajimi filter. Moreover, the massive superstructure of a fuel storage tank is also considered in the optimization procedure. To optimize the nonlinear behaviour of dampers, we use a Bouc–Wen hysteretic model; the relevant nonlinear differential equations are reduced to a system of linear equations through the stochastic equivalent linearization technique. The optimized system is successively verified against natural seismic records by means of nonlinear transient time history analyses. Finally, we determine the dispersion relations for the relevant periodic metafoundation.

An agile very low frequency radio spectrum explorer

The very low frequency (VLF) regime below 30 MHz in the electromagnetic spectrum has presently been drawing global attention in radio astronomical research due to its potentially significant science outcomes exploring many unknown extragalactic sources, transients, and so on. However, the nontransparency of the Earth’s ionosphere, ionospheric distortion and artificial radio frequency interference (RFI) have made it difficult to detect the VLF celestial radio emission with ground-based instruments. A straightforward solution to overcome these problems is a space-based VLF radio telescope, just like the VLF radio instruments onboard the Chang’E-4 spacecraft. But building such a space telescope would be inevitably costly and technically challenging. The alternative approach would be then a ground-based VLF radio telescope. Particularly, in the period of post 2020 when the solar and terrestrial ionospheric activities are expected to be in a ‘calm’ state, it will provide us a good chance to perform VLF ground-based radio observations. Anticipating such an opportunity, we built an agile VLF radio spectrum explorer co-located with the currently operationalMingantu Spectra Radio Heliograph (MUSER). The instrument includes four antennas operating in the VLF frequency range 1–70 MHz. Along with them, we employ an eight-channel analog and digital receivers to amplify, digitize and process the radio signals received by the antennas. We present in the paper this VLF radio spectrum explorer and the instrument will be useful for celestial studies of VLF radio emissions.

Optical signatures of shear collective modes in strongly interacting Fermi liquids

The concept of Fermi liquid lays a solid cornerstone to the understanding of electronic correlations in quantum matter. This ordered many-body state rigorously organizes electrons at zero temperature in progressively higher momentum states, up to the Fermi surface. As such, it displays rigidity against perturbations. Such rigidity generates Fermi-surface resonances which manifest as longitudinal and transverse collective modes. Although these Fermi-liquid collective modes have been analyzed and observed in electrically neutral liquid helium, they remain unexplored in charged solid-state systems up to date. In this paper I analyze the transverse shear response of charged three-dimensional Fermi liquids as a function of temperature, excitation frequency and momentum, for interactions expressed in terms of the first symmetric Landau parameter. I consider the effect of momentum-conserving quasiparticle collisions and momentum-relaxing scattering in relaxation-time approximation on the coupling between photons and Fermi-surface collective modes, thus deriving the Fermi-liquid optical conductivity and dielectric function. In the high-frequency, long-wavelength excitation regime the electrodynamic response entails two coherent and frequency-degenerate polaritons, and its spatial nonlocality is encoded by a frequency- and interaction-dependent generalized shear modulus; in the opposite high-momentum low-frequency regime anomalous skin effect takes place. I identify observable signatures of propagating shear collective modes in optical spectroscopy experiments, with applications to the surface impedance and the optical transmission of thin films.