Low-frequency Regime Research Articles

Incompressible limit for the compressible viscoelastic fluids in critical space

Abstract In this article, we consider the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the compressible viscoelastic fluids in the sense of critical Besov framework. We decouple our compressible system into two coupling sub-systems by introducing a skew symmetric matrix, which is related to the deformation tensor. This work generalizes the similar result obtained by Hu et al. (Incompressible limit for compressible viscoelastic flows with large velocity, Advances in Nonlinear Analysis 12 (2023), 20220324) to the critical functional space with respective to the natural scaling of the system. The proof relies on the dispersive property of the linear system on the high-frequency regime and the parabolic property on the low-frequency regime. The dispersion tends to disappear when λ \lambda tends to infinite, but having large λ \lambda provides strong dissipation on the potential part of the velocity and thus makes the flow almost incompressible. In addition, by exploiting the intrinsic structure of the viscoelastic system, we obtain the global uniform estimates of the solutions near equilibrium.

Turbulence scale and strength analysis in the roughness and inertial sublayers over urban areas: A wind tunnel study

The dissimilarity of dynamics and turbulence structures between the roughness and inertial sublayers (RSL, ISL) over roughness elements show that ISL turbulence is much more homogeneous. Conventional logarithmic law of the wall is merely applicable for the RSL mean-wind-speed profiles. To characterize the turbulence scales and elucidate the mechanism, the flows in the atmospheric surface layer (ASL) over real urban morphology are measured in wind tunnel experiments fabricated by 3D-printing, reduced-scale model of downtown Kowloon Peninsula, Hong Kong. Elevated dispersive stress at urban canopy signifies the influence from individual buildings and inhomogeneous RSL flows. A positive momentum contribution appears in the low-frequency regime. The large-scale turbulence in RSL thus enhances the mixing and transport, resulting in inhomogeneous flows. The contribution from ejection Q2 and sweep Q4 increases and decreases, respectively, with increasing RSL motion strength. The conventional −5/3 law is observed by empirical mode decomposition (EMD) and the largest amplitude fluctuation occurs more often when the turbulence length scale is comparable to the turbulent boundary layer (TBL) thickness. The single-point amplitude modulation (AM) shows that the large- and small-scale turbulence correlates tightly at the bottom of RSL. Besides, the joint probability density function (JPDF) illustrates that accelerating large scales often occur with decelerating small scales, and they are intensified with increasing wall-normal distance. As a result, large-scale turbulence influences substantially the flow structures over urban areas and the small-scale turbulence (even) in RSLs in the vicinity of building obstacles.

Enhanced high-frequency continualization scheme for inertial beam-lattice metamaterials

A multifield continualization technique is introduced that offers a thermodynamically consistent description of the constitutive and dispersive properties of beam-lattice inertial metamaterials with periodic microstructures. The balance equations governing the mechanics of the discrete Lagrangian system are appropriately handled using an innovative continualization scheme to derive an equivalent integral-type continuum model. Based on formal Taylor series expansion of the integral kernels or the corresponding pseudo-differential functions incorporating shift operators and appropriate pseudo-differential downscaling laws, the proposed multifield enhanced continualization scheme allows the derivation of a gradient-type continuum model of given rank and equivalent to lattices. Two different resolution techniques are proposed. Firstly, the corresponding infinite-order average differential equations are tackled using a perturbative approach to describe the forced Bloch wave propagation in the metamaterial. Secondly, higher-order continuum models are employed through proper differential equation truncation to characterize the dispersive properties of the metamaterial in both high- and low-frequency regimes. Moreover, an energetically consistent generalized equivalent Micropolar continua, with non-local inertial terms, are here identified. The multifield continualization procedure is applied to two-dimensional periodic microstructures with tetrachiral, hexachiral, and hexa-tetrachiral topologies. Illustrative examples highlight the ability of the equivalent continuum model to accurately describe the effective constitutive properties of inertial metamaterials with periodic microstructures and to define a dynamic response consistent with the discrete Lagrangian model, validated and tested through virtual experimental verification under free and forced wave conditions.

Internal transport barrier triggered by phase synchronization of zonal flow with energetic particle modes

Abstract The suppression of the microturbulence associated
to the emergence of a spontaneous internal transport barrier has been
recently demonstrated in a system showing a possible amplification
of the zonal flow component in the low-frequency regime $\left[\right.$A.
Ghizzo and D. Del Sarto D 2023 \textit{Nucl. Fusion}
\textbf{63} 104002$\left.\right]$.
We use here numerical experiments performed with a ``particle mode''
model based on a double average over the fast cyclotron phase
and over the bounce (or transit) phase to show the major role played
by energetic particles and shear flows in this scenario. \textquotedbl Particle
modes\textquotedbl{} are meant here as classes of particles, identified
by some adiabatic invariant after a gyro-average procedure, which
are associated to the description of some specific linear modes of
the plasma. The introduction of energetic circulating ions or shear
flows into the system makes a larger number of particle modes being
involved in the synchronization process. A global synchronization
of the Fourier modes of the turbulent spectrum can be this way achieved.
This process allows for a bifurcation towards self-organization, which
is associated to the emergence of a staircase-like structure. This
is known to be an essential element in the modification of the zonal
flow pattern in phase space during the suppression of microturbulence
in tokamaks.

Optical effects in unmagnetized cold plasmas by a chiral axion factor

Abstract Unmagnetized cold plasma modes are investigated in the context of the chiral Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics, where the axion chiral factor acts retrieving some typical properties of magnetized plasmas. The Maxwell equations are rewritten for a cold, uniform, and collisionless fluid plasma model, allowing us to determine the dispersion relation, new refractive indices, and propagating modes. We find four distinct refractive indices modified by the purely timelike CFJ background that plays the magnetic conductivity chiral parameter role associated with right-circularly polarized (RCP) and left-circularly polarized (LCP) waves. For each refractive index, the propagation and absorption zones are determined and illustrated for some specific parameter values. Modified RCP and LCP helicons are found in the low-frequency regime. The optical behavior is investigated, revealing that the chiral factor induces birefringence, measured in terms of the rotatory power (RP). The dichroism coefficient is carried out for the absorbing zones. The negative refraction zones may enhance the involved RP, yielding RP sign reversion, a feature of rotating plasmas and MCFJ chiral plasmas. Charge density oscillations and Langmuir waves are also discussed, revealing no modified dispersion relation due to the chiral axion factor.

Susceptibility to Low-Frequency Breakdown in Full-Wave Models of Liquid Crystal-Coaxially-Filled Noise-Shielded Analog Phase Shifters

Building on the fully encapsulated architecture of liquid crystal (LC) coaxial phase shifters, which leverages noise-shielding advantages for millimeter-wave wideband reconfigurable applications, this study addresses the less-explored issue of low-frequency breakdown (LFB) susceptibility in modern full-wave solvers. Specifically, it identifies the vulnerability nexus between the tuning states (driven by low-frequency bias voltages) and the constitutive elements of LC-filled coaxial phase shifters—namely, the core line, housing grounding, and radially sandwiched tunable dielectrics—operating at millimeter-wave frequencies (60 GHz WiGig), microwave (1 GHz), and far lower frequency regimes (down to 1 MHz, 1 kHz, and 1 Hz) for long-wavelength or quasi-static conditions, with specialized applications in submarine communications and geophysical exploration. For completeness, the study also investigates the device state prior to LC injection, when the cavity is air-filled. Key computational metrics, such as effective permittivity and characteristic impedance, are analyzed. The results show that at 1 kHz, deviations in effective permittivity exceed four orders of magnitude compared to 1 GHz, while characteristic impedance exhibits deviations of three orders of magnitude. More critically, in the LFB regime, theoretical benchmarks from 1 MHz to 1 kHz and 1 Hz demonstrate an exponential increase in prediction error for both effective permittivity, rising from 16.8% to 1.5 × 104% and 1.5 × 107%, and for characteristic impedance, escalating from 8.1% to 1.15 × 103% and 3.9 × 104%, respectively. Consequently, the prediction error of the differential phase shift, minimal at 60 GHz (0.16%), becomes noticeable at 1 MHz (4.39%), increases sharply to 743.88% at 1 kHz, and escalates dramatically to 2.18 × 1010% at 1 Hz. The findings reveal a pronounced frequency asymmetry in LFB susceptibility for the LC coaxial phase shifter biased at extremely low frequencies.

High Frequency Gravitational Wave bounds from galactic neutron stars

High-Frequency Gravitational Waves (HFGWs) constitute a unique window on the early Universe as well as exotic astrophysical objects. While the current gravitational wave experiments are more dedicated to the low frequency regime, the graviton conversion into photons in a strong magnetic field constitutes a powerful tool to probe HFGWs. In this paper, we show that neutron stars, due to their extreme magnetic field, are a perfect laboratory to study the conversion of HFGWs into photons. Using realistic models for the galactic neutron star population, we calculate for the first time the expected photon flux induced by the conversion of an isotropic stochastic gravitational wave background in the magnetosphere of the ensemble of neutron stars present in the Milky Way. We compare this photon flux to the observed one from several telescopes and derive upper limits on the stochastic gravitational wave background in the frequency range 108 Hz–1025 Hz. We find our limits to be competitive in the frequency range 108 Hz–1012 Hz.

Holographic zero sound for [formula omitted] SCFTs in 4d

We build up the notion of metallic holography for N=2 SCFTs in four dimensions, in the presence of a finite U(1) chemical potential. We compute two point correlation functions and study their properties in the regime of low frequency and low momentum. The color sector reveals gapless excitations, one of which propagates with a finite phase velocity while the other mode attenuates through scattering. The flavour sector, on the other hand, reveals spectrum that contains quasiparticle excitations which propagate with a definite phase velocity together with modes that propagate with a finite group velocity which quantum attenuates quite similar in spirit as that of Landau's zero sound modes. We also compute associated AC conductivities, which exhibit different characteristics for different (color and flavour) sectors of N=2 SCFTs.

High bulk modulus pentamodes: the three-dimensional metal water

Despite significant advances in the field of phononic crystals, the development of acoustic metafluids that replicate the behaviour of liquids in three dimensions remains elusive. For instance, water – the quintessential pentamode (PM) material – has a bulk modulus two orders of magnitude higher than current state-of-the-art PMs. The need for a low shear modulus inherently conflicts with the desire of high bulk modulus and density. In this letter, we shed light on the limitations of existing PM geometries and propose an innovative shape for the links that constitute the network. Inspired by the kinematics of ropes, these links are constructed from thin fibres and demonstrate the potential to create PMs with properties akin to those of liquids. As a prime example, we propose the design of the first metamaterial that fully deserves the name 3D metal water, since its acoustic properties in the low frequency regime are indistinguishable from water. Additionally, we highlight a shear band gap in the lattice dispersion diagram, and illustrate the influence of geometric parameters on the dynamic properties at higher frequencies. This novel design of metafluids holds promise for applications requiring anisotropic materials such as acoustic lenses, waveguides, and cloaks.

(General Student Poster Award Winner, 3rd Place) Designing and Evaluating Microelectrodes for Molten Salt Corrosion Electrochemistry

Due to the coupling of high temperature operation (>500°C) and propensity to contain oxidizing impurities (e.g., moisture, metallic cations), corrosion of structural alloys in molten chloride and fluoride salts is a major concern among developers of Generation IV nuclear reactors. To mitigate corrosion, it is essential to understand the corrosion mechanism and accurately determine its rate. Prior studies employ a forensic approach for corrosion testing, which does not provide insights on instantaneous rate of corrosion [1]. The use of electrochemical impedance spectroscopy (EIS) can provide in-operando method to interrogate dissolution processes. However, due to the high electrical conductivity and double-layer capacitance of metal salt interface [2], low frequency regimes normally dominated by polarization resistance (Rp) in aqueous systems require data acquisition at low frequencies. (<10-3 Hz). This renders access to charge-transfer resistance (Rct) and diffusional impedance effects difficult. This difficulty is compounded by issues such as signal noise associated with the use of long cables in conventional molten salt corrosion cells [2].To overcome this challenge, a working electrode may be designed as a 2D microdisk electrode to was used to interrogate the low-frequency impedance regimes. This disk has a non-uniform current distribution at such low Wagner number but it is easier to access the charge transfer and/or diffusional impedance regime, otherwise unattainable with the conventionally used partially immersed 3D macro-electrodes utilized in most studies [3]. In this work, a flush mounted microdisk electrode, compatible for use in molten LiF-NaF-KF (i.e., FLiNaK) salts at 600°C was designed and evaluated for its effectiveness towards accurately determining Rp through the EIS method. Pure Cr was selected as the model working electrode since its corrosion behavior in FLiNaK at 600°C has been thoroughly investigated [4,5,6],. Cr microdisks, with areas ranging from 100 to 10-2 cm2, were fabricated and subsequently exposed in FLiNaK containing 1 wt.% of EuF3 at 600°C for 24 hrs. EIS measurements were carried out over the commonly utilized frequency range from 105 to 10-2 Hz. Moreover, the error introduced by implementing various low “cut off” frequencies was examined. Acknowledgment Research is primarily supported as part of the fundamental understanding of transport under reactor extremes (FUTURE), an Energy Frontier Research Center (EFRC) funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES). This work was performed in the Department of Materials Science and Engineering (DMSE) in the Center for Electrochemical Science and Engineering (CESE) at the University of Virginia. Utilization of the Malvern-Panalytical Empyrean diffractometer was supported by Nanoscale Materials Characterization Facility (NMCF) with National Science Foundation (NSF) under award CHE-2102156. H.C. acknowledges the National Science Foundation Graduate Research Fellowship (GRFP), GRANT#: 1842490.

New implicit time integration schemes for structural dynamics combining high frequency damping and high second order accuracy

The time integration schemes, GA-23 and GA-234, recently proposed by the authors for first order problems, are extended to solve second-order problems in structural dynamics. The resulting methods maintain unconditional stability and user-controlled high-frequency damping. They offer improved accuracy and exhibit less numerical damping in the low-frequency regime, outperforming the well-known generalised-α method. When the high-frequency damping is maximised the new schemes can be cast in the format of backward difference formulae, offering more accurate alternatives to the standard second order formula. The effectiveness of the new time integration schemes is validated through a number of numerical examples, including a linear elastic cantilever beam, a nonlinear spring pendulum, and wave propagation on a string.

Magnetic behavior of manganese doped aluminum iron oxide

This paper reports the structural and magnetic properties of undoped and manganese doped aluminum iron oxide. The samples were prepared through a conventional solid-state reaction route using the planetary ball milling technique. The XRD profile showed a body centered tetragonal crystalline behavior in a perovskite structure. The field emission scanning electron microscopy images displayed segregated grain into different clusters. The significant magnetic loss tanδ is marked for the manganese doped aluminum iron oxide, which may dissipate as heat radiation and subsequently make it suitable in thermomagnetic devices for medical related research. The well-resolved peaks as observed in the absorption of the imaginary part of the magnetic modulus correspond to the spin resonance. The characteristic frequency is detected to shift rightward and signifying the lone presence of spin rotations in the high-frequency regime. The magnitude of the imaginary part of magnetic modulus increases with both the milling time and Mn content. This implies the more absorption of magnetic energy from the alternating magnetic field that in turn leading to decrease spin rotations and follows the decreasing trend in the grain size. The release of substantial amount of heat associated with the significant magnetic loss tanδ is noticed for the sample AFMO-3 h that mark it as a suitable candidate for thermotherapy in the low-frequency regime, which may be asserted as the novelty of this study. The semicircles in their Nyquist plots represent the single magnetic relaxation of the samples and thus, an equivalent circuit may be assumed consisting of inductance and resistance in series.

Hierarchical meta-porous materials as sound absorbers

The absorption of sound has great significance in many scientific and engineering applications, from room acoustics to noise mitigation. In this context, porous materials have emerged as a viable solution towards high absorption performance and lightweight designs. However, their performance is somewhat limited in the low-frequency regime. Inspired by the concept of recursive patterns over multiple length scales, typical of many natural materials, here, we propose a hierarchical organization of multilayered porous media and investigate their performance in terms of sound absorption. Two types of designs are considered: a hierarchical periodic (HP) and a hierarchical gradient (HG). In both cases, it is found that in some frequency ranges the introduction of multiple levels of hierarchy simultaneously allows for: (i) an increase in the level of absorption compared with the corresponding bulk block of porous material (or to the previous hierarchical levels (HLs)), and (ii) a reduction in the quantity of porous material required. Another advantage of using this approach is on the fabrication, since only one porous material is required. The performances are examined for both normal and oblique incidences, as well as for different values of the static air-flow resistivity. The methodological approach is based on the transfer-matrix method, optimization algorithms such as the metaheuristic greedy randomized adaptive search procedure (GRASP), finite-element calculations and measurements performed in an impedance tube.

Numerical investigation on the effect of an orifice plate on the flow-induced and acoustically induced vibration of a gas transmission pipe

In this paper, a numerical method is proposed for investigating the flow-induced vibration (FIV) and acoustically induced vibration (AIV) of a straight pipe with an orifice plate. First, the turbulent pressure (TP) and acoustic pressure (AP) signals on the pipe wall were obtained through the simulation of an unsteady flow field and the application of Mohring's analogy, respectively. Subsequently, the FIV and AIV of the pipe were calculated by means of one-way fluid-structure interaction and acoustic-structure interaction, respectively. The calculated pressures, flow velocities, and sound powers at the monitoring point were in good agreement with the experimental results reported in the literature. The numerical results revealed that the power spectral densities of the AP were significantly higher than those of the TP on the surface of the tested end pipe, particularly at the natural frequencies of the acoustic modes. In the low-frequency regime, FIV was the dominant factor, whereas in the medium-high frequency regime, particularly above the cutoff frequency of the plane wave, AIV was the dominant factor. The findings of the parametric studies demonstrated that the AP and AIV of the pipe exhibited a considerable increase with the Mach number. Conversely, the TP and FIV demonstrated a more pronounced rise when the Mach number increased from 0.1 to 0.2, followed by a less pronounced increase when the Mach number increased from 0.2 to 0.3. A reduction in the orifice diameter resulted in an increase in the AP and AIV. In contrast, the TP and FIV exhibited a comparatively minor increase.

Metabarriers for mitigating traffic-induced surface waves: Mechanism dependence on buried arrangements

Locally resonant metamaterials provide exceptional wave manipulation capabilities in the low-frequency regime. This study introduces a buried metabarrier, which can simultaneously harness both resonant and geometric scatterings, to attenuate surface Rayleigh waves at both low and high frequencies induced by traffic. In particular, how the buried arrangements of metabarriers influence their resonant- and geometric-scattering mechanisms is investigated by considering the metabarrier units buried vertically and horizontally in the ground. To this purpose, a numerical finite element model, which is verified through comparisons with existing studies, is developed to analyze the attenuation performance of the metabarrier. Using this model, we perform parametric studies to examine the effects of the material properties and dimensions of the metabarriers on their attenuation behavior. Due to resonant scattering, low-frequency Rayleigh waves are mainly reflected by the vertical metabarriers; in contrast, they are predominantly converted into refracted bulk waves by the horizontal metabarriers. Additionally, the geometric scattering of horizontal metabarriers yields Bragg effects, which can reflect more high-frequency Rayleigh waves and induce a partial mode conversion to transverse bulk waves. Our systematic investigations will, to some extent, facilitate the future design of a well-performing metabarrier attenuating broadband Rayleigh waves.

Overlooked Ionic Contribution of a Chiral Dopant in Cholesteric Liquid Crystals.

This study focuses on the ionic contribution by a chiral dopant added into a nematic host for preparing cholesteric liquid crystals (CLCs). Chiral structures were designated by individually incorporating two enantiomers, R5011 and S5011, into the nematic E44 to construct right- and left-handed CLCs, respectively. Characterized by the space-charge polarization, the dielectric spectra of the CLCs were investigated in the low-frequency regime, where f ≤ 1 kHz. The role of the individual chiral dopant, R5011 or S5011, at concentrations of 0-4.0 wt.% in altering the ionic properties of the CLC material was analyzed by deducing the electrical conductivity, ion density, and ion diffusivity. Regardless of the cell structure to be antiparallel or twisted by 90°, a significant ionic response was observed in the right-handed CLCs in comparison with the left-handed counterparts, suggesting that excess ions originating from our R5011 were introduced into the mesogenic mixtures. This work alarms the potential contribution of notorious impurity ions by a chiral dopant, which is often ignored in fabricating CLCs for electro-optical applications.

Utilizing polydispersity in three-dimensional random fibrous based sound absorbing materials

The distribution of fiber diameters plays a crucial role in the transport and sound absorbing properties of a three-dimensional random fibrous (3D-RF) medium. Conventionally, volume-weighted averaging of fiber diameters has been utilized as an appropriate microstructural descriptor to predict the static viscous permeability of 3D-RF media. However, the long wavelength acoustical properties of a 3D-RF medium are also sensitive to the smallest fibers, this is particularly true in the high-frequency regime. In our recent research, we demonstrated that an inverse volume-weighted averaging of fiber diameters can effectively serve as a complementary microstructural descriptor to capture the high-frequency behavior of polydisperse fibrous media. In the present work, we reexamine the identification of two representative volume elements (RVEs) which relies on the reconstruction of 3D-RF microstructures having volume-weighted and inverse-volume weighted averaged fiber diameters, respectively in the low-frequency and high frequency regimes. We investigate the implication of such a weighting procedure on the transport and sound absorbing properties of polydisperse fibrous media, highlighting their potential advantages. Furthermore, we discuss the challenges associated with this research field. Finally, we provide a brief perspective of the future directions and opportunities for advancing this area of study.

Dynamical tidal Love numbers of Kerr-like compact objects

We develop a framework to compute the tidal response of a Kerr-like compact object in terms of its reflectivity, compactness, and spin, both in the static and the frequency-dependent case. Here we focus on the low-frequency regime, which can be solved fully analytically. We highlight some remarkable novel features, in particular, the following: (i) Even in the zero-frequency limit, the tidal Love numbers (TLNs) depend on the linear-in-frequency dependence of the object’s reflectivity in a nontrivial way. (ii) Intriguingly, although the static limit of the (phenomenologically more interesting) frequency-dependent TLNs is continuous, it differs from the strictly static TLNs for compact objects other than black holes. This shows that earlier findings regarding the static TLNs of ultracompact objects correspond to a measure-zero region in the parameter space, though the logarithmic behavior of the TLNs in the black hole limit is retained. (iii) In the nonrotating case, the TLNs in the zero-frequency limit (just like for a black hole), except when the reflectivity is R=1+O(Mω), in which case they vanish with a model-dependent scaling, which is generically logarithmic, in the black-hole limit. The TLNs initially grow with frequency, for any nonzero reflectivity, and then display oscillations and resonances tied up with the quasinormal modes of the object. (iv) For rotating compact objects, the TLNs decrease when the reflectivity decreases or the rotation parameter increases. Our results lay the theoretical groundwork to develop model-independent tests of the nature of compact objects using tidal effects in gravitational-wave signals. Published by the American Physical Society 2024

Electron microscopy of seismic waves.

Changes in the surrounding environment, if transmitted to the electron microscope, are frequently perceived as noise that diminishes the quality of the images. However, in fact, 'noises' contain rich information about the environment. This work reports a very rare event where aberration-corrected HAADF-STEM images were acquired during the impact of seismic waves, resulted from a mild earthquake. By analysing these images, we found that the drift and vibration of the sample are detectable and quantifiable. Despite many potential challenges, this work demonstrates the utilisation of electron microscopes in detecting and monitoring seismic waves with high spatial resolution, which may lead to unique applications in the low-frequency regime.

Centrifugal pump impeller wheel inspired acoustic metamaterial for low frequency sound absorption

Addressing low-frequency noise is a significant concern within the realm of acoustics and noise management. Labyrinthine channel based acoustic metamaterials have been proved to control low frequency noise using local resonance effect and thermoviscous dissipations. Drawing inspiration from centrifugal pump impeller wheel, an acoustic metamaterial absorber has been devised. The design incorporates impeller vanes to create a channel with variable widths and a micro-perforate panel through which sound wave propagates to the channels. Numerical simulations using COMSOL Multiphysics and experimental analysis are conducted employing Two microphone impedance tube method. Acoustic pressure and acoustic particle velocity distribution plots from numerical simulation study are used to comprehend the sound absorption mechanism. Sound absorption coefficient results reveal that this design offers a tunable sound absorption peak in low frequency regime. Furthermore, this paper discusses the influence of various geometric parameters such as, number of vanes, panel thickness and micro-hole diameter. The subwavelength dimensions of the design contribute to noise control in machineries with space constraints.