Low-frequency Regime Research Articles

Effect of Salt on Dynamic Mechanical Behaviors of Polyampholyte Hydrogels

Understanding the dynamic mechanical behaviors of tough hydrogels with ionic dynamic bonds in saline solution is crucial for applications, particularly in the biomedical field. In this work, using polyampholyte hydrogels, dually crosslinked with a primary network from covalent crosslinkers and/or trapped entanglements, and a dynamic network from ionic bonds, as a model system, we investigate the salt effect on rheological response and mechanical behaviors. Through a systematic study on one gel without a chemical crosslinker and one gel with a chemical crosslinker, we demonstrate that the salt effect on mechanical properties, including small-strain moduli, large deformation energy dissipation, and fracture stretch ratio, can be effectively converted into frequency or strain rate dependences following the time–salt superposition principle. Accordingly, we access a wide range of observation time scales from 10–11 to 102 rad/s at room temperature, covering three regimes: (I) the high-frequency plateau regime from the dynamic and primary networks, (II) the viscoelastic regime from sticky Rouse motion of ionic associations, and (III) the low-frequency plateau regime from the primary network. Moreover, we disclose an in-depth understanding of the entanglement’s behavior in the long-timescale regime III. This work not only provides a guide to biological applications of hydrogels in saline environments but also gives important insights into the toughening mechanism via dynamic bonds in other systems with dually crosslinked structures.

Uncertainty quantification and global sensitivity analysis of seismic metabarriers

Seismic metabarriers consist of an array of locally resonant elements (i.e., mechanical resonators) installed over the soil surface, whose design is rationally engineered to reduce ground-induced vibrations and shield vulnerable structures against seismic surface waves. Successful design and implementation of seismic metabarriers require a comprehensive knowledge and characterization of the role played by the model parameters (and their associated uncertainty) governing soil-barrier dynamic interaction. In this context, sensitivity analysis techniques allow assessing the response of a given model through the quantification of the influence and action of model inputs (and model input uncertainties) concerning a target model output. This study relies on global sensitivity analysis techniques to investigate the influence that the uncertainty associated with three key mechanical parameters of a metabarrier (i.e., soil density, soil shear modulus, and mass of mechanical resonators) has on its seismic isolation performance. The latter is measured in terms of transmission coefficient (TC). We do so by employing a two-dimensional wave finite element model developed under the plane-strain conditions to evaluate the dispersion relation and transmission coefficient of a metabarrier interacting with Rayleigh waves in the low-frequency regime (i.e., frequencies between 2 Hz and 7 Hz). Our results suggest that the shear modulus is the uncertain parameter with the most significant influence on the transmission coefficient of the metabarrier across the entire frequency range of interest. Otherwise, the resonator mass plays a substantial role in the frequency range close to the metabarrier resonant frequency.

The enhanced multifunctional behavior in G-type antiferromagnetic BiFeO3 due to the modification by MgTiO3

We have opted for modifying/mixing the conventional BFO multiferroic by Mg-based structure MgTiO3, resulting in the given structural form as (BiFeO3)0.6 (MgTiO3)0.4. The structural distortions from the spin cycloid rhombohedral structure for pure BFO to the orthorhombic arrangement were verified, both from the POWD and Rietveld analysis of the XR-Diffraction database, specifically being transformed to the space group: Pbnm. High εr values, specifically at low-frequency regimes unclog the ceramic's high electric storage ability, which might be as the layered capacitor. Observation of saturated low tangent dielectric loss (tanδ) at higher frequency suggests the compound's applicability for microwave-related applications. It was perceived from the temperature-dependent CIS study that the sharpness of the relaxation mechanism enhances following the contraction in ImZ curves. The fall in the maxima height of the ImZ curves with temperature rise indicates the reduction in the magnitude of (jωC)−1 . The rising peak heights of the M″ curves with rising temperature evince the dominance of long-range thermal conductivities in the solid complex. The optical band gap was found to be tapered relative to the host (BiFeO3), making it a potential candidate for optoelectronics applicability. The Cole-Cole plots suggest the sample's semiconducting feature, together with some non-Debye characteristics induced by electrode-surface irregularities. Weak leakage conduction was observed from the J-E curve, together with a non-linear (non-ohmic) response. The induction of weak ferromagnetism and enhanced saturation trend in the M − H curve suggests partial suppression in the spin cycloid AFM arrangements, brought in by a factor such as bond angle depression between the adjacent ferrite ions.

Modal analysis of electromagnetic resonators: User guide for the MAN program

All electromagnetic systems, in particular resonators or antennas, have resonances with finite lifetimes. The associated eigenstates, also called quasinormal modes, are essentially non-Hermitian and determine the optical responses of the system. We introduce MAN (Modal Analysis of Nanoresonators), a software with many open scripts, which computes and normalizes the quasinormal modes of virtually any electromagnetic resonator, be it composed of dispersive, anisotropic, or non-reciprocal materials. MAN reconstructs the scattered field in the basis formed by the quasinormal modes of the resonator and provides a transparent interpretation of the physics.The software is implemented in MATLAB and has been developed over the past ten years. MAN features many toolboxes that illustrate how to use the software for various emblematic computations in low and high frequency regimes. A specific effort has been devoted to interface the solver with the finite-element software COMSOL Multiphysics. However, MAN can also be used with other frequency-domain numerical solvers. This article introduces the program and summarizes the relevant theoretical background. MAN includes a comprehensive set of classical models and toolboxes that can be downloaded from the web. Program summaryProgram title: MAN (Model Analysis of Nanoresonators)CPC Library link to program files:https://doi.org/10.17632/wdz5pd4sb4.1Licensing provisions: GNU General Public License 3Developer's repository link:https://doi.org/10.5281/zenodo.7400937Programming language: MatlabNature of problem: Compute and normalize the quasinormal modes of resonators and antennas of any type, be they composed of dispersive, anisotropic, or non-reciprocal materials, or be they operated at high or low frequencies. Use the quasinormal modes to reconstruct the resonator responses in the near field and far field.Solution method: Two methods are gathered. The quasinormal modes are computed and normalized either by solving the linearized Maxwell equations or searching poles in the complex frequency plane. The reconstruction is then performed analytically with closed form expressions of the excitation coefficients. A presentation of the software capabilities is found in the video (https://www.youtube.com/watch?v=SOdQsXdBGv0). To see how to use the software, please also watch the demo (https://www.youtube.com/watch?v=BSf9A1qyUBE).

Hydrodynamic Low-Frequency Regimes of Unstable Combustion and Methods of Their Suppression in Low-Emission Combustors of Gas-Turbine Units

Hydrodynamic Low-Frequency Regimes of Unstable Combustion and Methods of Their Suppression in Low-Emission Combustors of Gas-Turbine Units

Microwave-activated gates between a fluxonium and a transmon qubit

We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual $ZZ$ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below $100\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above $99%$ can be obtained with gate times between 100 and $300\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.

Low-frequency vibrational states in ideal glasses with random pinning.

Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency ω_{BP}, and their vibrational densities of state follow g(ω)∝ω^{4} (ω is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of appearance below ω_{BP} and g(ω)∝ω^{4}. Our results provide important insight into the material properties of ideal glasses.

Light as a quantum back-action nullifying meter

We propose a new, to the best of our knowledge, method to overcome quantum back-action in a measurement process using oscillators. An optical oscillator is used as a meter to measure the parameters of another open oscillator. The optical oscillator is synthesized such that the optical restoring force counters any perturbations induced by the quantum back-action phenomena. As a result, it is shown that the quantum back-action in continuous measurement is suppressed in the low frequency regime, i.e., for frequencies much smaller than the resonance frequency of the open oscillator. As the meter plays the role of measuring parameters as well as suppressing the quantum back-action, we call it a quantum back-action nullifying meter. As an application of this method, synthesis of the quantum back-action nullifying optical oscillator for suppressing radiation pressure force noise in linear and non-linear optomechanics is described.

Dynamical conductivity of disordered quantum chains

We study the transport properties of a one-dimensional quantum system with disorder. We numerically compute the frequency dependence of the conductivity of a fermionic chain with nearest-neighbor interaction and a random chemical potential by using the Chebyshev matrix product state (CheMPS) method. As a benchmark, we investigate the noninteracting case first. Comparison with exact diagonalization and analytical solutions demonstrates that the results of CheMPS are reliable over a wide range of frequencies. We then calculate the dynamical conductivity spectra of the interacting system for various values of the interaction and disorder strengths. In the high-frequency regime, the conductivity decays as a power law, with an interaction-dependent exponent. This behavior is qualitatively consistent with the bosonized field theory predictions, although the numerical evaluation of the exponent shows deviations from the analytically expected values. We also compute the characteristic pinning frequency at which a peak in the conductivity appears. We confirm that it is directly related to the inverse of the localization length, even in the interacting case. We demonstrate that the localization length follows a power law of the disorder strength with an exponent dependent on the interaction, and find good quantitative agreement with the field theory predictions. In the low-frequency regime, we find a behavior consistent with the one of the noninteracting system omega ^{2}(ln omega )^{2} independently of the interaction. We discuss the consequences of our finding for experiments in cold atomic gases.Graphical abstract

KIC 6951642: A confirmed Kepler γ Doradus – δ Scuti star with intermediate to fast rotation in a possible single-lined binary system

Context. KIC 6951642 has been reported as a candidate hybrid pulsator of type-γ Doradus – δ Scuti from observations of the first quarters of the Kepler mission. The regular patterns seen in the Fourier spectra of the Kepler and Transiting Exoplanet Survey Satellite TESS light curves and the sinusoidal modulation of its surface brightness suggest the additional presence of rotational modulation and stellar activity, respectively. Aims. We aim to investigate the pulsating nature of KIC 6951642 and to search for the signature of rotation and/or activity in the light curves. Methods. We performed an iterative frequency search of both Fourier spectra, and searched for regular patterns in them. We applied spectrum synthesis to determine the atmospheric stellar parameters. Since KIC 6951642 was reported to belong to a spectroscopic binary system, we fitted the time delays derived from the light curves with the radial velocities obtained from published as well as new spectra in an attempt to improve the quality of the first orbit. Results. Follow-up spectroscopy showed that KIC 6951642 is a fast-rotating F0-type star in a possible single-lined binary with a period of ∼4.8 yr. In the low-frequency regime, we identified the frequencies of 0.721 d−1 as well as of 0.0087 d−1. We attribute the first frequency to stellar rotation, and the second one to stellar activity with a cycle of length of 3.2 yr. We also detected g modes, with the strongest mode located at 2.238 d−1, as well as three asymmetric multiplets (with a mean spacing of 0.675 ± 0.044 d−1). In the high-frequency regime, we detected frequencies of type-δ Scuti, with the strongest mode located at 13.96 d−1, as well as seven asymmetric multiplets (with a mean spacing of 0.665 ± 0.084 d−1). We subsequently identified a few more frequencies that appear to be combinations of a g or p mode and one of the higher cited frequencies not due to pulsations. Conclusions. We propose that KIC 6951642 accomadates for a fast-rotating γ Dor – δ Sct hybrid star with various rotationally split multiplets of g and p modes and that it also displays a cycle lasting years of (possible) stellar activity.

Millennial-scale climate variability over land overprinted by ocean temperature fluctuations

Variations in regional temperature have widespread implications for society, but our understanding of the amplitude and origin of long-term natural variability is insufficient for accurate regional projections. This is especially the case for terrestrial temperature variability, which is currently thought to be weak over long timescales. By performing spectral analysis on climate reconstructions, produced using sedimentary pollen records from the Northern Hemisphere over the last 8,000 years, coupled with instrumental data, we provide a comprehensive estimate of regional temperature variability from annual to millennial timescales. We show that short-term random variations are overprinted by strong ocean-driven climate variability on multi-decadal and longer timescales. This may cause substantial and potentially unpredictable regional climatic shifts in the coming century, in contrast to the relatively muted and homogeneous warming projected by climate models. Due to the marine influence, regions characterized by stable oceanic climate at sub-decadal timescales experience stronger long-term variability, and continental regions with higher sub-decadal variability show weaker long-term variability. This fundamental relationship between the timescales provides a unique insight into the emergence of a marine-driven low-frequency regime governing terrestrial climate variability and sets the basis to project the amplitude of temperature fluctuations on multi-decadal timescales and longer.

Lateral response of a layered material with interlayer friction

ABSTRACT We investigate the mechanical properties of a layered material with interlayer friction. We propose a model that contains lateral elasticity and interlayer friction to obtain the response function both in the Fourier and real spaces. By investigating how the internal deformation is laterally induced due to the applied surface displacement, we find that it is transmitted into the material with an apparent phase difference. We also obtain the effective complex modulus of the layered material and show that it exhibits an intermediate power-law behavior in the low-frequency regime. Our results can be used to estimate the internal deformation of layered materials that exists on various different scales.

A fractional nonlocal elastic model for lattice wave analysis

This paper investigates the link between lattice elasticity and nonlocal continuum mechanics from one-dimensional and multi-dimensional wave propagation problems. Eringen (1983) closed the bridge between one-dimensional linear lattice elasticity (called Lagrange lattice) and nonlocal elastic continuum. The Born-Kármán wave dispersive properties of the one-dimensional lattice are accurately fitted by Eringen's nonlocal differential elastic law using asymptotic or phenomenological arguments. A fractional version of Eringen's nonlocal model based on the introduction of a fractional Laplacian for the nonlocal differential operators can improve the accuracy in matching the wave dispersive curve of lattice dynamics. A multi-dimensional generalization of Lagrange lattice for cubic crystals is the lattice of Gazis et al. composed of central and angular interactions. We show in this paper that the differential Eringen's nonlocal elasticity differs from the lattice-based nonlocal elasticity continuum. In particular, Eringen's nonlocal elasticity preserves the isotropic property, whereas the cubic lattice is only isotropic in the low frequency regimes. The fractional generalization of Eringen's model accurately fitted the wave dispersive properties of the cubic crystal in the first Brillouin zone. The fractional generalization of Eringen's model highlights an isotropic response in the low frequency regimes and a cubic symmetry in the high frequency regime.

Spectral approaches in momentum space for dynamics of atoms in strong laser fields: application to long pulses and low-frequency regime

In this work, we present in detail a novel approach to solve the time-dependent Schrödinger equation in the momentum space (TDSE-). It is based on the expansion of the electron wavepacket and the nonlocal interacting Coulomb potential in a Coulomb Sturmian basis. It allows a spectral treatment of the TDSE- from which another formulation of our previous model potential is proposed. This latter enables us to go easily beyond the 1s + 2sp states, and accordingly, may help to have more insight on the role of the Coulomb potential or the atomic structure in the ionization process. In order to bring out the improvement of this approximation and as an illustration, the case of 3spd states supported by the Coulomb potential is derived analytically, leaving the other cases for later investigations. Physical observables such as oscillator strengths, bound states populations, ionization probabilities, energy spectra, momentum and energy-angle distributions, are described in detail and their formulas employed in our ab initio computations are given in compact matrix forms The calculations can be done either by using the ionized wave function or by projecting the wavepacket onto the incoming Coulomb wave function. For illustrative purpose, we apply these theories in the dipole approximation to two one-electron atomic targets initially prepared in the ground and excited electronic states, and driven by intense low-frequency electromagnetic fields. We consider several laser parameters for long pulses recently reported in the literature. Our results compare remarkably well with reference data of atomic structure, and their agreement with the atomic dynamics outcome of previous treatments is quite satisfactory.

Separation of binary gas mixture in a microchannel with oscillating barriers

The time-dependent flow of a neon–argon mixture in a microchannel interrupted by a row of oscillating barriers is numerically studied using the Direct Simulation Monte Carlo method in a range of Knudsen numbers from 0.1 to 10 and in a wide range of oscillation frequencies. The emphasis of the study is on the effect of mixture separation. It is demonstrated that in addition to a mid-frequency (“resonance”) regime, as discovered in the author's previous works [Kosyanchuk et al., “Numerical simulation of novel gas separation effect in microchannel with a series of oscillating barriers,” Microfluid. Nanofluid. 21, 116 (2017) and Kosyanchuk and Pozhalostin, “Non-stationary rarefied gas flow in a plane channel with a series of oscillating barriers,” Eur. J. Mech.-B/Fluids 92, 90–99 (2022)], two other enhanced separation regimes at very low and at very high oscillation frequencies are present. It is also demonstrated that the effect in the mid-frequency regime degrades with decreasing Knudsen number and is almost absent for Kn values around 0.1. The effect in the high-frequency regime is shown to be dictated both by the high frequency of barrier oscillations and by the high speed of barrier motion, and it is shown that with decreasing Knudsen number, the impact of barriers speed becomes dominant. The effect in the low-frequency regime is present for all Knudsen numbers and significantly depends on the phases of barrier motion, which is not observed in other regimes. The separation factor in the low-frequency regime also increases with the number of barriers but only up to the level of molecular diffusion. It was also shown that in the low-frequency regime, there is a trade-off between the separation factor and the gas flow rate.

Tunable Reflection Properties and Photonic Bandgap Behavior of a One-Dimensional Metamaterial-Superconductor-Based Ternary Photonic Crystal

In the present communication, we have investigated the tunable reflection properties and photonic bandgap variation of a one-dimensional metamaterial and superconductor based ternary photonic crystal. To design the 1D ternary photonic crystal, we have taken three alternate layers of metamaterial, superconductor (BSSCO), and silica (SiO2). Transfer matrix method (TMM) is employed to determine the optical reflection properties of the considered 1DPC for TE-mode by varying five parameters, viz. incident angle, superconductor temperature, thickness and refractive index of dielectric layer, and number of unit cells. It is noted that the ternary PC exhibits the features of tunable narrow band reflector, whose width increases with increase in the incident angle with a blue shift, and decreases with operating temperature of superconductor with red shift. It also enhances with increase in the dielectric layer thickness in low frequency region, and decreases in high frequency regime with red shifts. We obtain only one PBG at n3=1.46 in low frequency regime, while with increase in the refractive index multiple gaps are obtained in different frequency regions having distinct widths at n3=2.4 and 3.4. An increase in the number of unit cells causes increase in the reflectance, wherein no PBG is found below N=8. This analysis gives some insights to design tunable devices based on narrowband reflectivity in the terahertz frequency regime, including THz-metadevices, emitters, thermo-optical devices, and security sensors.

Time-reversal in phononic crystal-based water filled pipe

Time-reversal based source localization in a conventional water-filled pipe using acoustic waves is hamstrung by the diffraction limit (λ/2). In this paper, time reversal in a novel metamaterial-based water pipeline is studied where a conventional rigid pipe is modified to have periodic square corrugations. Based on the choice of periodicity, such a novel waveguide can support subwavelength resonance in the low frequency regime while exhibiting Bragg resonance, avoided crossing of modes and forbidden bands in diffraction regime. This paper focuses on the latter such that a band structure is obtained. Full wave simulation performed on COMSOL verifies the phononic crystal-like properties in the diffraction regime. Time reversal refocusing is performed by placing a point source in the middle of the corrugated section while a receiver outside the said section records the response of the system. The receiver acts as a Time Reversal Mirror (TRM) such that it flips and reinjects the recorded signal into the system which retraces its path and focuses on its source. Time-reversal refocusing is found to be sensitive to the recorded frequency grains in addition to the energy propagated from the source such that if the source encompasses a band gap, the time reversal quality deteriorates.

Sensitivity of acoustic parameters on the reflected signal from a rigid porous medium in the low-frequency range of ultrasound

Porous materials are two-phase media consisting of pores saturated with a fluid emerging from a solid skeleton. There are several parameters describing the porous medium. These parameters are classified into two categories: the high-frequency parameters and the low-frequency parameters. During the excitation by an acoustic wave, two cases can occur; the vibration of both phases simultaneously in the case where the structure is flexible, this case is well studied by Biot theory. For a rigid structure, it is the movement of the fluid that is taken into account; this last case is treated by the equivalent fluid theory which is a particular case of Biot theory. Previous work [Proc. Mtgs. Acoust. 45, 045004 (2021)] has shown the influence of the parameters involved in the corrected Johnson-Allard model recently introduced by Sadouki [Phys. Fluids 33, (2021)] on the transmitted signal from a rigid-porous material in the low-frequency regime of ultrasound. The objective of this work is to show, once again, the influence of the same parameters on the reflected signal by providing a comparative study between transmitted and reflected modes.

Omnidirectional acoustic cloaking against airborne sound realized by a locally resonant sonic material

We report that a locally resonant sonic material realizes omnidirectional acoustic invisibility in air. To achieve acoustic cloaking in the low-frequency regime, we axisymmetrically placed elastic rods comprised of silicone rubber and lead around a cloaked object. The radii of the rods are designed to minimize their total scattering cross section for a given frequency. The optimization is performed using an algorithm incorporating multiple scattering theory and gradient-based nonlinear programming. We numerically confirmed that the designed cloaking device suppressed the scattering cross section by almost 92% for all incident directions at the target frequency.

Frequency modes of unstable spiral waves in two-dimensional Rosenzweig–MacArthur ecological networks

The existence of two frequency regimes in a two-dimensional (2D) Rosenzweig–MacArthur ecological network is debated. The semi-discrete approximation differentiates the two regimes, each described by a 2D complex Ginzburg–Landau equation. Using the standard theory of the linear stability analysis, a generalized expression for the modulational instability growth rate is derived for each frequency mode. The parametric study of the growth rate of modulational instability reveals its sensitivity to the changes in the recruitment rate of the resources. Moreover, direct numerical simulations are carried out to confirm our analytical results. Over the prolonged evolution of the perturbed plane wave solution, the high-frequency mode entertains spiral wave patterns. In contrast, the appearance of target waves manifests the low-frequency regime. In that context, we further explore the impact of the recruitment rate of resources and give the qualitative meaning of the obtained dynamical behaviors and their ecological implications. This work may additionally provide more insight into the mechanism leading to spiral and target waves in environmental systems.