Low-frequency Regime Research Articles

Improved A-EFIE System for Electromagnetic Simulation in Low Frequency Regime

In this letter, the quasi-Helmholtz projectors are applied to address numerical cancellation of augmented electric field integral equation (A-EFIE). The projectors rescale the term <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\overline{\bf V} \cdot i{k}_0{\bf j}$</tex-math></inline-formula> and right-hand side to guarantee that the solution is stable at very low frequency. The improved system is full rank without removing the singularity caused by charge neutrality. Compared to the EFIE with quasi-Helmholtz projectors, this letter presents a better convergence performance and takes less computational cost. The numerical results show that the solution of both scattering problems and circuit problems can ensure the accuracy in the low-frequency regime.

Environmental context dependency in species interactions

Ecological interactions are not uniform across time and can vary with environmental conditions. Yet, interactions among species are often measured with short-term controlled experiments whose outcomes can depend greatly on the particular environmental conditions under which they are performed. As an alternative, we use empirical dynamic modeling to estimate species interactions across a wide range of environmental conditions directly from existing long-term monitoring data. In our case study from a southern California kelp forest, we test whether interactions between multiple kelp and sea urchin species can be reliably reconstructed from time-series data and whether those interactions vary predictably in strength and direction across observed fluctuations in temperature, disturbance, and low-frequency oceanographic regimes. We show that environmental context greatly alters the strength and direction of species interactions. In particular, the state of the North Pacific Gyre Oscillation seems to drive the competitive balance between kelp species, asserting bottom-up control on kelp ecosystem dynamics. We show the importance of specifically studying variation in interaction strength, rather than mean interaction outcomes, when trying to understand the dynamics of complex ecosystems. The significant context dependency in species interactions found in this study argues for a greater utilization of long-term data and empirical dynamic modeling in studies of the dynamics of other ecosystems.

Density of states below the first sound mode in 3D glasses.

Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses' unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes D(ω) depends on the frequency ω has been debated for decades. Recent simulation studies of 3D glasses suggest that D(ω) scales universally with ω4 in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated D(ω) below the first sound mode in 3D glasses over a wide range of frequencies. We find D(ω) scales with ωβ with β < 4 at very low frequencies examined, while the ω4 law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The ω4 law of D(ω) below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.

Spectral induced polarization monitoring of induced calcite precipitation in subsurface sediments

SUMMARY Co-precipitation of contaminants within the crystalline structure of calcite is a promising natural attenuation or remedial technology being considered at contaminated sites. We explore the sensitivity of the spectral induced polarization (SIP) method to induced calcite precipitation in natural sediments as a path forward to non-invasively monitor these sites. We performed time-lapse column experiments using phased (I–IV) injections over 40 d on natural sediments from the Hanford Site (WA, USA). In the phased injections, abiotic calcite precipitation was induced and confirmed to have occurred. Previous work on glass beads and homogeneous sand was limited to high frequency detection of calcite, however in this work we observed the development of two polarization mechanisms, one at high frequency (&amp;gt;100 Hz) and one at low frequency (&amp;lt;100 Hz). Based on the characteristic frequencies from the SIP high and low frequency regimes, characteristic length scales (L) were computed where the adsorption mode of Na+ versus Ca2+ was compared by using diffusion coefficients corresponding to Na+ versus an arithmetically averaged value for Na+ and Ca2+. Using the diffusion coefficient of Na+, the high frequency L was found to correlate well with the size of the calcite crystals. The low frequency L correlated well with the individual natural sediment grain sizes within the columns. During late experimental times (day 36 and 40), the characteristic low frequency in two of the experimental columns shifted to lower frequencies (&amp;lt;0.001 Hz) which may signify SIP sensitivity of the formed calcite with the sediment grains. In field applications, the development of a low frequency polarization length scale to monitor calcite precipitation is promising for field monitoring applications, however further laboratory work needs to be performed to examine the SIP sensitivity of calcite formation in the presence of natural sediments.

Complex impedance formalism: An alternative approach for exploration of relaxation dynamics in conductive materials

A new method, the complex impedance formalism, is presented to disclose the relaxation process of conducting materials. This method is an extrapolation of the dielectric modulus formalism in the Bode representation of the impedance. As in the dielectric modulus formalism, the relaxation process can be approached in both the frequency and time domains for non-Debye relaxation type. The complex impedance formalism is tested by analysis of the relaxation process of the solid BaTiO3 material at high temperatures. A combination of complex impedance and dielectric modulus formalism provides us with a better understanding concerning individual relaxation regions. The complex impedance formalism allows the hidden relaxation process at low frequency regime to be accessible, whereas the dielectric modulus formalism discloses the relaxation process at high frequency in mixed electronic-ionic conductors.

Temperature-activated dielectric relaxation in lead-free halide perovskite single crystals

Lead-free metal-halide perovskites have recently appeared as a promising candidate in optoelectronics and photovoltaics because of their non-toxicity, stability, and unique photophysical properties. Much scientific research has been done on optoelectronic characteristics and photovoltaic applications of lead-free perovskites, but the dielectric characteristics and insight into the relaxation phenomenon remain elusive. Here, we study the dielectric relaxation and conduction mechanism in the single crystalline (SC) A3Bi2X9 (A = MA+/FA+) perovskite using temperature-dependent electrochemical impedance spectroscopy in correlation with the modulus spectroscopy. With increasing temperature, the peak of −Z″(ω) shifts toward a high-frequency regime which specifies the thermally dependent relaxation mechanism in both crystals. The activation energy was estimated as 381 meV for MA3Bi2I9 (MBI) crystal and 410 meV for the FA3Bi2I9 (FBI) crystal suggesting hopping of mobile ions between lattice sites. The connected orientational polarization with the thermal motion of molecules leads to the enhancement in the dielectric constant (ϵ′) with temperature. The ϵ″(ω) in these crystals shows the significant ionic conductivity with a typical 1/fγ type characteristics (in the low-frequency regime) where γ is found to be in the range of 0.93–1.0 for MBI crystal and 0.88–0.98 for FBI crystal. The correlated imaginary part of impedance (−Z″) and modulus (M″) demonstrate the temperature-activated delocalized relaxation (non-Debye toward the Debye type) in these crystals. Stevels model suggests that the contribution of traps reduces with temperature rise and therefore conductivity enhances. Our study provides a comprehensive analysis and in-depth knowledge about the dielectric and conductivity relaxation mechanism in these lead-free perovskite SCs, which will help to implement efficient energy storage devices using these materials.

Measuring the propagation speed of gravitational waves with LISA

The propagation speed of gravitational waves, cT , has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent cT . Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of cT from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ansätze for cT (f), and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on cT (f) obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart.

Photon Frequency Diffusion Process

We introduce a stochastic multi-photon dynamics on reciprocal space. Assuming isotropy, we derive the diffusion limit for a tagged photon to be a nonlinear Markov process on frequency. The nonlinearity stems from the stimulated emission. In the case of Compton scattering with thermal electrons, the limiting process describes the dynamical fluctuations around the Kompaneets equation. More generally, we construct a photon frequency diffusion process which enables to include nonequilibrium effects. Modifications of the Planck Law may thus be explored, where we focus on the low-frequency regime.

Phononic crystal based sensor to detect acoustic variations in methyl & ethyl nonafluorobutyl ether

Phononic crystals and metamaterials have been widely studied for wave manipulation applications. In this study, we propose a conceptual framework for a new type of acoustic bio-chemical sensor that works based on the principle of phononic crystals and metamaterials to detect the temperature and pressure changes in active solvents like Methyl Nonafluorobutyl Ether (MNE) and Ethyl Nonafluorobutyl Ether (ENE). First, a wide low-frequency bandgap is obtained from the proposed composite unit cell structure with trampoline effect. Then a defect is introduced to adjust the localize cavity modes inside the reported bandgap. Later, the cavity is filled with MNE and ENE solvents that eventually resulted into fluid-solid coupling physics. The numerical wave dispersion curves and transmission profiles show presence of Fano-like interference/resonance effect evident from the observation of asymmetrical transmission profile. Such robust asymmetrical transmission peak is generated due to coupling of incident waves with scattered wave field emitted from the MNE and ENE solvents upon excitation. The variation in acoustic properties of MNE and ENE caused by temperature and pressure fields on newly born Fano-like asymmetrical transmission profile is studied. The proposed acoustic bio-chemical sensor governed by Fano-interference effect efficiently capture the variation in acoustic properties of MNE and ENE solvents at relatively low-frequency regime that makes this approach favorable for sensing applications. Such smart acoustic bio-chemical sensors can have useful applications in pharmaceutical production, petrochemicals and capturing ingredients of cosmetic and beauty products.

Dynamical spacetimes from nonlinear perturbations

Analog gravity describes fluctuations of hydrodynamic systems in terms of a massless scalar field propagating on curved spacetimes. This analogy between hydrodynamic and gravitational systems remains largely unexplored for nonlinear dynamical effects. In this paper, we provide the first description of dynamical analog spacetimes up to arbitrary order nonlinear perturbations constructed about stationary solutions. We find a high frequency response that exhibit known properties of perturbed black holes, as well as a low frequency regime for analog spacetimes with novel characteristics. Our framework more generally describes nonlinear perturbations of compressible hydrodynamic systems as analogs of nonlinear wave phenomena on black hole spacetimes.

Exploring the High Frequencies AC Conductivity Response in Disordered Materials by Using the Damped Harmonic Oscillator

The AC conductivity response of disordered materials follows a universal power law of the form σ′(ω)∝ωn at the low frequency regime, with the power exponent values in the range 0 &lt; n &lt; 1. At the high frequency regime, in many experimental data of different disordered materials, superlinear values of the power exponent n were observed. The observed superlinear values of the power exponent are usually within 1&lt;n&lt;2, but in some cases values n&gt;2 were detected. The present work is based on the definitions of electromagnetic theory as well as the Havriliak–Negami equation and the damped harmonic oscillator equation, which are widely used for the description of dielectric relaxation mechanisms and vibration modes in the THz frequency region, respectively. This work focuses mainly on investigating the parameters that affect the power exponent and the range of possible n values.

Gauss–Bonnet holographic superconductors in lower dimensions

We disclose the effects of Gauss–Bonnet gravity on the properties of holographic s-wave and p-wave superconductors, with higher-order corrections, in lower-dimensional spacetime. We employ shooting method to solve equations of motion numerically and obtain the effect of different values of mass, nonlinear gauge field and Gauss–Bonnet parameters on the critical temperature and condensation. Based on our results, increasing each of these three parameters leads to lower temperatures and larger values of condensation. This phenomenon is rooted in the fact that conductor/superconductor phase transition faces with difficulty for higher effects of nonlinear and Gauss–Bonnet terms in the presence of a massive field. In addition, we study the electrical conductivity in holographic setup. In four dimension, real and imaginary parts of conductivity in holographic s- and p-wave models behave similarly and follow the same trend as higher dimensions by showing the delta function and divergence behavior at low-frequency regime that Kramers–Kronig relation can connect these two parts of conductivity to each other. We observe the appearance of a gap energy at $$\omega _{\mathrm{g}}\approx 8T_{\mathrm{c}}$$ which shifts toward higher frequencies by diminishing temperature and increasing the effect of nonlinear and Gauss–Bonnet terms. Conductivity in three dimensions is far different from other dimensions. Even the real and imaginary parts in s- and p-wave modes pursue various trends. For example in $$\omega \rightarrow 0$$ limit, imaginary part in holographic s-wave model tends to infinity but in p-wave model approaches to zero. However, the real parts in both models show a delta function behavior. In general, real and imaginary parts of conductivity in all cases that we study tend to a constant value in $$\omega \rightarrow \infty $$ regime.

Effects of fracture-surface geometries on the third-order acoustoelastic constants for aligned fluid-saturated fractures

SUMMARYThe pressure sensitivity of stiffness in fractured rocks is closely related to fracture-surface geometries. The resulting stress-dependence of stiffness can be represented by the third-order elastic constants (3oECs). Fracture surfaces are generally rough at various scales, and can significantly affect the 3oECs of pre-stressed fractures as well as the wave-induced fluid flow (WIFF) induced by the Biot slow P-wave between fractures and the background medium. The WIFF usually depends on the fracture width relative to the slow P-wavelength and the fracture-surface roughness. We generate various fracture-surface geometries at different scales of random roughnesses parametrized by the surface standard deviation (SSD) of fracture-surface heights. With theoretical analyses and numerical simulations, we investigate the effect of fracture-surface geometries on the stress- and frequency-dependent stiffness through the 3oECs for pre-stressed rocks with aligned fractures. For the elastic wave in the low-frequency regime of Biot theory with the fracture scale much less than the wavelength, the induced WIFF significantly enhances the effect of fracture-surface geometries on the 3oECs and P- and S-wave moduli. The stiffness of fractured rocks increases with increasing SSDs, yielding a high sensitivity to pre-stresses. Toward the high-frequency limit, however, the fluid diffusion between fractures and the porous background decreases, which reduces the influence of fracture-surface roughnesses with the 3oECs much less than that in the low-frequency regime. The resulting P-wave modulus of aligned fluid-saturated fractures approximates to the background value.

Deconvoluting interrelationships between low‐energy vibrational modes and elastic properties in CaO–Al2O3 glasses

AbstractBy employing a nonconventional melting technique, namely, the aerodynamic levitation combined with CO2 laser melting, we have been able to synthesize a series of glasses in the binary system xCaO − (1 − x)Al2O3, (x = 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, and 0.80). Utilizing Raman spectroscopy, we have systematically followed the compositionally induced spectral changes in the low‐frequency regime of the spectra, the so‐called Boson Peak (BP) region, and unraveled interesting interrelationships between the low‐energy vibrational modes and the elastic properties of calcium aluminate (CA) glasses. It was found that the BP frequency is not only systematically dependent on altering CaO content by exhibiting a minimum close to the eutectic composition. Interestingly, the above‐mentioned compositional dependence of the BP, which is exhibited in the shift of the BP frequency versus the altering CaO content, is also strongly correlated with its elastic properties and seems to follow similar patterns for the binary CA glassy system. The above observations point toward the estimation that the eutectic point can serve as a strong indicator for various physicochemical phenomena taking place in the solid–liquid transition and thus provide new insights in an effort to deconvolute the ambiguous interrelationships occurring in the low vibrational frequency regime of these glasses.

Enhanced Structural and Dielectric Properties of Calcium and Chromium-Based M-Type Hexagonal Ferrites with Polyvinyl Alcohol (PVA) Polymer Composites

[Formula: see text]-type hexagonal ferrites with compositions Ca[Formula: see text]CrxFe[Formula: see text]O[Formula: see text] at ([Formula: see text], 0.2, 0.3, 0.4, 0.5) were successfully prepared by sol–gel auto combustion method and then immersed with polyvinyl alcohol (PVA) by ultrasound-assisted in situ emulsion technique. The results indicate that the synthesized nanoparticles were diffused homogeneously in PVA retaining the size and shape of the particle. The single-phase [Formula: see text]-type hexagonal structure was revealed by X-ray diffraction (XRD) with extra 101 peak of PVA at 2[Formula: see text]. The suitable signal-to-noise ratio in the high density recording media can be achieved due to the small particle size of the prepared composites as compared to pure hexaferrites. The interaction between PVA and nanoparticles was confirmed by Fourier transform infrared spectroscopy (FTIR). Scanning electron microscopy (SEM) images revealed the homogeneous distribution of grains, the crystallite size was measured from SEM (25–38[Formula: see text]nm), and it is also in agreement as calculated from the Scherer formula. Dielectric properties were also explored in the range of 1 MHz–3 GHz frequencies. Dielectric constant and dielectric loss were found to decrease with increasing frequency and decrease with the addition of ferrite ratio in the polymer matrix. This impact is because of the grain boundary at low frequency regime. The occurrence of resonance at high frequency regime recommends the investigated samples for multilayer chip inductor.

Floquet electronic bands and transport in magic-angle bilayer graphene

We theoretically study Floquet band structures and transport properties of twisted bilayer graphene at the magic-angle under the irradiation of variously polarized light. The magic-angle bilayer graphene is depicted by the newly proposed ten-band tight-binding model and the iterative continued fraction method is adopted to facilitate the calculations of electronic properties in the low-frequency regime. The transitions between Floquet sidebands induce discontinuous electronic bands and energy gaps which further give rise to the antiresonances in longitudinal conductivity calculated by the Kubo formula. Furthermore, significant Hall conductivity is generated by circularly polarized light and its magnitude and sign are sensitive to light polarization as well as photoinduced bandgap-opening, offering a feasible way to tune Hall conductivity by manipulating light polarization. We finally take into account the interplay between light irradiation and short-range disorder, and reveal that disorder scattering remarkably enhances the photoinduced Hall conductivity and can be viewed as an extrinsic source to Hall conductivity.

Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays.

We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining existing multipole methods for arrays of ideal cylinders with the method of matched asymptotic expansions. We construct asymptotically close representations for the dispersion equations of the first band surface, correcting and extending an established lowest-order (isotropic) result in the literature for thin-walled resonator arrays. The descriptions we obtain for the first band are accurate over a relatively broad frequency and Bloch vector range and not simply in the long-wavelength and low-frequency regime, as is the case in many classical treatments. Crucially, we are able to capture features of the first band, such as low-frequency anisotropy, over a broad range of filling fractions, wall thicknesses and aperture angles. In addition to describing the first band we use our formulation to compute the first band gap for both thin- and thick-walled resonators, and find that thicker resonator walls correspond to both a narrowing of the first band gap and an increase in the central band gap frequency.

Effects of selective distribution and migration of poly(methyl methacrylate)-grafted nanoclays on the phase behavior of poly(methyl methacrylate)/poly (styrene-co-acrylonitrile) blends

The effect of selective distribution and migration behavior of two kinds of poly (methyl methacrylate)-grafted nanoclays (PMMA- g -clay) on the phase behavior of PMMA/poly (styrene- co -acrylonitrile) (SAN) blends is investigated. The grafting ratios of our two modified nanoclays are similar, but their grafting density and grafted chain lengths are different, resulting in their different initial locations and subsequent migration behaviors in the blend matrix. The PMMA- g -clay(d) nanosheets (NSs) with relatively dense and short chains are always distributed at the interfacial region and further form the percolation networks to block the concentration fluctuation and retard the domain coarsening of blend matrix more remarkably, while the PMMA- g -clay(s) NSs with relatively sparse and long chains are distributed at first in the SAN-rich domains and subsequently move slowly to the interfacial region, resulting in their inhibition of the phase separation for PMMA/SAN blend from retarding SAN chains’ viscous diffusion to their gradual interfacial aggregation for stabilizing the morphology. The variation of storage modulus for three systems in low frequency and long-time regimes are also affected by different selective distributions of two grafted clay NSs in PMMA/SAN blend matrix. • The compatibilization effects of two clay nanosheets grafted with different length and grafting density of PMMA chains were compared. • The two nanosheets have the same thermodynamically stable location but different migration behaviors. • Both the two nanosheets hardly affect the phase coarsening of polymer blend at the early stage of the spinodal decomposition. • The inhibition effects of the two nanosheets are different at intermedium and late stages.

Correlation effects in high-order harmonic generation from finite systems

Using the Hubbard model we study how the process of high-order harmonic generation (HHG) is modified by beyond mean-field electron-electron correlation for both finite and bulk systems. A finite-size enhancement of the HHG signal is found and attributed to electrons backscattering off the lattice edges. Additionally, with increasing strength of the electron-electron correlation an enhancement of the high-frequency regime of the HHG spectrum is found. This is attributed to the on-site Coulomb repulsion between electrons giving rise to a localized quiver motion of the electrons. The finite-lattice enhancement dominates the HHG spectra from a few harmonic orders until a threshold from which the correlational enhancement dominates. This threshold is determined by the degree of correlation and decreases into the low-frequency regime for increasing electron-electron correlation. This infers that as the Mott insulator limit of high electron-electron correlation is approached, the finite-size effect on the electron dynamics becomes negligible.

Arm locking performance with the new LISA design

The laser interferometer space antenna (LISA) is a future space-based gravitational wave detector designed to be sensitive to sources radiating in the low frequency regime (0.1 mHz to 1 Hz). LISA’s interferometer signals will be dominated by laser frequency noise which has to be suppressed by about seven orders of magnitude using an algorithm called time delay interferometry (TDI). Arm locking has been proposed to reduce the laser frequency noise by a few orders of magnitude to reduce the potential risks associated with TDI. In this paper, we present an updated performance model for arm locking for the new LISA mission using 2.5 Gm arm lengths, the currently assumed clock noise, spacecraft motion based on LISA Pathfinder data and shot noise. We also update the Doppler frequency pulling estimates during lock acquisition.