Low-frequency Regime Research Articles

Selective Detection in Impulsive Low-Frequency Raman Imaging Using Shaped Probe Pulses

Impulsive stimulated Raman scattering (ISRS) using a single short femtosecond pump pulse to excite molecular vibrations offers an elegant pump-probe approach to perform vibrational imaging below $200\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. One shortcoming of ISRS is its inability to offer vibrational selectivity as all the vibrational bonds whose frequencies lie within the short pump-pulse bandwidth are excited. To date, several coherent control techniques have been explored to address this issue and selectively excite a specific molecular vibration by shaping the pump pulse. There has not been any systematic work that reports an analogous shaping of the probe pulse to implement preferential detection. In this work, we focus on vibrational imaging and report vibrational selective detection by shaping the probe pulse in time. We demonstrate numerically and experimentally two pulse-shaping strategies with one functioning as a vibrational notch filter and the other functioning as a vibrational low-pass filter. This enables fast ($25\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}/$pixel) and selective hyperspectral imaging in the low-frequency regime ($<200\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$).

Interphase-assisted suppression of electrode polarization in nanoparticulate-elastomeric composites

The electrical properties of polymer nanocomposites are governed by the behavior of the internal charges. In particular, the interphase around the nanoparticles strongly influences the distribution and mobility of charge carriers within the nanocomposites, which, in turn, impacts the performance of these materials. In this work, we probe the internal charge behavior in the presence of nanoparticles with a focus on the low-frequency regime using a suite of techniques. By investigating the depolarizing currents and the dependence of the dielectric properties on the frequency and temperature, we demonstrate that the interphases redistribute the space charges, increase their trap depth, and suppress the electrode polarization in an elastomeric nanocomposite. Additionally, we study the effect of the nanoparticle content on the dielectric behavior by comparing the internal charge behavior of 1, 2, and 4 vol. % nanocomposites. At only 4 vol. % loading, the mobility of charge carriers is effectively limited, leading to lower dc conductivity compared to the unfilled elastomer, and 1 and 2 vol. % nanocomposites. These findings are based on the model materials used in this study, TiO2 nanoparticles and polydimethylsiloxane, and can be extended to other nanoparticulate-filled elastomer composites to design lightweight dielectrics, actuators, and sensors with improved capabilities. Judicious manipulation of interfacial phenomena in polymer nanocomposites—especially those with a dilute content of nanoparticles—provides a promising path forward for the design of materials with exceptional electrical and other physical properties.

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations.

This research article investigates the behavior of elastic waves in an inhomogeneous isotropic three-layered sandwich plate with soft-core and stiff-skin layers embedded in Winkler foundations, using anti-plane shear motion. The study establishes the exact antisymmetric dispersion relation, low-frequency spectrum, and overall cut-off frequency of the wave propagation. A shortened polynomial dispersion relation is developed for the long-wave low-frequency regime by considering the contrasting material setup and compared with the exact dispersion relation. This article also provides exact and asymptotic formulas for stresses and displacements in each layer of the plate, as well as approximate one-dimensional equations of motion. The results suggest that the approximate equations of motion for the three-layered sandwich plate are valid throughout the entire low-frequency range, despite the presence of Winkler foundations on both sides of the plate. This research is significant as it provides insights into the behavior of waves in composite materials and can be used to improve the design of sandwich structures used in various engineering applications. Additionally, the findings that the approximate equations of motion for the three-layered sandwich plate are valid throughout the low-frequency range, despite the presence of Winkler foundations, can help simplify calculations and make the design process more efficient.

New formalism to define vacuum states for scalar fields in curved spacetimes

The problem of finding a vacuum definition for a single quantum field in curved spacetimes is discussed under a new geometrical perspective. The phase space dynamics of the quantum field modes are mapped to curves in a two-dimensional hyperbolic metric space, in which distances between neighbor points are shown to be proportional to the Bogoliubov coefficients associated with their corresponding mode solutions in phase space. The vacuum state for each mode is then defined as the unique trajectory from which all mapped phase space solutions move within thin annular regions around it. This property implies the stability of the vacuum state: solutions evolved from a point in this trajectory stay close to it as both evolve, and the particle creation is therefore minimized. The new approach is applied to the well-known cases of the time-independent dynamics, where the solutions draw circles around this curve, and to the time-dependent dynamics where adiabatic approximation is valid. Additionally, our analysis is extended to more challenging cases of time-dependent dynamics, where the adiabatic approximation is not possible, such as in the super-Hubble or low frequency regimes. It is shown that stability trajectories can also be found in these situations, and stable quantum vacua can be obtained. This new formalism is applied to two situations: de Sitter space, where the Bunch-Davies vacuum is obtained in a completely different manner through an analysis in the super-Hubble regime, and in the context of cosmological bouncing models, in which the contracting phase is dominated by a cosmological constant in the asymptotic past. A new vacuum state for cosmological perturbations is proposed in this situation.

Identification of two vibration regimes of underwater fibre optic cables by distributed acoustic sensing

SUMMARYDistributed acoustic sensing (DAS) enables data acquisition for underwater Earth Science with unprecedented spatial resolution. Submarine fibre optic cables traverse sea bottom features that can lead to suspended or decoupled cable portions, and are exposed to the ocean dynamics and to high rates of marine erosion or sediment deposition, which may induce temporal variations of the cable’s mechanical coupling to the ocean floor. Although these spatio-temporal fluctuations of the mechanical coupling affect the quality of the data recorded by DAS, and determine whether a cable section is useful or not for geophysical purposes, the detection of unsuitable cable portions has not been investigated in detail. Here, we report on DAS observations of two distinct vibration regimes of seafloor fibre optic cables: a high-frequency (>2 Hz) regime we associate to cable segments pinned between seafloor features, and a low-frequency (<1 Hz) regime we associate to suspended cable sections. While the low-frequency oscillations are driven by deep ocean currents, the high-frequency oscillations are triggered by the passage of earthquake seismic waves. Using Proper Orthogonal Decomposition, we demonstrate that high-frequency oscillations excite normal modes comparable to those of a finite 1-D wave propagation structure. We further identify trapped waves propagating along cable portions featuring high-frequency oscillations. Their wave speed is consistent with that of longitudinal waves propagating across the steel armouring of the cable. The DAS data on cable sections featuring such cable waves are dominated by highly monochromatic noise. Our results suggest that the spatio-temporal evolution of the mechanical coupling between fibre optic cables exposed to the ocean dynamics and the seafloor can be monitored through the combined analysis of the two vibration regimes presented here, which provides a DAS-based method to identify underwater cable sections unsuitable for the analysis of seismic waves.

Acoustic resonators for detecting low frequency events

Acoustic resonators and related concepts have long been the subject of research for acoustic filtering in free space or energy harvesting applications. In this work, we instead apply acoustic resonators to low frequency (< 50 Hz) non-contact bio-signal sensing within a vehicle cabin. We describe our approach to the design of the resonator and method of simulation in this low frequency regime. Validation of select designs through experiments in both free space and using a coupled bodies method is discussed. We also demonstrate the bio-signal collection in situ and discuss challenges associated with a real-world, noisy, dynamic environment. Future work including signal processing of noisy data to recover the base bio-signal and ideas for miniaturization of the device are touched upon.

Dispersive equations on asymptotically conical manifolds: time decay in the low-frequency regime

On an asymptotically conical manifold, we prove time decay estimates for the flow of the Schrödinger wave and Klein–Gordon equations via some differentiability properties of the spectral measure. To keep the paper at a reasonable length, we limit ourselves to the low-energy part of the spectrum, which is the one that dictates the decay rates. With this paper, we extend sharp estimates that are known in the asymptotically flat case (see Bouclet and Burq in Duke Math J 170(11):2575–2629, 2021, https://doi.org/10.1215/00127094-2020-0080 ) to this more general geometric framework and therefore recover the same decay properties as in the Euclidean case. The first step is to prove some resolvent estimates via a limiting absorption principle. It is at this stage that the proof of the previously mentioned authors fails, in particular when we try to recover a low-frequency positive commutator estimate. Once the resolvent estimates are established, we derive regularity for the spectral measure that in turn is applied to obtain the decay of the flows.

Dynamical renormalization of electron-phonon coupling in conventional superconductors

The adiabatic Born-Oppenheimer approximation is considered to be a robust approach that very rarely breaks down. Consequently, it is predominantly utilized to address various electron-phonon properties in condensed matter physics. By combining many-body perturbation and density functional theories we demonstrate the importance of dynamical (nonadiabatic) effects in estimating superconducting properties in various bulk and two-dimensional materials. Apart from the expected long-wavelength nonadiabatic effects, we found sizable nonadiabatic Kohn anomalies away from the Brillouin zone center for materials with strong intervalley electron-phonon scatterings. Compared to the adiabatic result, these dynamical phonon anomalies can significantly modify electron-phonon coupling strength $\ensuremath{\lambda}$ and superconducting transition temperature ${T}_{c}$. Further, the dynamically induced modifications of $\ensuremath{\lambda}$ have a strong impact on transport properties, where probably the most interesting is the rescaling of the low-temperature and low-frequency regime of the scattering time $1/\ensuremath{\tau}$ from about ${T}^{3}$ to about ${T}^{2}$, resembling the Fermi liquid result for electron-electron scattering. Our goal is to point out the potential implications of these nonadiabatic effects and reestablish their pivotal role in computational estimations of electron-phonon properties.

Concentration Scaling on Linear Viscoelastic Properties of Cellular Suspensions and Effects of Equilibrium Phase Behavior.

Concentration scaling on linear viscoelastic properties of cellular suspensions has been studied by rheometric characterisation of Phormidium suspensions and human blood in a wide range of volume fraction under small amplitude oscillatory shear experiments. The rheometric characterisation results are analysed by the time-concentration superposition (TCS) principle and show a power law scaling of characteristic relaxation time, plateau modulus and the zero-shear viscosity over the concentration ranges studied. The results show that the concentration effect of Phormidium suspensions on their elasticity is much stronger than that of human blood due to its strong cellular interactions and a high aspect ratio. For human blood, no obvious phase transition could be observed over the range of hematocrits studied here and with respect to a high-frequency dynamic regime, only one concentration scaling exponent could be identified. For Phormidium suspensions with respect to a low-frequency dynamic regime, three concentration scaling exponents in the volume fraction Region I (0.36≤ϕ/ϕref≤0.46), Region II (0.59≤ϕ/ϕref≤2.89) and Region III (3.11≤ϕ/ϕref≤3.44) are identified. The image observation shows that the network formation of Phormidium suspensions occurs as the volume fraction is increased from Region I to Region II; the sol-gel transition takes place from Region II to Region III. In combination with analysis of other nanoscale suspensions and liquid crystalline polymer solutions reported in the literature, it is revealed that such a power law concentration scaling exponent depends on colloidal or molecular interactions mediated with solvent and is sensitive to the equilibrium phase behaviour of complex fluids. The TCS principle is an unambiguous tool to give a quantitative estimation.

Tailoring Magnetic Properties and Magnetoimpedance Response in Nanocrystalline (Fe3Ni)81Nb7B12 Ribbons for Sensor Applications

Today, there is an increasing demand for progress in the magnetoimpedance (MI) response of cost-effective soft-magnetic materials for use in high-performance sensing devices. In view of this, we investigate here the field-annealing effects on soft-magnetic properties, magnetoimpedance response, and field sensitivity in the nanocrystalline (Fe3Ni)81Nb7B12 alloy ribbons. We observe that within the low-frequency regime, between 2 and 5 MHz, the zero-field-annealed (ZFA) ribbons exhibit the highest magnetoimpedance values. By magneto-optical Kerr effect measurements, we show that this result stems from the formation of irregular transversally patched magnetic domains after annealing, which in turn explains the induced transverse anisotropy necessary to increase the GMI response. In addition, we discuss this increment in terms of skin effect. Moreover, we report that the highest sensitivity of ca. 189%/(kA/m)—15%/Oe—is achieved for the field-annealed samples whose magnetic field was applied transverse to the ribbon axis. These findings are of practical importance to develop and refine highly sensitive magnetic sensors.

Single-phase continuum soft elastic metamaterial design based on variable boundary conditions through topology optimization

Wide bandgaps are challenging to achieve in the low-frequency regime. Herein, we develop a mode conversion-based method that considers variable boundary conditions. Based on this method, a soft single-phase continuum elastic metamaterial is designed. Unlike the previous method, which needs to balance design trade-offs such as bending and shearing stiffness, mass, and moment of inertia, this method provides a pure bending stiffness-based design with frequency-dependent boundary conditions. Furthermore, for weight reduction, we perform topology optimization for the unit cell components (i.e., the plate and mass block). The boundary conditions of the plate can be regarded as either being clamped on one end at a low frequency or clamped on both ends at a high frequency. The fundamental eigenfrequency and bandgap are thus maximized. Finally, we experimentally validate the proposed design and successfully achieve a lightweight metamaterial with wide bandgaps at low frequencies.

Barrow entropy and stochastic gravitational wave background generated from cosmological QCD phase transition

In this work we investigate the stochastic gravitational wave background generated during the first-order cosmological QCD phase transition of the early universe in the framework of the Barrow entropy. We first derived the Barrow corrections to the expression of stochastic gravitational wave background spectrum in presence of trace anomaly. Then, by taking account of Bubble wall collisions, sound waves and magnetohydrodynamic turbulence as the sources of stochastic gravitational wave, an analysis of the influence of Barrow entropy on the total energy density and the peak signal of stochastic gravitational wave signal is carried out. Finally, we discuss the possibility of detectors for the detection of these stochastic gravitational wave signals. Our results show that effect of Barrow entropy plays an important role in the temporal evolution of temperature of the universe as a function of the Hubble parameter, which leads to the signal of stochastic gravitational wave to shift towards the lower frequency regime, making the signal of stochastic gravitational wave possible to be probed by relevant ongoing and upcoming gravitational waves experiments.

Strategic Asset Allocation and Inflation Resilience

Inflation risk poses a significant challenge to strategic asset allocators and is forcing many to reevaluate the suite of quantitative tools they use. In particular, standard simulation methods are inadequate for modeling inflation dynamics and do not generate uncertainty in long-term average inflation. Furthermore, despite low-frequency regime switching between negative and positive stock–bond correlation regimes, linked to inflation dynamics, standard methods do not incorporate this either. Finally, when markets are undergoing long-term structural changes, modeling choices should be able to integrate the forward-looking expectations of subject matter experts on joint economic and market dynamics. This article describes a simple way of retrofitting these features to an existing simulation engine.

Analytical model of critical buckling transition for smectic liquid crystal based on the viscoelastic scaling of coarse-grained molecular dynamics.

The buckling transition of smectic liquid crystals (LCs) is important not only as fundamental physics but also for the rational design of devices to make use of their optical and mechanical properties. However, there exists a huge gap between the specific knowledge and universal analytical formulation. We have conducted coarse-grained molecular dynamics (CGMD) simulations with the force field optimized for the description of buckling phenomena including topological defects to link the molecular nature and continuum formulation. The simulations reveal the viscoelastic characteristics where the critical strain and the compression modulus highly depend on the strain rate as well as the number of layers. Therefore, we formulate the scaling model whose coupling constants depend on both strain rate and domain size. The model reproduces the CGMD results as well as experimental and theoretical values in existing literature. Furthermore, we elucidate from this model that the critical buckling behavior is determined by the competition between the suppression of compression-induced flow and the undulation fluctuation of layers. The framework consisting of the CGMD simulation and the scaling model enables us to estimate the buckling characteristics of smectic LCs reflecting their molecular structures in a wide range from the low-frequency regime that can be verified by experiments to the high-frequency regime beyond the reach of it.

Analysis of temporal structure of laser chaos by Allan variance.

Allan variance has been widely utilized for evaluating the stability of the time series generated by atomic clocks and lasers, in time regimes ranging from short to extremely long. This multiscale examination capability of the Allan variance may also be beneficial in evaluating the chaotic oscillating dynamics of semiconductor lasers- not just for conventional phase stability analysis. In the present study, we demonstrated Allan variance analysis of the complex time series generated by a semiconductor laser with delayed feedback, including low-frequency fluctuations (LFFs), which exhibit both fast and slow dynamics. While the detection of LFFs is difficult with the conventional power spectrum analysis method in the low-frequency regime, the Allan variance approach clearly captured the appearance of multiple time-scale dynamics, such as LFFs. This study demonstrates that Allan variance can help in understanding and characterizing diverse laser dynamics, including LFFs, spanning a wide range of timescales.

Efficient finite element modelling of guided wave scattering from a defect in three dimensions

ABSTRACT The scattering matrix (S-matrix) encodes the elastodynamic scattering behaviour of a defect. For the case of guided waves in the low-frequency regime, we explore how to minimise the number of incident/scattered directions used to accurately simulate the S-matrix of an arbitrary defect. The general approach is to use three-dimensional finite element (FE) analysis, implemented in a commercial FE package, to simulate the wave-defect interactions. The scattered wave field is measured at monitoring nodes on a circle that surrounds the defect. These scattered waves are decomposed into the multi-modal far-field scattering amplitudes. The angular order of the scattering is found and used to minimise the number of incident and scattered directions that must be computed. The method is then used to simulate the S-matrices of surface-breaking semi-elliptical cracks and circular through-holes with arbitrary sizes. It is found that the required number of incident/scattered directions varies with the scattered mode, and this is due to the differing scattering orders of these scattered fields. These results demonstrate how to achieve more efficient modelling of guided wave scattering, and also contribute to an understanding of experimental defect characterisation.

The boson peak in silicate glasses: insight from molecular dynamics.

In the low-frequency regime, ≈1 THz, glasses show an anomalous excess in their vibrational density of states called the boson peak (BP). The origin of BP has been a subject of debate since its first discovery a few decades ago. Although BP has been the focus of numerous studies, no conclusive answers have been found about its origins, which remained elusive to date. Here, we present results based on molecular dynamics of several binary and ternary silicate glasses with different network intermediates and modifier oxides. The vibrational density of states and the BP are reported for all the studied glasses. Their correlation with the elastic constant C44, structural, and dynamical properties are extensively discussed in terms of Voronoi atomic volume and the vibrational mean square displacement of Q4 species specifically. We also question the classical classification of alkali oxides as modifiers, and we suggest that Li2O plays the role of pseudo-intermediate oxide in lithium silicate glasses. This claim is supported by the effect of Li on various vibrational modes, and this effect differs from the other alkali metals. Furthermore, we demonstrate a correlation between the BP intensities and both the Voronoi volume of the Q4 and Q3 units and vibrational mean square displacements.

Dielectric spectroscopy investigation of relaxation processes in the low-frequency regime and validity of the Stokes–Einstein–Nernst/Stokes–Einstein–Debye relation in poly(propylene glycol)

Dielectric spectroscopy investigation of relaxation processes in the low-frequency regime and validity of the Stokes–Einstein–Nernst/Stokes–Einstein–Debye relation in poly(propylene glycol)

Dichotomous behaviors of stress and dielectric relaxations in dense suspensions of swollen thermoreversible hydrogel microparticles.

While the mechanical disruption of microscopic structures in complex fluids by large shear flows has been studied extensively, the effects of applied strains on the dielectric properties of macromolecular aggregates have received far less attention. Simultaneous rheology and dielectric experiments can be employed to study the dynamics of sheared colloidal suspensions over spatiotemporal scales spanning several decades. Using a precision impedance analyzer, we study the dielectric behavior of strongly sheared aqueous suspensions of thermoreversible hydrogel poly(N-isopropylacrylamide) (PNIPAM) particles at different temperatures. We also perform stress relaxation experiments to uncover the influence of large deformations on the bulk mechanical moduli of these suspensions. All the sheared PNIPAM suspensions exhibit distinct dielectric relaxation processes in the low and high frequency regimes. At a temperature below the lower consolute solution temperature (LCST), the complex permittivities of highly dense PNIPAM suspensions decrease with increase in applied oscillatory strain amplitudes. Simultaneously, we note a counter-intuitive slowdown of the dielectric relaxation dynamics. Contrary to our rheo-dielectric findings, our bulk rheology experiments, performed under identical conditions, reveal shear-thinning dynamics with increasing strain amplitudes. We propose the shear-induced rupture of fragile clusters of swollen PNIPAM particles to explain our observations. Our work illustrates that rheo-dielectric studies have enormous potential for providing deep insights into the length scale-dependent dynamical properties of complex systems such as dense suspensions and soft glasses.

Probing primordial black holes with anisotropies in stochastic gravitational-wave background

Primordial black holes, if considered to constitute a significant fraction of cold dark matter, trace the inhomogeneous large-scale structure of the Universe. Consequently, the stochastic gravitational-wave background, originating from incoherent superposition of unresolved signals emitted by primordial black hole binaries, is expected to display anisotropies across the sky. In this work, we investigate the angular correlations of such anisotropies for the first time and demonstrate their difference from the analogous signal produced by astrophysical black hole binaries. We carefully evaluate the associated uncertainties due to shot-noise and cosmic variance, and demonstrate that the studied signal in the low-frequency regime can be differentiated from the signal of astrophysical origin. Our results are particularly promising in the stellar mass-range, where the identification of the merger origin has been particularly challenging.