Frequency Dispersion Research Articles

Multi-Layered and Homogenized Models for In-Plane Guided Wave Excitation, Sensing, and Scattering in Anisotropic Laminated Composites

The numerical evaluation of elastic guided wave (EGW) phenomena is an important stage in the development and configuration of ultrasonic-based non-destructive testing/structural health monitoring (NDT/SHM) systems. To reduce the computational costs, which are typical for EGW simulations in laminated composite structures, and to make the corresponding parametric analysis possible, the latter could be treated by employing an effective single-layer model with homogenized anisotropic material properties. The present study investigates the applicability of such an approach to simulate EGW excitation, propagation, scattering, and sensing in laminate composite structures, which are among the typical problems for ultrasonic-based NDT/SHM. To this end, two homogenized models have been implemented: the well-known static long-wave homogenization approach and the advanced Lamb wave homogenization method, where the effect of angular and frequency dispersion of EGWs is taken into account. To illustrate their performance, in-plane elastic guided wave excitation and sensing with surface-mounted piezoelectric transducers as well as wave scattering by a T-shaped stringer in cross-ply symmetric anisotropic laminates are examined by employing a recently developed semi-analytical hybrid approach. The limits of the applicability of both homogenized models are demonstrated and discussed via the comparison with the multi-layered model. The general conclusion from the obtained results is that only a qualitative, although computationally efficient, description of the EGW phenomena in the considered composites can be achieved using single-layer models.

Influence of top-coat thickness of thermal barrier coating on time–frequency domain and dispersion characteristics of laser-induced surface acoustic wave

Thermal barrier coating is commonly used to insulate the hot end components of aero engine and gas turbine in order to meet extreme high temperature service conditions. The performance of the thermal barrier coating will be significantly impacted by thinning or even spalling during the service process. Given the uniqueness of thermal barrier coating in structure and composition materials, and the fact that laser-induced surface acoustic waves are extremely sensitive to material surface characteristic parameters, laser-induced ultrasonic technology is used to detect the thermal barrier coating in this paper. To characterize the size and defect of thermal barrier coating, the excitation mechanism and propagation law of surface acoustic waves are very crucial. Firstly, the surface acoustic wave propagation law is investigated using spectral analysis and wavelet transform. Then, to study the influence of top-coat thickness on laser-induced surface acoustic wave, the surface acoustic wave velocity dispersion curves of thermal barrier coating with different top-coat thicknesses are extracted using wavelet analysis. The simulative and experimental results indicate that the time–frequency domain and dispersion characteristics of laser-induced surface acoustic wave in multilayered heterostructure are strongly affected by the top-coat thickness. By the establishment of the relationship between phase velocity of laser-induced surface acoustic wave and top-coat thickness, a theoretical basis is provided to characterize the top-coat thickness of multilayered heterostructure.

(Ba0.6Sr0.4)TiO3/PEEK composites modified by polyethersulfone with low dielectric constant and high dielectric tunability under DC bias

Ceramic/polyetheretherketone (PEEK) composites show a wide range of applications and have attracted extensive interest in the scientific community due to their outstanding dielectric and mechanical characteristics. However, the interface connection between the ceramic and PEEK is a vital issue that must be addressed to improve their physical and electrical properties. In this work, the polyethersulfone resin (PES) was selected as interface modifier between barium strontium titanate (Ba0.6Sr0.4TiO3, BST) and PEEK. Cold-pressing sintering was used to create BST/PEEK materials with superior dielectric frequency stability and dielectric tunability. The effects of PES content on the morphology and dielectric characteristics of PES modified BST/PEEK materials were investigated. The results showed PES could improve the dispersion of BST particles in polymer. The dielectric constant, dielectric tunability, and breakdown strength increased first, then reduced as PES content increased. The composite had the most homogeneous microstructure and the best dielectric properties when the PES content was 7.5 vol%. The frequency dispersion factor F(x) was much smaller than that of other ceramic/polymer composites reported. In addition, the dielectric tunability of the composites could reach a relatively high level (34.18%) while the dielectric constant was as low as 14. The dielectric tunable efficiency (TuE) was proposed to evaluate the property of low dielectric constant and high dielectric tunability under DC bias. The TuE of PES modified BST/PEEK composites show the highest value comparing with reported dielectric tunable composites. This research laid the path for the development of a novel ceramic/polymer composite with good interface bonding and high dielectric tunability.

Propagation of Rayleigh Wave in Sandy Media with Imperfect Interface

In the present study, the propagation of Rayleigh wave in a sandy layer overlying a sandy semi-infinite media is investigated, with the interface considered imperfect. Expressions for displacement components are obtained. The dispersion frequency equation is derived using suitable boundary conditions. In particular cases, when interface is perfect and elastic media replace sandy media are also discussed. The effects of imperfectness and sandy parameter on the Rayleigh waves’ phase velocity are investigated using MATLAB software. The theoretical results obtained may find useful applications in geophysics, civil engineering and soil mechanics

Structural stability, mechanical, and optoelectronic properties of A2TlBiI6 (A = Cs and Rb) for energy harvesting: A first principles investigation

Halide double perovskite materials have potential application in renewable energy devices. Herein, the optoelectronic properties and mechanical stability of A2TlBiI6 (A = Cs and Rb) determined using density functional theory utilizing WIEN2k code have been presented. The traditional and recently modified versions of the tolerance factors have helped identify these compounds as structurally stable, whereas the enthalpy and positive values of the frequency of phonon dispersion indicate the dynamical stability of these perovskite materials. Density of states and band structure calculations indicate that the electronic transition occurs from the top of the valence band [Tl(6p)+Bi(6p)+I(5s)] to the bottom of the conduction band [Tl(6p)+Bi(6p)]. These electronic transitions are responsible for inherently direct band gap at the Γ-point of the first Brillouin zone. The energy band gap calculations for Cs2TlBiI6 and Rb2TlBiI6 give direct band gap values of 2.0 and 2.1 eV, respectively. Our results show that Tl–Bi based double perovskites exhibit considerable stability, suitable band gaps, and excellent light absorption. In particular, direct band gap materials are very promising for use in a multi-junction solar cell. We hope that our work will stimulate the interest of experimental and theoretical experts to synthesize new materials for the solar industry.

Dispersive landslide

Considering the non-hydrostatic mass flow model (Pudasaini, 2022 [1]), here, I derive a novel dispersive wave equation for landslide. The new dispersive wave for landslide recovers the classical dispersive water waves as a special case. I show that the frequency dispersion relation for landslide is inherently different than the classical frequency dispersion for water waves. The wave frequency with dispersion increases non-linearly as a function of the wave number. For dispersive landslide, the wave frequency without dispersion appears to heavily overestimate the dispersive wave frequency for higher wave number. Due to the dispersion term emerging from the non-hydrostatic contribution for landslide, the phase velocity becomes a function of the wave number. This gives rise to the group velocity that is significantly different from the phase velocity, characterizing the dispersive mass flow. The dispersive phase velocity and group velocity decrease non-linearly with the wave number. Yet, the group velocity is substantially lower than the phase velocity. I analytically derive a dispersion number as the ratio between the phase velocity and the group velocity, which measures the deviation of the group velocity from the phase velocity, provides a dynamic scaling between them and summarizes the overall effect of dispersion in the mass flow. The dispersion number for landslide increases rapidly with the wave number, which is in contrast to the dispersion in water waves. With the definition of the effective dispersive lateral stress, I prove the existence of an anti-restoring force in landslide. I reveal the fact that due to the anti-restoring force, landslides are more dispersive than the piano strings. So, the wave dispersion in landslide is fundamentally different than the wave dispersion in the piano string. My model constitutes a foundation for the wave phenomenon in dispersive mass flows.

Experimental investigations of linear and nonlinear periodic travelling waves in a viscous fluid conduit

Conduits generated by the buoyant dynamics between two miscible Stokes fluids with high viscosity contrast, a type of core–annular flow, exhibit a rich nonlinear wave dynamics. However, little is known about the fundamental wave dispersion properties of the medium. In the present work, a pump is used to inject a time-periodic flow that results in the excitation of propagating small- and large-amplitude periodic travelling waves along the conduit interface. This wavemaker problem is used as a means to measure the linear and nonlinear dispersion relations and corresponding periodic travelling wave profiles. Measurements are favourably compared with predictions from a fully nonlinear, long-wave model (the conduit equation) and the analytically computed linear dispersion relation for two-Stokes flow. A critical frequency is observed, marking the threshold between propagating and non-propagating (spatially decaying) waves. Measurements of wave profiles and the wavenumber–frequency dispersion relation quantitatively agree with wave solutions of the conduit equation. An upshift from the conduit equation's predicted critical frequency is observed and is explained by incorporating a weak recirculating flow into the full two-Stokes flow model. When the boundary condition corresponds to the temporal profile of a nonlinear periodic travelling wave solution of the conduit equation, weakly nonlinear and strongly nonlinear, cnoidal-type waves are observed that quantitatively agree with the conduit nonlinear dispersion relation and wave profiles. This wavemaker problem is an important precursor to the experimental investigation of more general boundary value problems in viscous fluid conduit nonlinear wave dynamics.

Coupling interactions of anisotropic hyperbolic phonon polaritons in double layered orthorhombic molybdenum trioxide

The natural hyperbolic phonon polariton material-orthorhombic molybdenum trioxide (α-MoO<sub>3</sub>) has recently attracted much interest , due to the associated ultra-confinement of light and enhanced light-matter interactions. We theoretically propose and study the in-plane anisotropic phonon polaritons (APhPs) in the Kretschmann structure with monolayer and dual layers α-MoO<sub>3</sub>. The excitation of phonon polaritons and the corresponding dispersion properties in this multilayer system are studied by using a generalized 4×4 transfer matrix method (TMM). The frequency dispersions with geometrical parameters are also discussed in detail. The results confirm that the interlayer coupling can be modulated by stacking the multilayer films and regulating the thickness of each layer. More interestingly, when the distance between double α-MoO<sub>3</sub> layers is much smaller than the propagation length of PhPs, a strong coupling phenomenon occurs, and the photon tunneling probability and intensity can be greatly improved. When the incident angle is greater than the total internal reflection angle, the phase matching condition for SPhP excitation can be satisfied. Within the 40° incident angle, the SPhP blue-shifts rapidly with the increase of incident angle. But then the dispersion curve no longer changes with increase of incidence angle. The enlargement of the interstitial layer can also lead the Fabry-Perot (FP) resonance mode to be excited. The APhP in layered heterostructure is an important part of today's nanophotonic technology, our study can help optimize and design tunable optoelectronic devices based on hyperbolic materials.

Influence of Aspect Ratio on Wave Propagation in Granular Crystals Consisting of Ellipse-Shaped Particles

The behavior of waves in granular materials is very complex and closely related to the macro-micro properties such as particle shape, packing, and particle size distribution. In this study, the influence of the aspect ratio (AR) and confining stress on wave propagation in 2D granular crystals consisting of ellipse-shaped particles is investigated based on discrete element method. The energy attenuation, wave velocity, wavefront shape, and frequency dispersion are mainly focused. The results show that the energy attenuation exhibits an increasing trend with bigger confining stress and smaller AR in the direction of wave propagation. The wave velocities increase with increasing AR, and the relation between compressive wave velocities and the confining stress and AR is obtained. Wavefront has the elliptical shape which has the same AR as elliptical particles of specimen, and its analytical expression is also obtained. The dispersion is affected by AR, which is mainly reflected in the modified particle spacing in sine fitted frequency dispersion curve. Larger confining stress allows a larger maximum frequency, and produces stronger dispersion. The above conclusion can provide a reference for wave-guided granular crystals design.

Automatic recognition of tweek atmospherics and plasma diagnostics in the lower ionosphere with the machine learning method

Tweek atmospherics are ELF/VLF pulse signals with frequency dispersion characteristics that originate from lightning discharges and propagate in the Earth-ionosphere waveguide over long distances. In this paper, we developed an automatic method to recognize tweek atmospherics and diagnose the lower ionosphere based on the machine learning method. The differences (automatic-manual) of each ionosphere parameter between the automatic method and the manual method are 0.07  2.73 km, 0.03  0.92 cm-3, and 91  1068 km for h, Ne, and d, respectively. Moreover, the automatic method is capable of recognizing higher harmonic tweek sferics as well. These evaluation results of the model suggest that the automatic method is a powerful tool to investigate the long-term variations of the lower ionosphere.

Сравнение качества оптимальной фильтрации наклона дисперсионной характеристики фильтром Стратоновича и сигма-точечным фильтром Калмана

The article deals with the reception and transmission of broadband signals through the ionospheric channel. An increase in the width of the spectrum of transmitted signals leads to a significant effect of the frequency dispersion of the Earth's ionosphere on the quality of information reception. Estimation of dispersion distortions of broadband signals and compensation of their influence in the article is carried out by methods of optimal filtering. Two algorithms for nonlinear optimal filtering of the slope of the dispersion characteristic of the ionospheric channel are compared: using the Stratonovich filter and using the sigma-point Kalman filter. The article presents general analytical expressions for calculating the estimate of the slope of the dispersion characteristic for both algorithms: Stratonovich filtering and filtering using the unscented Kalman filter. In addition, the results of simulation modeling are presented, the purpose of which was to compare the two above-mentioned filtering algorithms within the framework of the task. Three cases of the dependence of the slope of the DC on time are studied: a Markov damped process, a constant process, and a process with random increments for phase-shift keyed signals with different spectral widths under the assumption of large signal-to-noise ratios. It is shown that for signals with a spectral width from 500 kHz to 1 MHz, the unscented Kalman filter adjusts on average 2 times faster, however, the standard deviation of the estimate of the slope of the dispersion characteristic from the true value is up to 1.5 times larger compared to the Stratonovich filter. The duration of the filter adjustment decreases with a decrease in the width of the signal spectrum from 1 MHz to 250 kHz. In the 250 kHz band, both considered filters have approximately the same tuning speed and filtering quality.

Characterization of boron-doped single-crystal diamond by electrophysical methods (review)

A critical analysis of the existing methods of controlling the concentration of impurity and majority charge carriers in wide bandgap semiconductors and the issues of improvement of modern diagnostics of the main electrophysical properties of single-crystal diamond are considered based on the results of our studies and the works of other authors. It was found that independent assessment of impurity concentration and concentration of free charge carriers is of fundamental importance for semiconductor diamond due to very low (less than 1%) degree of ionization of the introduced impurity. The advantages and prospects of admittance spectroscopy as a diagnostic method for ultrawide bandgap semiconductors are shown and solutions aimed at the correct interpretation of the experimental data are proposed. The high ionization energy of boron impurity in diamond (370 meV) results in a strong frequency dispersion of the measured barrier capacitance. It is shown that under disturbance of quasi-static conditions in capacitance-voltage measurements, low frequencies and high temperatures should be used for correct assessment of the charge carrier concentration. The results of electrophysical studies are compared with traditional measurements of impurity concentration in diamond by optical methods. A decrease of hole activation energy from the boron impurity level from 325 to 100 meV was found upon increasing the boron concentration NA from 2·1016 to 4·1019 cm-3. The transition to the hopping mechanism of conductivity within the impurity (acceptor) band with thermal activation energy of 10-20 meV was registered for NA≥5·1018 cm-3 at temperatures of 120-150 K. Keywords: single-crystal diamond, boron impurity, charge carrier concentration, activation energy, admittance spectroscopy, capacitance-voltage measurements.

A study of radar reflection signal characteristics in multi-domain using a closed plasma generator

This paper theoretically and experimentally studies the radar reflection signal characteristics in a multi-domain using a closed plasma generator, especially for a correlation domain. A multi-domain computation method is proposed for a radar signal reflected by a metal covered with plasma. The reflected signal characteristics are studied in the time, frequency, and correlation domain. A closed plasma generator device is designed to verify the computation method for the radar signal reflected from metal plate covered with plasma experimentally. The plasma in the device is terminated by a transmission window at one end and a metal plate at another end, which is able to provide the environment for a radar signal reflection experiment. Based on the theoretical and the experimental results, the time and frequency domain of radar reflection signal not only show the amplitude attenuation characteristics but also frequency dispersion phenomenon. For the correlation domain characteristics of the radar reflection signal, the peak value in correlation domain significantly decreases, which demonstrates the stealth effect of the plasma. The effect of plasma and radar parameters on the peak value decrease phenomenon, as well as the stealth effect in the correlation domain, is further analyzed.

Дисперсия диэлектрической проницаемости и электрического модуля в соединениях Ag-=SUB=-x-=/SUB=-HfS-=SUB=-2-=/SUB=- со слоистой структурой

According to the impedance spectroscopy data, a significant frequency dispersion of the real and imaginary components of the permittivity was found in the intercalated AgxHfS2 samples. Using the modular formalism, the dielectric relaxation times were determined, which decrease in magnitude with an increase in the silver content in the samples. Their coincidence with the relaxation times determined from the frequency dependences of the imaginary parts of the complex impedance was shown.

Paper] Bendable Electro-Acoustic Transducer Fabricated Utilizing Frequency Dispersion of Elastic Modulus

Paper] Bendable Electro-Acoustic Transducer Fabricated Utilizing Frequency Dispersion of Elastic Modulus

Raman spectroscopy of a few layers of bismuth telluride nanoplatelets.

We can shape the electronic and phonon properties of Bi2Te3 crystals via the variation of the number of layers. Here, we report a Raman study with the aid of first-principles calculations on few-layered Bi2Te3 systems ranging from 5 to 24 nm layer thickness using 1.92, 2.41 and 2.54 eV excitation energies. We examine how the frequency position, intensity and lineshape of the main Raman modes (A11g, E2g, and A21g) behave by the variation of the layer thickness and excitation energy. We observed a frequency dispersion on the number of layers of the main modes, indicating changes in the inter- and intra-layers interaction. A resonant Raman condition is reached for all modes for samples with 11 and 18 nm thickness because of van Hove singularities at the electronic density of states. Also, the Breit-Wigner-Fano line shape of the A21g mode shows an increase of electron-phonon coupling for thick layers. These results suggest a relevant influence of numbers of layers on the Raman scattering mechanics in Bi2Te3 systems.

DIELECTRIC PROPERTIES OF CONTAMINATED SOIL BY SALT CRYSTALS

Dielectric permittivity is a physical property that reflects the electric polarizability of a medium. This property is highly sensitive to the components of the studied material. It can be affected by varying the water content and the salinity of the sample. In this work, an impedance analyzer and a capacitive cell have been used to measure the complex permittivity of different samples composed of a mixture of salt crystals and soil for a frequency range between 100-10<sup>7</sup> Hz and for various proportions of salt crystals in each sample. Experimental results for permittivity spectra exhibit frequency dispersion and dielectric relaxation phenomena for all samples. The relaxation occurs in the range of frequency from 1 kHz to 100 kHz. The real and imaginary parts of the permittivity are strongly correlated with the salt crystal volume fraction at 1 kHz. However, the sensitivity at 100 kHz decreases, especially for the imaginary part. Three composite dielectric mixing models (alpha models) fitting the relationship between the permittivity and the salt crystal content are evaluated with the experimental dataset. The results indicate a good estimation of the real and imaginary parts of the complex permittivity using the complex refractive index model (CRIM). However, the experimental results are misestimated by the "parallel" and "series" models. Experimental results are better fitted at 1 kHz.

Exploration of the structural, vibrational, electronic, mechanical and thermal properties of Ru4Al3B2 and Ru9Al3B8: a DFT study.

The structural, dynamical, electro-optical, mechanical, and thermal characteristics of the newly synthesized intermetallic compounds Ru4Al3B2 and Ru9Al3B8 have been studied under ambient and elevated pressure through density functional theory (DFT). The obtained lattice parameters of the compounds are consistent with the experimental values. The metallic character of these compounds is established by the band structure and density of states (DOS). The electronic charge density distribution and bond analysis imply that Ru4Al3B2 and Ru9Al3B8 have mainly both ionic and covalent bonding. The non-negative phonon dispersion frequency of the compounds reaffirms their dynamical stability. Both compounds are tough as well as have high melting points, and hence, can be applied in harsh conditions. Mechanical properties are significantly improved under pressure. Thermal barrier coating (TBC) is a possible field of application for both compounds. The different thermal properties such as the Debye temperature (ΘD), Grüneisen parameter (γ), melting temperature (Tm), minimum thermal conductivity (Kmin) and lattice thermal conductivity (κph) of these compounds have been studied to figure out the suitable application areas in thermally demanding situations. The pressure and temperature dependent bulk modulus (B) and other thermodynamic properties have also been analyzed, which suggested that the present compounds are strong candidates for device applications at high temperature and pressure. Owing to their high optical absorptivity and reflectivity in the UV region, they are also candidates for UV-based applications. Furthermore, they also have applicability in the fields of electronics, aviation, energy storage, and supercapacitor devices for their superior electronic, thermal and mechanical properties.

Structural, dielectric, magnetic and magnetoelectric studies of (1-x) BaFe12O19-x BiFeO3 composites

The synthesis of multiferroic (1-x) BaFe12O19-x BiFeO3; (x = 0.05, 0.08, 0.10) composites was carried out with solid state reaction. The XRD data confirmed the formation of the composites with phases of both compounds. The low values of Rietveld refinement parameters along with modified lattice parameters of both hexaferrite and multiferroic phase reconfirmed the amalgamation of phases. FESEM with EDX were utilized for morphological study and elemental compositional analysis in the composites. The dielectric constant and tanδ both parameters showed typical low frequency dispersion. A mild anomaly in dielectric constant and tangent loss is quite noticeable near to magnetic transition temperature (TN) of BiFeO3 suggests the possible occurrence of magnetoelectric effect in prepared composite system. The fitting of AC conductivity data suggested the OLPT (overlapping large polaron tunneling) conduction process in the composite system. The saturation magnetization (Ms) showed a decreasing trend with increment of BiFeO3 content in composites owing to substituted Fe3+ ion in spin-up state. Coercivity (Hc) found in good agreement with magnetocrystalline anisotropy of hexaferrite phase. The improvements in magnetoelectric coupling coefficient of barium hexaferrite were clearly noticeable with the introduction of BiFeO3 phase owing to piezoelectric coefficient and magnetostriction of ferroelectric and ferrite phases respectively.

Investigation of first hyper-polarisability molecular switches between enol–keto equilibrium of phenyl benzodifurantrione: a DFT-based computational study

The contrast of the second-order nonlinear optical response between the enol (anti and syn) and keto tautomeric equilibrium of 7-Phenyl-7H-benzo[1,2-b;4,5-b’]difuran-2,3,6-trione (PBDT) with donor/acceptor substitution at the para position of phenyl group have been computed involving electron correlation, frequency dispersion, and solvent polarity effects. The Hyper Rayleigh Scattering (HRS) first-hyperpolarisability contrast between the enol and keto forms for PBDT and Nitro-substituted PBDT is 3.5 and 2.8, respectively. However, in NMe2-substituted PBDT, a large contrast (12 times) of HRS first hyper-polarisability between enol (anti and syn) and keto form is observed. Present study reveals that electron donor group (–NMe2) in PBDT plays a pivotal role for obtaining very high contrast in the first hyper-polarisability (β HRS and β vec) values between the enol and keto forms compare to the electron acceptor (–NO2) group substitution at the same position. The solvent effect also plays a significant role in further improving the first hyper-polarisability value and its switching behaviour between the enol and keto forms of NMe2-PBDT. NLO switching contrast between the enol and keto forms of donor/acceptor substituted PBDT is also explained using the electronic features including UV-Vis absorption spectra, HOMO–LUMO electron densities, optical energy gaps, charge transfer contribution etc.