Variation Of Wavenumber Research Articles

Mechanisms affecting microwave dielectric properties of Li2Mg2TiO5 ceramics based on lithium excess

Herein, the feasibility was assessed through first principles, and the effect of lithium excess on both the structure and dielectric properties of Li(1+x)2Mg2TiO5 (0.000 ≤ x ≤ 0.200) ceramics was investigated by solid-phase reaction method. An appropriate excess of lithium can moderately inhibit the volatilization of lithium and reduce the production of the secondary phase MgTi2O4, though it cannot completely inhibit its production. Li(1+0.050)2Mg2TiO5 exhibits the best dielectric properties with εr =14.55, Q × f =127,393 GHz (@9.6 GHz), and τf = −19.91 ppm/°C. The influence of non-inherent factors on the dielectric properties is dominant, with the increase in relative density to 93.53 % and the growth in average grain size to 28.67 μm contributing to the reduction of dielectric loss. The decrease in εr is due to the decrease in secondary phase content. Results from bond ionicity and Raman wavenumber variations in the intrinsic factors show that the intrinsic factors have little effect on the εr. Whereas, the increase in lattice energy as well as the decrease in FWHM contribute to the decrease in dielectric loss. In addition, a proper excess of lithium helps to increase the bonding energy thereby optimizing the temperature stability. The optimized Li(1+0.050)2Mg2TiO5 has great potential for application in microwave communications.

Inextensional vibrations of thin spherical shells using strain gradient elasticity theory

We study inextensional vibrations of the spherical shell using strain gradient elasticity theory under Kirchhoff-Love hypotheses. For admissibility of the inextensional deformations the shell is punctured by making a tiny hole. The shell is assumed to be made of linearly elastic, homogeneous, and isotropic material. The closed form expression for the frequencies of inextensional modes of vibration of spherical caps of various polar angles and that of nearly complete spherical shell are derived using Rayleigh's method. Towards this, the displacement and velocity fields are obtained by setting the membrane strains to zero. Further, to facilitate the existence of inextensional vibrations, boundaries are assumed to be traction free. The frequencies are computed for the positive and negative signs in the strain gradient term of the constitutive law. The computed frequencies, employing negative sign are found to be higher than those computed using classical elasticity theory. The opposite effect is seen when the frequencies are computed with the positive sign. Further, the frequencies are found to saturate when the positive sign is used in the constitutive law. Parametric studies viz. variation in frequencies with the circumferential wavenumbers for different values of length scale parameter, variation in frequencies with circumferential wavenumbers for different values of polar angles and a given length scale parameter, variation of frequency with increasing polar angle for a given circumferential wavenumber, variation of saturation wavenumber with increasing polar angle, and increasing length scale parameter are carried out. The frequencies of nearly a spherical shell with increasing circumferential wavenumber are also computed.

Lattice dynamics and phase transitions in FAPbBr3 single crystals: Temperature‐ and pressure‐dependent Raman spectroscopy

AbstractThe rapidly emerging perovskites hold immense potential for revolutionizing optoelectronic and photovoltaic applications. However, understanding the complex structural dynamics and their response at extreme conditions in robust environments is crucial for optimizing the practical performance of perovskite‐based devices. Previous X‐ray diffraction studies have shown great potential for studying the average structures of these materials, but for more complex analysis at the local atomic level, Raman spectroscopy is a powerful tool. In this study, temperature‐ and pressure‐dependent Raman spectroscopy was used to elucidate the intricate lattice dynamics, phase transitions, and amorphization of FAPbBr3 single crystals at extreme conditions such as low temperature or high pressure. Temperature‐dependent Raman spectra unveiled significant variations in wavenumbers, full width at half maximum, and the vanishing of specific modes at higher temperatures. These were ascribed to symmetry changes caused by two crystallographic phase transitions at −127°C from orthorhombic to tetragonal and at −33°C from tetragonal to cubic phase. In addition, some of the Raman modes disappeared upon heating at −90°C, which was associated with a crystallographically unresolved transition. Pressure‐dependent Raman scattering revealed two phase transitions at 0.3 GPa and 2.2 GPa, which corresponded to the contraction of the PbBr6 octahedra and their tilting distortion, respectively. Further compression uncovered amorphization at 3.6 GPa, characterized by the vanishing of crystalline Raman modes together with the emergence of broad new modes due to the disorder within the crystal structure. Upon pressure release, the original Raman modes were recovered, indicating the reversibility of the pressure‐induced phase transitions. The changes in the Raman spectra were the most significant, especially in the low‐wavenumber lattice modes, when the FAPbBr3 underwent orthorhombic phase transition. It indicates that the inorganic sublattice is affected by the structural change into the orthorhombic phase caused either by temperature or pressure variation.

Optimal profile design for acoustic black holes using Timoshenko beam theory.

We revisit the problem of constructing one-dimensional acoustic black holes. Instead of considering the Euler-Bernoulli beam theory, we use Timoshenko's approach, which is known to be more realistic at higher frequencies. Our goal is to minimize the reflection coefficient under a constraint imposed on the normalized wavenumber variation. We use the calculus of variations to derive the corresponding Euler-Lagrange equation analytically and then use numerical methods to solve this equation to find the "optimal" height profile for different frequencies. We then compare these profiles to the corresponding ones previously found using the Euler-Bernoulli beam theory and see that in the lower range of the dimensionless frequency Ω (defined using the largest height of the plate), the optimal profiles almost coincide, as expected.

Original study on mathematical models for analysis of cellulose water content from absorbance/wavenumber shifts in ATR FT-IR spectrum

The aim of this research was to evaluate the applicability of the attenuated total reflectance Fourier-transform infrared (ATR FT-IR) spectroscopy in the quantitative analysis of the moisture content in cellulose (from 0.5 to 11.0 wt.%). Innovatively, this work describes the variations in both absorbance and wavenumber of 16 absorption bands plotted as a function of cellulose water amount measured with Karl-Fischer titration. Different regression models were investigated (simple linear, semilogarithmic, power) and the adjusted coefficient of determination (R2) was given for each calculation. While model exhibited R2 > 90%, the standard error of calibration (SEC) was presented and an external validation has been performed. Regarding the absorbance-water content relationship, data recorded for sixteen peaks was successfully fitted with linear functions exhibiting R2 > 90%. The highest value of R2 = 98.7% and standard error of prediction SEP = 0.3wt.% have been assigned to the maximum from 3339 to 3327 cm−1 (–OH), proving ATR FT-IR usefulness in quantitative analysis.

Propagation length enhancement of surface plasmon polaritons in ultrafine Au nanodisk array, the role of kinky breather and periodic lump

We deal with a non-radiative approach to investigate the propagation of Surface Plasmon Polaritons (SPPs) in an Au nanodisk array in touch with an analyte medium. We obtain a nonlinear equation with solutions as in the form of kinky breather and periodic lump. The nonlinear response depends on the dielectric constant and wavenumber variation in analyte zone. It is shown that the periodic feature can guarantee the enhanced propagation length of SPPs stationary modes. Analytical results also reveal the occurrence of Fano resonance while numerical results show that the propagation length can go beyond 56 μm. On the other hand, using Kretschmann-Raether approach, we reach the Fano resonance in consequence of the interaction of dark and bright plasmon modes which is in agreement with our model and interpretation. Our nonlinear model can give a sketch for SPPs propagation especially in bio-sensing application.

Dual-Principal Component Analysis of the Raman Spectrum Matrix to Automatically Identify and Visualize Microplastics and Nanoplastics.

As emerging contaminants, microplastics are challenging to characterize, particularly when their size is at the nanoscale. While imaging technology has received increasing attention recently, such as Raman imaging, decoding the scanning spectrum matrix can be difficult to achieve result digitally and automatically via software and usually requires the involvement of personal experience and expertise. Herewith, we show a dual-principal component analysis (PCA) approach, where (i) the first round of PCA analysis focuses on the raw spectrum data from the Raman scanning matrix and generates two new matrices, with one containing the spectrum profile to yield the PCA spectrum and the other containing the PCA intensity to be mapped as an image; (ii) the second round of PCA analysis merges the spectrum from the first round of PCA with the standard spectra of eight common plastics, to generate a correlation matrix. From the correlation value, we can digitally assign the principal components from the first round of PCA analysis to the plastics toward imaging, akin to dataset indexing. We also demonstrate the effect of the data pretreatment and the wavenumber variations. Overall, this dual-PCA approach paves the way for machine learning to analyze microplastics and particularly nanoplastics.

Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Abstract. Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

Effect of Varying Bottom Topography on the Radiation of Water Waves by a Floating Rectangular Buoy

In the present study, the effect of an undulated bottom topography on the radiation of water waves by a floating rectangular buoy is analyzed. Various physical quantities of interest such as the added mass and damping coefficients associated with the surge, heave, and pitch motions are analyzed for a variety of parameters associated with the incident waves and bottom undulations. The study reveals that the added mass and damping coefficients associated with the surge and pitch motions of the floating buoy vary in an oscillatory manner with the variation in wavenumber for a sinusoidally varying bottom topography. Moreover, the oscillation amplitude is higher around the primary Bragg value. Further, this oscillatory pattern and oscillation amplitude increase with an increase in the ripple amplitude and the number of ripples for a sinusoidally varying bottom. However, a reverse pattern is formed with an increase in the depth ratio. In the long-wave regime, the added mass and damping coefficient corresponding to the surge motion become higher for a protrusion-type bed profile and lower for a depression-type bed profile. However, a reverse pattern is observed in the intermediate- and short-wave regimes.

A rigorous approach to optimal profile design for acoustic black holes.

Calculus of variations is used to determine a profile shape for an acoustic black hole without a layer of viscoelastic dampening material with fixed parameters of geometry (i.e., length, maximal and minimal thickness), which minimizes the reflection coefficient, without violating the underlying assumptions of existence for acoustic black holes. The additional constraint imposed by keeping the normalized wave number variation (NWV) small everywhere in the acoustic black hole is handled by the use of Lagrange multipliers. From this method, closed-form expressions for the optimal profile, its reflection coefficient, and the NWV are derived. Additionally, it is shown that in the special case where only the NWV (and not the reflection coefficient) is considered, the optimal profile reduces to the well-known thickness profile for acoustic black holes, h(x)=ϵx2. We give a numerical example of the difference between an acoustic black hole with optimal profile and classical profile, h(x)=ϵxm, m > 2. For close to identical reflection coefficients, the optimal profile vastly outperforms the classical profile in terms of having low NWV at a large range of frequencies.

Unveiled density wave in Saturn’s rings

We unveil a two-dimensional visualization of the Mimas 5:3 density wave in Saturn’s rings, created directly from 31 radial optical depth profiles of the rings obtained between 2005 and 2008 from Cassini Radio Science Subsystem (RSS) occultation observations, assuming only its predicted pattern speed and taking advantage of its evident four-armed structure. Using a variety of interpolation and smoothing methods to combine the observations, the resulting image of the density wave is a striking confirmation of the expected wave properties based on dynamical theories. From measurements of the radial locations of the wave peaks and troughs, we measure the variation of wavenumber across the wave and use this information to compute the variable background surface density in the wave region. We are able to compute the angular momentum luminosity in the linear regime by two methods, using either the satellite potential or the observed optical depths. The two methods give results of the same order of magnitude.

Complex ray theory applied to instability of a two-dimensional wake

Complex ray theory successfully describes temporal and spatial development of a two-dimensional wave packet into steady and semi-infinite distribution of very large disturbances in the wake accompanied by a region of reverse flows. Final formation of the steady state is caused by the existence, on integral path of propagation equations, of a logarithmic singularity, at which the group velocity and wave-number variation both vanish and the temporal growth rate is positive. Nearly singular frequencies around the complex frequency defined at the singularity pass through a close vicinity of the singular point while spending a very large time and then compose the distributed disturbances at the limit of large time. Propagation of the nearly singular frequencies can be pursued by an appropriate application of the complex-time method of integral to the region away from the singularity and the complex-coordinate method of integral to its neighborhood.

Partition of Unity Finite Element Method for the modelling of Acoustic Black Hole wedges

The Acoustic Black Hole (ABH) phenomenon can be exploited to manipulate and mitigate flexural wave propagation in thin-walled structures. ABH structures feature unique space-dependent wavenumber variation and wave celerity reduction in the tapered ABH area, thus posing challenges to the existing modelling techniques. In this work, the Partition of Unity Finite Element Method (PUFEM) is revamped to simulate the structural response of an ABH wedge subject to a harmonic loading. This method allows the incorporation of auxiliary enrichment functions into the finite element framework in order to cope with the ABH-induced wave oscillating behaviour, exemplified by the varying wavenumber and amplitude in space. The PUFEM tapered Timoshenko beam elements are constructed by employing wave enrichment functions with the Wentzel-Kramers-Brillouin (WKB) approximation method. A wavelet enrichment is also investigated as hierarchic refinement. Using these enriched elements, the frequency responses of an ABH wedge and the convergence of numerical solutions are computed and compared with the classical linear FEM and the elements enriched with ‘local’ wave solutions. An adaptive meshing scheme is designed and implemented to further accelerate the solution convergence. It is shown that the PUFEM offers a good computational accuracy and drastic reduction of degrees of freedom for solving the broadband ABH problems, outperforming the classical FEM.

Dynamics of acoustic impedance matching layers in contactless ultrasonic power transfer systems

The acoustic impedance mismatch between transducer materials and medium in ultrasonic power transfer systems narrows the transduction bandwidth and causes losses through the back reflection of progressive pressure waves at the boundary between the transducers and medium. Capturing both resonances and losses due to impedance mismatch of interwoven elements is essential for advancing the development of these systems. We present a unified approach, based on the multiplication of a sequence of transfer matrices, to determine an equivalent acoustic impedance. The analytical model couples the properties of the transmitter and receiver with multiple matching layers and a single classical quarter-wave layer in controlled setups with the objective of minimizing reflections through acoustic impedance mismatch alleviation. Losses due to ultrasonic attenuation in the material layers and medium are also considered. The acoustic field at the receiver location constitutes the input to the coupled electro-elastic equations of the fluid-loaded and electrically-loaded piezoelectric receiver. Experiments are performed to identify the input acoustic pressure from a cylindrical transmitter to a receiver disk operating in the 33-mode of piezoelectricity. The results show significant enhancements in terms of the receiver’s electrical power output when implementing a two-layer matching structure. We present the results showing non-dimensional wave number variations versus characteristic impedance, which can be used to calculate the materials’ thicknesses for acoustically matching ultrasonic power transfer systems to an acoustic medium of interest at any desired resonant frequency while considering any type of glue or epoxy as the bonding layer. The derived physical models facilitate the development of high-fidelity matched systems with enhanced contactless power transmission.

A Study of Wave Refraction in a Marginal Ice Zone: Frazil-Pancake Ice

Theoretical estimates based on both offline calculation and an online model are made to study the wavenumber variations during wave refraction in a marginal ice zone (MIZ). Analysis of in situ observations from the MIZ of the Arctic Ocean confirms the conclusion drawn based on theoretical estimates as well as the simulation ability of our new model to describe wave evolution in the MIZ. In wave refraction, variation of wavenumber in magnitude is determined by the incident wavenumber and the ice mass. A larger incident wavenumber or a larger ice mass leads to a larger variation of wavenumber in magnitude, though during refraction, the variation of wavenumber in magnitude is more sensitive to the incident wavenumber because it is proportional to the cube of the incident wavenumber, while it is linearly proportional to the ice mass. On the other hand, both the angle of refraction and the deflection are determined by the angle of incidence, the incident wavenumber and the ice mass. A larger angle of incidence, a shorter wave or larger ice mass results in a larger angle of refraction and a larger deflection. All these conclusions are supported by offline calculations, an online model and in situ observations. The online model also suggests that the instrument should be kept at a distance from the ice edge to obtain more general information of the open ocean.

Stochastic wave finite element quadratic formulation for periodic media: 1D and 2D

Abstract Periodic structures have properties of controlling mechanical waves. These solutions are used in aircraft, trains, submarines, space structures, where high level of robustness has to be ensured in presence of uncertainty in the numerical models. The paper presents a stochastic formulation for the Bloch analysis of periodic structures, based on the quadratic 1D and 2D forms of the Wave Finite Element method. In 1D case, numerical examples of periodic rod and metamaterial rod systems are considered; for the 2D case, homogeneous and periodic plates are considered. In both cases, the effect of uncertainties on wavenumber variation is studied. The accuracy and performance of the developed method is compared with Monte Carlo Simulation (MCS) results. It is found that the uncertainties affects the wavenumber scattering. Maximum variation of wavenumber occurs at the band gap edge frequencies and trends are increasing in higher frequency. In terms of computational cost, the presented formulation offers advantages over MCS. The obtained computational cost savings can be a remarkable achievement for the optimization and reliability study under uncertainties of complex structures.

Microwave Tunable Devices on the YIG-VO2 structures

The theory describing a tunability of the spin-wave spectrum for the ferrite/vanadium dioxide layered structures through changing the VO2 conductivity is suggested. An influence of the various parameters on the spin-wave wavenumber variations and damping decrement is studied. We show that an effective wavenumber variation with minimal losses is achieved by matching the thicknesses of the ferrite and vanadium dioxide films, as well as the value of external magnetic field. We show also that owing to the electrodynamic interaction, a quality of contact between the ferrite and vanadium dioxide layers is not critical.

Dipole–dipole interactions between tryptophan side chains and hydration water molecules dominate the observed dynamic stokes shift of lysozyme

The fluorescence intensity of tryptophan residues in hen egg-white lysozyme was measured up to 500 ps after the excitation by irradiation pulses at 290 nm. From the time-dependent variation of fluorescence intensity in a wavelength range of 320–370 nm, the energy relaxation in the dynamic Stokes shift was reconstructed as the temporal variation in wavenumber of the estimated fluorescence maximum. The relaxation was approximated by two exponential curves with decay constants of 1.2 and 26.7 ps. To interpret the relaxation, a molecular dynamics simulation of 75 ns was conducted for lysozyme immersed in a water box. From the simulation, the energy relaxation in the electrostatic interactions of each tryptophan residue was evaluated by using a scheme derived from the linear response theory. Dipole–dipole interactions between each of the Trp62 and Trp123 residues and hydration water molecules displayed an energy relaxation similar to that experimentally observed regarding time constants and magnitudes. The side chains of these residues were partly or fully exposed to the solvent. In addition, by inspecting the variation in dipole moments of the hydration water molecules around lysozyme, it was suggested that the observed relaxation could be attributed to the orientational relaxation of hydration water molecules participating in the hydrogen-bond network formed around each of the two tryptophan residues.

Investigation of the permeation enhancer strategy on benzoylaconitine transdermal patch: the relationship between transdermal enhancement strength and physicochemical properties of permeation enhancer

Permeation enhancer strategy is used to develop Benzoylaconitine (BA) of high molecular weight (603.7 Da) into transdermal patch. The present study was to achieve a patch with good analgesic and anti-inflammatory effects and investigate the relationship between physicochemical parameters of enhancers and enhancement strength. In vitro skin permeation study was used to evaluate the effect of enhancers, and correlation study was conducted to clarify the relationship between physicochemical parameters of enhancer and permeation amount. The enhancement molecular mechanism was characterized using FT-IR and molecular modeling. Finally, pharmacodynamic effect of BA patch was evaluated with analgesic and anti-inflammatory assessment. The correlation analysis indicated that the optimized patch containing permeation enhancer Plurol® Oleique CC497 with high surface tension (43.0 dyne/m), demonstrated the strongest skin permeation amount of 5.50 ± 0.21 μg/cm2. According to the FT-IR and molecular modeling study, the enhancer with high surface tension demonstrated maximum interaction strength (Emix = −9.20 kcal/mol) with skin lipid and affected the skin protein region, which strongly disturbed skin lipid arrangement according to the results of ATR-FTIR study (wavenumber variation of νas CH2 of skin lipid > 2.00 cm−1) and molecular modeling (Cohesive Energy Density of skin lipid bilayer = 1.04E + 08 kcal/mol). It was indicated that only based on sufficient interaction strength and disturbing of both lipophilic and hydrophilic area of stratum corneum, permeation enhancer was able to demonstrated great permeation enhancement effect. Finally, BA transdermal patch was developed and showed excellent analgesic and anti-inflammatory effect, which was a potential preparation for the treatment of inflammatory pain.

A novel Nd3+‐doped MgO‐Al2O3‐SiO2‐based transparent glass‐ceramics: Toward excellent fluorescence properties

AbstractGenerally, glass‐ceramics have superior properties compared to their parent glasses. Here, we prepared a novel Nd3+‐doped MgO‐Al2O3‐SiO2‐based transparent glass‐ceramics with excellent fluorescence properties. The effects of Nd2O3 content on the structure and properties of glass‐ceramics were studied, aiming to provide a key guidance for preparing this transparent glass‐ceramics. The results revealed that the glass stability increased originally and then decreased with increasing Nd2O3 content, so did the variation of wavenumbers in infrared spectra. And these glass‐ceramics are mainly composed of cordierite with residual glassy phase. The three phenomenological intensity parameters (Ω2,4,6) and radiative properties were estimated by Judd‐Ofelt theory, and the values of Ω2 first decreased and then increased with increasing Nd2O3 content. Three main emission peaks ascribed to the transitions from 4F3/2 to 4I9/2, 4I11/2, 4I13/2 at 898, 1057, 1330 nm were observed, respectively. The branching ratios for 4F3/2→4I11/2 transition increased as the Nd2O3 content raised, and the fluorescence lifetimes of the 4F3/2 level were found to increase first and then decrease with Nd2O3 content (from 181 to 726 μs). The excellent fluorescence properties indicate that this novel glass‐ceramics can be used as a potential solid‐state optical functional material for 1.06 μm laser emission.