Plane Wave Model Research Articles

A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase-lag model

Purpose In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium. Design/methodology/approach The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis. Findings The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed. Originality/value To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

Memory-dependent derivative effect on 2D problem of generalized thermoelastic rotating medium with Lord–Shulman model

The model of two-dimensional plane waves is studied in a generalized thermoelastic medium under memory-dependent derivative in the Lord–Shulman model. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, the displacement component and the thermal stress component. The resulting formulation is applied to a concrete problem that deals with a thick plate subjected to a time-dependent heat source on each face. According to the graphical representations, corresponding to the numerical results, the effect of the different kernel has studied different thermophysical quantities at different times. Moreover, graphs are drawn to show the influence of rotation in all the thermophysical quantities. Some three-dimensional figures also are drawn for a better understanding of thermophysical quantities in the different positions of the body. As per the author’s knowledge, the effect of rotation with the memory effect is not available in the literature till now. The differences for different kernel functions are also presented at different times.

Absorbance and optical responsivity of two-dimensional mechanical resonators at oblique incidence

Optical reflectometry is a well known technique employed to measure the displacement response of mechanical resonators. This technique consists in shining monochromatic light on the resonator at normal incidence and measuring the intensity of reflected light. In the case of resonators fabricated from suspended membranes of two-dimensional materials, fluctuations of distance between the membrane and the underlying substrate are transduced into fluctuations of reflected light intensity. Here we consider an alternate configuration where we shine light at oblique incidence. Within the plane wave model, we calculate the absorbance of the membrane, the reflectance of the device composed of the membrane and the reflective substrate, and the optical responsivity defined as the derivative of reflectance with respect to membrane displacement. We illustrate our calculations with the example of a resonator based on monolayer molybdenum disulfide and find that these quantities can be tuned by changing the angle of incidence, especially in the case of s-polarized light. These results may serve to design experiments where the absorbance and optical responsivity of the resonator are tuned by tilting the device.

Gaussian beam scintillation index for slant path in weak turbulence: closed form expressions

The scintillation index (SI) is an important issue in studying the effect of the atmospheric turbulence in the light waves. With the Rytov weak fluctuation theory, the SI is commonly referred to the Rytov parameter. The previous studies dealt with the plane wave and spherical wave models. Each of these gives an idea of how an optical beam will react to turbulence but are not realistic. One is infinitely long, while the other is an infinitesimal point source. The Gaussian beam wave is the most realistic of the optical waves, but also the most complex to use for calculations. In this paper, a closed form expression for Gaussian beam SI propagation in slant path and through weak fluctuation is derived using the polynomial model of the refractive index structure parameter. The slant path SI model of the plane and spherical waves can be generated from the SI expression of Gaussian beam. The analytic expressions are obtained and are then used to analyze the effect of propagation distance, transmitter/receiver heights, and elevation angle on the SI. Signal to noise ratio and bit error rate are calculated for performance evaluation showing a significant enhancement at elevation angles greater than 45°.

Observation of ultraviolet whispering gallery modes in ZnMgO microrods

Abstract We report on the fabrication of ZnO and Zn0.9Mg0.1O microrods using nanoparticle assisted pulsed laser deposition (NAPLD). Micro-photoluminescence studies reveal that Zn0.9Mg0.1O microrods exhibited a blue shift in the ultraviolet (UV) emission relative to unintentionally doped ZnO that was attributed to the increase in bandgap due to Mg doping. High-resolution micro-photoluminescence clearly indicated the presence of whispering gallery modes (WGMs) for both ZnO and Zn0.9Mg0.1O. Transverse electric (TE) and transverse magnetic (TM) optical WGMs were identified using the existing plane-wave model. The observation of lower order WGM modes in Zn0.9Mg0.1O microrods may be of great interest for future UV WGM lasing.

The role of the time delay in the reflection and transmission of ultrashort electromagnetic pulses on a system of parallel current sheets

The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by current sheets embedded in three dielectrics, all with different index of refraction. The dynamics of the surface currents and the scattered radiation field are described by the coupled system of Maxwell–Lorentz equations. When applying the plane wave modeling assumptions, these reduce to a hybrid system of two delay differential equations for the electron motion in the layers and a recurrence relation for the scattered field. The solution is given as the limit of a singularly perturbed system and the effects of the time delay on the dynamics is analyzed.

A New Approximate Method for Quantifying Tsunami Maximum Inundation Height Probability

Regional and global tsunami hazard analysis requires simplified and efficient methods for estimating the tsunami inundation height and its related uncertainty. One such approach is the amplification factor (AF) method. Amplification factors describe the relation between offshore wave height and the maximum inundation height, as predicted by linearized plane wave models employed for incident waves with different wave characteristics. In this study, a new amplification factor method is developed that takes into account the offshore bathymetry proximal to the coastal site. The present AFs cover the North-Eastern Atlantic and Mediterranean (NEAM) region. The model is the first general approximate model that quantifies inundation height uncertainty. Uncertainty quantification is carried out by analyzing the inundation height variability in more than 500 high-resolution inundation simulations at six different coastal sites. The inundation simulations are undertaken with different earthquake sources in order to produce different wave period and polarity. We show that the probability density of the maximum inundation height can be modeled with a log-normal distribution, whose median is quite well predicted by the AF. It is further demonstrated that the associated maximum inundation height uncertainties are significant and must be accounted for in tsunami hazard analysis. The application to the recently developed TSUMAPS-NEAM probabilistic tsunami hazard analysis (PTHA) is presented as a use case.

Electronic and optical properties of double perovskite oxide Pb2ScMO6 (M = Ta, Sb) using a first principles approach

In this study, the electronic and optical properties of the double perovskite (DP) oxides Pb2ScMO6 (M = Sb, Ta) were systematically investigated using the full-potential linearized augmented plane wave model. Calculations were performed using both the generalized gradient approximation and modified Becke–Johnson potentials. The results showed that the O-atom is responsible for the maxima in the density of states (DOS) in the valence band, whereas the Sc-atom contributes to the maximum DOS in the conduction band. The dielectric constants, absorption coefficients, and reflectivity were also calculated for these systems. The results indicated the presence of wide band gaps in both of these DPs, thereby indicating their insulating semiconducting nature.

Simplification of roughness bottom backscattering model at small grazing angle in shallow-water

Bottom backscattering due to roughness seafloor is the main source of shallow water reverberation, especially in the waveguide with downward reflection profile or a calm sea-surface. Empirical backscattering models with a simple form has an important limitation to analyzing other characteristics of reverberation except for the intensity characteristics, which originates from optics and describes the relationship between the bottom backscattering strength and scattering grazing angle of plane-wave in half-infinite space. In the shallow water, such a plane-wave backscattering model cannot be used due to frequency dispersion. The model of bottom backscattering based on physical scattering principle is made to relieve such a limitation, but thereby bringing about another restraint by a geoacoustics model. The bottom backscattering model, which is formulated during modeling the full-wave reverberation theory at small grazing angle in range-independent shallow water waveguide, is simplified by combining with bottom reflection coefficient model which is independent of the geoacoustics model. The bottom reflection coefficient model as referred to the proposed phase parameter <i>P</i> in this paper is equivalent to velocity and density of sediment to describe sound field interacted with sea-bottom. Therefore simplification of bottom backscattering model can be handled by the phase parameter without any knowledge of bottom geoacoustic parameters. The angular dependency and intensity dependency of bottom backscattering due to roughness seafloor at small grazing angle are studied more in depth through such a simplified model. Marking 2/<i>P</i> as the cut-off point, the grazing angle is divided into two stages. Near the critical angle, as grazing angle is greater than 2/<i>P</i> and less than critical grazing angle, the angular dependency of bottom backscattering due to roughness seafloor is weighted by phase parameter of bottom reflection coefficient, while the intensity dependency is independent of phase parameter. At each small grazing angle, as grazing angle is less than 2/<i>P</i>, the angular dependency of bottom backscattering due to roughness seafloor is proportional to incident and scattering grazing angle squared and irrespective of phase parameter of bottom reflection coefficient which is like the empirical bottom backscattering model, while the intensity dependency is proportional to the fourth power of phase parameter. So the bottom has different influences on the angular dependency and intensity dependency of bottom backscattering in different stages of grazing angle.

Use of the corrected plane wave model for the determination of the reflection coefficient during horizontal plate swell interaction

The main objective of this work, is to calculate variations of the reflection coefficient of the regular wave by a submerged horizontal plate, using the corrected plane wave model, by choosing appropriately the immersion and the relative length of the plate. It is shown that with this correction the reflection coefficient has a good agreement with the experimental results (Brossard et al., Liu C.R).

Multichannel Phase Calibration for Linear Array Based on Extended <inline-formula> <tex-math notation="LaTeX">$\omega K$</tex-math> </inline-formula> Algorithm and Minimum-Entropy Method

Millimeter-wave imaging techniques have been used for security inspection at important checkpoints. With the increase of working frequencies of the imaging systems, the precise multichannel phase calibration becomes more and more important. Most of the traditional algorithms are used for the calibration of passive receiving antenna array, based on the signal model of far-field plane wave. However, the near-field spherical wave model should be utilized for the active wideband near-field imaging applications. Consequently, the traditional calibration algorithms cannot be used in wideband near-field imaging systems. The metal plate is usually employed for the calibration of wideband near-field imaging systems, but the precision is very sensitive to the flatness of the surface of the metal plate, which will result in additional phase error after calibration. In this letter, a multichannel phase error estimation and calibration method is proposed for the wideband linear array system. By using an extended $\omega K$ algorithm and the minimum-entropy method, the additional phase error of each channel after preliminary calibration is estimated and calibrated. Simulations and experimental results show the effectiveness of the proposed method.

Comparison of Plane Wave and Spherical Vector Wave Channel Modeling for Characterizing Non-Specular Rough-Surface Wave Scattering

This letter demonstrates advantages of modeling the nonspecular wave scattering from surfaces of a multiple-input multiple-output (MIMO) channel in terms of the spherical vector wave (SVW) mode expansion. We propose the SVW mode coupling matrix $\boldsymbol {M}$ as a more efficient alternative to the commonly used set of distinct plane waves. $\boldsymbol {M}$ incorporates the scattered field components through the limited number of modes due to the cutoff property. A planar surface with random roughness is used to simulate the nonspecular scattering contribution to the radio channel, which is computed using physical optics. The matrix $\boldsymbol {M}$ and the plane wave channel model parameters are estimated from simulated radio channels. The estimates are used to compare the contribution of the nonspecular scattering to the radio channel reproduced from these two approaches. The comparison is performed for a small array antenna arrangement. Compared are the error of the magnitudes of MIMO channel transfer matrix, the narrowband channel eigenvalues, the correlation matrix distance, and the mutual information. It is found that $\boldsymbol {M}$ from the SVW channel modeling performs better in reproducing the radio channel of nonspecular scattering from the studied rough surface.

Tunable and switchable lasing in a ZnO microwire cavity at room temperature

We present the concept for a wavelength tunable, single mode laser and its realization. The laser is based on a tapered microwire that is mechanically moved relative to the optical pumping area. The radius dependence of the whispering gallery mode (WGM) properties is thus translated into wavelength tuning of the emission. Since the spectral separation of the WGMs is as large as the spectral width of the gain spectrum (both about 50 meV for the demonstrated ZnO wire with radius of around 0.5 μm), continuous single mode tuning is achieved. We thoroughly model the laser properties such as gain spectrum and mode positions based on a plane wave model, taking into account absorption and gain regions within the wire due to inhomogeneous pumping.

Dual-Wavelength Temporal Dynamics of a Gain-Switched 2-μm Tm3+:Lu2O3 Ceramic Laser

We provide a detailed experimental investigation of the energy efficiency and rich temporal dynamics of a gain-switched 2-μm Tm3+:Lu2O3 ceramic laser pumped near 800 nm. A tunable Ti3+:sapphire laser was used to determine the full excitation spectrum and the optimum pumping bands for the 1.5% Tm3+:Lu2O3 ceramic gain medium. These bands were centered at 774, 796, and 811 nm. The highest output pulse energy was obtained when the pump wavelength was set to 796 nm. In the experiments, a free-running x-cavity was used to investigate the energy efficiency of the Tm 3+:Lu2O3 ceramic laser. Extracavity grating-dispersed output and prism-tuned resonator were used to further assess the role of cross-relaxation for the 1.5% Tm3+:Lu2 O3 ceramic. Finally, we demonstrate that as the pump energy was increased, a transition occurred from single-wavelength output (2068 nm) to dual-wavelength multipulse output (2068 and 1968 nm). We performed systematic temporal and spectral characterization measurements by using the free-running resonator, extracavity-grating-dispersed laser output, and prism-tuned resonator to investigate how the laser pulses at 1968 and 2068 nm evolved in time. A plane-wave rate equation model was further used to investigate the temporal dynamics of the Tm3+:Lu2O3 ceramic laser and provided predictions in qualitative agreement with experimental data.

Channel Characterization for Wideband Large-Scale Antenna Systems Based on a Low-Complexity Maximum Likelihood Estimator

Wideband large-scale array systems operating at millimeter-wave bands are expected to play a key role in future communication systems. It is recommended by standardization groups to use spherical-wave models (SWMs) to characterize the channel in near-field cases because of the large array apertures and the small cell size. However, this feature is not widely reflected in channel models yet, mainly due to the high computational complexity of SWMs compared to that of the conventional plane-wave model (PWM), especially when ultrawideband signals are considered. In this paper, a maximum likelihood estimator of low computational complexity is implemented with an SWM for ultrawideband signals. The measurement data obtained from an ultrawideband large-scale antenna array system at 28–30 GHz are processed with the proposed algorithm. The power azimuth-delay profiles estimated from the SWM and the PWM are compared to those obtained from rotational horn antenna measurement, respectively. It shows that the multipath components (MPCs) are well-estimated with the proposed algorithm, and significant improvement in estimation performance is achieved with the SWM compared to the PWM. Moreover, the physical interpretation of the estimated MPCs is also given along with the estimated scatterers.

Crystallographic features of the approximant H (Mn7Si2V) phase in the Mn–Si–V alloy system

The intermetallic compound H (Mn7Si2V) phase in the Mn–Si–V alloy system can be regarded as an approximant phase of the dodecagonal quasicrystal as one of the two-dimensional quasicrystals. To understand the features of the approximant H phase, in this study, the crystallographic features of both the H phase and the (σ → H) reaction in Mn–Si–V alloy samples were investigated, mainly by transmission electron microscopy. It was found that, in the H phase, there were characteristic structural disorders with respect to an array of a dodecagonal structural unit consisting of 19 dodecagonal atomic columns. Concretely, penetrated structural units consisting of two dodecagonal structural units were presumed to be typical of such disorders. An interesting feature of the (σ → H) reaction was that regions with a rectangular arrangement of penetrated structural units (RAPU) first appeared in the σ matrix as the initial state, and H regions were then nucleated in contact with RAPU regions. The subsequent conversion of RAPU regions into H regions eventually resulted in the formation of the approximant H state as the final state. Furthermore, atomic positions in both the H structure and the dodecagonal quasicrystal were examined using a simple plane-wave model with 12 plane waves.

How to precisely measure the volume velocity transfer function of physical vocal tract models by external excitation.

Recently, 3D printing has been increasingly used to create physical models of the vocal tract with geometries obtained from magnetic resonance imaging. These printed models allow measuring the vocal tract transfer function, which is not reliably possible in vivo for the vocal tract of living humans. The transfer functions enable the detailed examination of the acoustic effects of specific articulatory strategies in speaking and singing, and the validation of acoustic plane-wave models for realistic vocal tract geometries in articulatory speech synthesis. To measure the acoustic transfer function of 3D-printed models, two techniques have been described: (1) excitation of the models with a broadband sound source at the glottis and measurement of the sound pressure radiated from the lips, and (2) excitation of the models with an external source in front of the lips and measurement of the sound pressure inside the models at the glottal end. The former method is more frequently used and more intuitive due to its similarity to speech production. However, the latter method avoids the intricate problem of constructing a suitable broadband glottal source and is therefore more effective. It has been shown to yield a transfer function similar, but not exactly equal to the volume velocity transfer function between the glottis and the lips, which is usually used to characterize vocal tract acoustics. Here, we revisit this method and show both, theoretically and experimentally, how it can be extended to yield the precise volume velocity transfer function of the vocal tract.

A plane wave model for direct simulation of reflection and transmission by discretely inhomogeneous plane parallel media

A formulation is developed for numerically solving the frequency domain Maxwell’s equations in plane parallel layers of inhomogeneous media. As was done in a recent work [1], the plane parallel layer is modeled as an infinite square lattice of W × W × H unit cells, with W being a sample width of the layer and H the layer thickness. As opposed to the 3D volume integral/discrete dipole formulation, the derivation begins with a Fourier expansion of the electric field amplitude in the lateral plane, and leads to a coupled system of 1D ordinary differential equations in the depth direction of the layer. A 1D dyadic Green’s function is derived for this system and used to construct a set of coupled 1D integral equations for the field expansion coefficients. The resulting mathematical formulation is considerably simpler and more compact than that derived, for the same system, using the discrete dipole approximation applied to the periodic plane lattice. Furthermore, the fundamental property variable appearing in the formulation is the Fourier transformed complex permittivity distribution in the unit cell, and the method obviates any need to define or calculate a dipole polarizability. Although designed primarily for random media calculations, the method is also capable of predicting the single scattering properties of individual particles; comparisons are presented to demonstrate that the method can accurately reproduce, at scattering angles not too close to 90°, the polarimetric scattering properties of single and multiple spheres. The derivation of the dyadic Green’s function allows for an analytical preconditioning of the equations, and it is shown that this can result in significantly accelerated solution times when applied to densely-packed systems of particles. Calculation results demonstrate that the method, when applied to inhomogeneous media, can predict coherent backscattering and polarization opposition effects.

Discretisation Schemes for Level Sets of Planar Gaussian Fields

Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic compact manifolds. Our work is motivated by questions about the geometry of such random functions, in particular relating to the structure of their nodal and level sets. We study four discretisation schemes that extract information about level sets of planar Gaussian fields. Each scheme recovers information up to a different level of precision, and each requires a maximum mesh-size in order to be valid with high probability. The first two schemes are generalisations and enhancements of similar schemes that have appeared in the literature (Beffara and Gayet in Publ Math IHES, 2017. https://doi.org/10.1007/s10240-017-0093-0; Mischaikow and Wanner in Ann Appl Probab 17:980–1018, 2007); these give complete topological information about the level sets on either a local or global scale. As an application, we improve the results in Beffara and Gayet (2017) on Russo–Seymour–Welsh estimates for the nodal set of positively-correlated planar Gaussian fields. The third and fourth schemes are, to the best of our knowledge, completely new. The third scheme is specific to the nodal set of the random plane wave, and provides global topological information about the nodal set up to ‘visible ambiguities’. The fourth scheme gives a way to approximate the mean number of excursion domains of planar Gaussian fields.

A method for the design of ultrasonic devices for scanning acoustic microscopy using impulsive signals

Scanning acoustic microscopy (SAM) using impulsive signals is useful for characterization of biological tissues and cells. The operating center frequency of an ultrasonic device strongly depends on the performance characteristics of the device if the measurement is conducted by using impulsive signals. In this paper, a method for the design of ultrasonic devices for SAM using impulsive signals was developed. A new plane-wave model was introduced to calculate frequency characteristics of loss of ultrasonic devices by taking into account the conversion loss at the ultrasonic transducer, the transmission loss at the acoustic anti-reflection coating, and the propagation loss in the couplant. Ultrasonic devices were fabricated with a ZnO ultrasonic transducer using two acoustic lenses with aperture radii of 1.0 mm and 0.5 mm, respectively. The frequencies at which measured losses became minima corresponded to the calculation results by the plane-wave model. This numerical calculation method is useful for designing ultrasonic devices for acoustic microscopy using impulsive signals.