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In this article, the dynamic characteristics of bimaterial composite spheres under spherical waves induced by cyclic pressure are studied. First, on the basis of the Lamb Decomposition and Variable Separation method, the analytical expression of spherical wave is conducted, which satisfies the stress equilibrium on the outer and inner surfaces of the sphere. Next, algebraic equations with respective boundary conditions are composed and solved by Legendre Polynomial expansion and effective truncation techniques. Obtained results enable to reveal the influence on the dynamic stress concentration factor intensity under proper conditions. The conclusions of this article are verified by comparing the analytical solutions to the ones obtained by the finite element method. This article can provide a theoretical method for the analysis of mechanical properties of multilayered spherical structure under dynamic loading. [ABSTRACT FROM AUTHOR]

Abstract Seismic source location is a classic inverse problem in seismology. In mathematical physics, inverse problems have multiple natural solutions. The objective of this study was to develop a generic theory and method of seeking the true solution from multiple solutions for the location of a coal mine seismic source in an idealized velocity structure model of a coal mine with a small scale and complex geological environment. Starting from the simplest velocity structure model, the complexity of the model gradually increased, until it approached the real velocity structure model, i.e., the multilayered horizontal and inclined velocity structure model, in order to find a generic method for solving the multi-solution inverse problem of coal mine seismic source location. Specifically, the wavefront distribution equation in a two-layer horizontal medium was derived and then expanded to any multi-layer horizontal medium. Based on this equation, a positive definite nonlinear equation system was established from the perspective of any observation system. The equation system contained four unknown variables of the spatiotemporal position of the seismic source. To determine the spatiotemporal parameters of the seismic source, nonlinear equations for four stations were required. To solve the nonlinear equation system, an initial iteration value was determined. In order to reduce the difficulty of determining the initial iteration value, the variable substitution method was used to reduce the number of location parameters. By rotating the original geodetic coordinate system of the station to be parallel and orthogonal to the medium interface, the wavefront method was extended to inclined medium. In conclusion, in this study, the problem of coal mine seismic source location in a multi-layer horizontal or inclined medium was effectively solved. The method proposed in this study provides a reference for solving the true solution from multiple solutions for the location of a coal mine seismic source in small-scale coal mines with complex geological environments.

This paper explores the potential near-field beamforming (NFBF) in integrated sensing and communication (ISAC) systems with extremely large-scale arrays (XL-arrays). The large-scale antenna arrays increase the possibility of having communication users and targets of interest in the near field of the base station (BS). The paper first establishes the models of near-field spherical waves and far-field plane waves. With the models, we analyze the near-field beam focusing ability and the far-field beam steering ability by finding the gain-loss mathematical expression caused by the far-field steering vector mismatch in the near-field case. Subsequently, we analyzed the performance degradation caused by traditional far-field beamforming in the near field for both communication and sensing. We formulate the transceiver NFBF design problem as maximizing the sensing signal-to-interference-plus-noise ratio (SINR) while ensuring the required communication quality-of-service (QoS) and total power constraint. We decompose it into two subproblems and solve them using the generalized Rayleigh entropy theory and the Semi-Definite Relaxation (SDR) technique. Additionally, we prove the attainability of the optimal solution for SDR. Additionally, a low-complexity design scheme is proposed as an alternative to the SDR approach for obtaining transmit beamforming. The simulation results validate the effectiveness of the proposed NFBF scheme, demonstrating its capability to manage co-angle interference and enhance both communication and sensing performance.

With the successful deployment of fifth-generation (5G) systems, both industry and academia anticipate the evolution of 6G systems to meet future data-intensive needs. 6G aims to enhance coverage, capacity, and spectral efficiency, with extremely large-input multiple-output (XL-MIMO) base stations (BS) being central to this vision. In addition, the mid-band spectrum (7-15 GHz) becomes a strategic choice, providing sufficient bandwidth and reasonable path loss characteristics. However, the implementation of XL-MIMO in the mid-band will bring fundamental changes to the electromagnetic signal propagation characteristics, especially due to the increase in Fraunhofer distance. Therefore, it is necessary to model the waves as spherical for near-field scenarios. Furthermore, the efficient operation of communication systems depends on accurate knowledge of channel state information (CSI). However, existing CSI feedback schemes (Type-1 and Type-2) were originally designed based on far-field assumptions and exhibit obvious limitations when applied to XL-MIMO systems operating within the mid-band spectrum. To address this issue, this paper proposes two innovative CSI feedback frameworks: Type-3 for single-user MIMO (SU-MIMO) scenarios and Type-4 for multi-user MIMO (MU-MIMO), providing comparable uplink overhead compared to Type-1 and Type-2 respectively. Furthermore, the performance of the proposed Type-3 and Type-4 feedback schemes in terms of spectral efficiency and overhead is also evaluated and compared with existing Type-1 and Type-2 feedback schemes. Results demonstrate the superiority of the proposed CSI feedback schemes over existing feedback schemes, remaining resilient to performance degradation with an increase in the oversampling factor while maintaining similar uplink overhead. Notably, Type-4 demonstrates significant performance improvements compared to existing Type-2 feedback, and the gain amplifies as the number of UEs increases in MU-MIMO scenarios. The results show that the proposed CSI feedback scheme alleviates the limitations of existing feedback schemes and significantly enhances the system performance in near-field XL-MIMO environments.

We study the electromagnetic radiation of a charged particle bunch with small size moving at a constant velo city and having a variable charge. The environment medium is considered to be isotropic and homogeneous, and it may have frequency dispersion, but not spatial dispersion. The general solution of the problem is obtained. The main attention is paid to the case when the bunch charge, starting from a certain moment, decreases exponentially with time. The saddle point metho d is used to obtain the approximate expressions for the field components that are valid in the wave zone. The energy characteristics of the excited spherical wave are studied and compared with the case of a decelerating charge. In the case of excitation of Vavilov–Cherenkov radiation, we obtain the asymptotics which are valid in the entire wave zone, including the region in which the field cannot be divided into the spherical and cylindrical waves. [ABSTRACT FROM AUTHOR]

A piecewise-homogeneous medium, consisting of anisotropic layers, is excited by a primary spherical sound wave due to a point source lying in the exterior of the medium or in one of its layers. The direct scattering problem is formulated by means of a modified scalar Helmholtz equation incorporating the anisotropic characteristics of the problem. The T-matrix of the problem is determined analytically by means of a suitable coordinate transformation. Then, the acoustic fields in all layers are obtained. Finally, specific reductions to special cases are presented. [ABSTRACT FROM AUTHOR]

A piecewise-homogeneous medium, consisting of anisotropic layers, is excited by a primary spherical sound wave due to a point source lying in the exterior of the medium or in one of its layers. The direct scattering problem is formulated by means of a modified scalar Helmholtz equation incorporating the anisotropic characteristics of the problem. The T-matrix of the problem is determined analytically by means of a suitable coordinate transformation. Then, the acoustic fields in all layers are obtained. Finally, specific reductions to special cases are presented.

The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it is necessary to achieve consistency between gradient, divergence and Laplace operators and to establish, beside the conventional radial Nabla operator ∂Φ/∂r, a new variant ∂rΦ/r∂r. The two Nabla operator variants differ in the near field term Φ/r whereas in the far field r≫0 there is asymptotic approximation. Surprisingly, the more complicated gradient ∂rΦ/r∂r results in unexpected simplifications for – and only for – spherical waves with the 1/r amplitude decrease. Thus the calculation always remains elementary without the wattless imaginary near fields, and the spherical Bessel functions are obsolete.

When developing oil fields, periodic wave disturbances are used to increase the well flow rate and increase the ultimate oil recovery of the reservoirs. In an inhomogeneous medium, in the presence of dissipation and/or dispersion, the harmonic oscillations generated in the well bottoms turn into sawtooth waves with periodic shock fronts. The article describes and investigates oneand two-dimensional nonlinear mathematical models of such processes. [ABSTRACT FROM AUTHOR]

In this work, we show that the near field of leaky-wave resonant antennas (LWAs) radiating into a dense medium can be locally represented as a spherical wave in a certain solid angle around broadside using an accurate definition of the phase center. The near field in this solid angle can be efficiently evaluated through the integration of the spectral Green’s function along the steepest descent path (SDP). Beyond this solid angle, defined as the shadow boundary angle, a residual contribution due to the leaky-wave pole must also be added to fully describe the near field. It is found that this shadow boundary angle can be used to define the phase center and geometry of a truncated lens that couples well to leaky-wave antennas, even in electrically small-to-medium sized lenses and low-contrast cases. To demonstrate the applicability of the proposed study, we combine the SDP field calculation with a Fourier optics (FO) methodology to evaluate the aperture efficiency and radiation patterns of small-to-medium sized lenses in reception. A truncated silicon lens with a diameter of only four free-space wavelengths is presented with almost 80% aperture efficiency. Excellent agreement with full-wave simulations is achieved, which demonstrates the accuracy of the proposed design and analysis methodology. [ABSTRACT FROM AUTHOR]

Multipolarized Uniform Rectangular Array (mURA) Massive Multiple Input Multiple Output systems (mMIMOs) is a promising technology in 5G wireless communications. Thus, in this paper, a three dimensional geometry (3-DG) channel model of mURA is established, mostly used in indoor or outdoor. The three-dimension channel model of mURA proposed is evaluated in which a Spherical-Wave (SW) is used to model the close-field, and compared with the Plane-Wave (PW) that model the far-field. The Channel Orthogonality (CO) is driven for various parameters characterize mMIMOs and communication environment. The proposed model provides the best performances. [ABSTRACT FROM AUTHOR]

The resolution-priority holographic stereogram uses spherical waves focusing on the central depth plane (CDP) to reconstruct 3D images. The image resolution near the CDP can be easily enhanced by modifying three parameters: the capturing depth, the pixel size of elemental image and the focal length of lens array. However, the depth range may decrease as a result. In this paper, the resolution characteristics were analyzed in a geometrical imaging model, and three corresponding methods were proposed: a numerical method was proposed to find the proper capturing depth; a partial aperture filtering technique was proposed after reducing pixel size; the moving array lenslet technique was introduced after increasing focal length and partial aperture filtering. Each method can enhance resolution within the total depth range. Simulation and optical experiments were performed to verify the proposed methods. [ABSTRACT FROM AUTHOR]

The Green's function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed. [ABSTRACT FROM AUTHOR]

A fractional-order wave equation is established and solved for a space of three dimensions using spherical coordinates. An equivalent fluid model is used in which the acoustic wave propagates only in the fluid saturating the porous medium; this model is a special case of Biot’s theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The basic solution of the wave equation is obtained in the time domain by analytically calculating Green’s function of the porous medium and using the properties of the Laplace transforms. Fractional derivatives are used to describe, in the time domain, the fluid–structure interactions, which are of the inertial, viscous, and thermal kind. The solution to the fractional-order wave equation represents the radiation field in the porous medium emitted by a point source. An important result obtained in this study is that the solution of the fractional equation is expressed by recurrence relations that are the consequence of the modified Bessel function of the third kind, which represents a physical solution of the wave equation. This theoretical work with analytical results opens up prospects for the resolution of forward and inverse problems allowing the characterization of a porous medium using spherical waves.

The scintillation index (SI) is an important issue in studying the effect of the atmospheric turbulence in light wave propagation. As the computation time is important in case of mobile applications, a closed form for the SI of slant path is more attractive than its integral form. In a previous work (Fayed et al. in Opt Eng 55:056113, 2016), we derived the slant path SI in a closed form for spherical waves proposing a polynomial model for the refractive index structure parameter. In this paper, closed form expressions for uplink and downlink slant path SI are derived from the integral forms using the polynomial model of refractive index structure parameters for a plane wave propagating through atmospheric turbulence. The obtained results reveal the effects of propagation distance, transmitter/receiver height and elevation angle on the uplink and downlink SI. A comparison between uplink and downlink SI is carried out. The derived expressions for the plane wave are compared with that previously derived for the spherical wave. The obtained results demonstrate a way to improve the uplink SI of the plane wave by increasing the transmitter height to 150 m. [ABSTRACT FROM AUTHOR]

The effect of anomalous transparency on the passage of sound from water to air is considered. A mathematical model is used to calculate the coefficient of pressure transmission through the water–air interface taking into account the influence of inhomogeneous plane waves. The features of the acoustic field in air are shown for an underwater source located at a distance from the media interface smaller than the wavelength. The theoretical dependences of the pressure transmission coefficient on the wave distance from the source to the interface are given. The conditions and methods for measuring the coefficient of transmission of spherical waves through a planar interface are described. The experimental dependences of the pressure transmission coefficient on the radiation frequency and depth of the source are presented. Oscillograms of acoustic signals transmitted from water to air are shown. [ABSTRACT FROM AUTHOR]

The resolution-priority holographic stereogram uses spherical waves focusing on the central depth plane (CDP) to reconstruct 3D images. The image resolution near the CDP can be easily enhanced by modifying three parameters: the capturing depth, the pixel size of elemental image and the focal length of lens array. However, the depth range may decrease as a result. In this paper, the resolution characteristics were analyzed in a geometrical imaging model, and three corresponding methods were proposed: a numerical method was proposed to find the proper capturing depth; a partial aperture filtering technique was proposed after reducing pixel size; the moving array lenslet technique was introduced after increasing focal length and partial aperture filtering. Each method can enhance resolution within the total depth range. Simulation and optical experiments were performed to verify the proposed methods.

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

This paper presents a beamforming-based acoustic imaging (BBAI) method employing a two-dimensional (2D) microphone array that not only can locate an acoustic source in the XY plane parallel to the array, but can also identify the distance between the source and array in the Z direction, denoted as the source depth, and thus provides three-dimensional (3D) localization ability. In this method, the acoustic field is reconstructed on virtual XY planes at different distances along the Z direction. The source depth is then determined according to the virtual plane providing the maximum response of the acoustic field. The location of the source in the X and Y directions of the identified virtual plane can then be easily determined based on the standard beamforming principles of a planar array. The proposed BBAI method is evaluated based on simulations involving single- and multiple-point sources, and corresponding experimental evaluations are similarly conducted in an anechoic chamber. Both simulation and experimental results demonstrate that the proposed method is capable of locating acoustic sources in 3D space.