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There is today a growing need to accurately model the angular scattering response of metasurfaces for optical analog processing applications. However, the current metasurface modeling techniques are not well suited for such a task since they are limited to small angular spectrum transformations, as shall be demonstrated. The goal of this work is to overcome this limitation by improving the modeling accuracy of these techniques and, specifically, to provide a better description of the angular response of metasurfaces. This is achieved by extending the current methods, which are restricted to dipolar responses and weak spatially dispersive effects, so as to include quadrupolar responses and higher-order spatially dispersive components. The accuracy of the newly derived multipolar model is demonstrated by predicting the angular scattering of a dielectric metasurface placed in a vacuum. This results in a modeling accuracy that is substantially better than the standard dipolar model.

Recently, reconfigurable intelligent surface (RIS) has attracted continuous attention in wireless communications. Because the normal incidence condition of electromagnetic waves cannot always be satisfied in practical applications, the angular insensitivity in RISs has become an important issue. The angular sensitivity in RISs may lead to the failure of RIS-assisted wireless communication networks that rely on the reciprocity of wireless channels. In this work, an angle-insensitive 3-bit RIS meta-atom is proposed. By introducing metallic vias in the substrate of programmable meta-atoms, the interference induced by multiple reflections in the multilayered structure is restrained, and the decoupling between adjacent meta-atoms makes the metasurface insensitive to the incident angle. Hence the angular insensitivity can be achieved. An RIS is fabricated using the proposed angleinsensitive programmable meta-atom with metallic vias, which is capable of maintaining stable phase and amplitude responses at oblique incidences. Both simulated and measured results show stable angle performance. A maximum of 3150 phase range and eight digital coding states with 450 stable interval are obtained for wide incidence angles from 00 to 600. Finally, numerical simulations and experimental results of anomalous reflections are performed to verify the angular reciprocity of the proposed RIS, which is important in wireless communications.

The set-theoretical convergence of models of continuous and discrete synthesis processes in the compositions of metals and non-metals at the action of ray sources is shown. The non-metal density function obtained by the IDS thermal impulses on the temperature axis projection has a periodic view with fi xed stationary temperatures. They coincide with the boundaries of diff erent areas of change in the speeds of metal heating. This convergence of models to the general periodic operator is possible under four conditions of beam scanning: separation, compactness, property of states, stability. Then the current reciprocity ratios of the system (metals/non-metals) allow the use of the temperature of stationary non-metals as support for metals and serves to determine the parameters of ray sources when synthesizing structures in the compositions of the volume of the material.

A novel time-domain (TD) integral-equation (IE) technique for analyzing the pulsed electromagnetic (EM) scattering by a 2-D metasurface, represented by a thin highly contrasting screen with combined dielectric and magnetic properties, is presented. The problem under consideration is formulated with the aid of the EM reciprocity theorem of the time-convolution time. Subsequently, upon discretizing the space–time solution domain, the reciprocity relation is cast into two independent matrix forms whose elements are derived analytically using the classic Cagniard–DeHoop (CdH) technique. The thus obtained convolution-type systems of equations are solved for induced electric and magnetic currents through a stable step-by-step updating procedure. The presented numerical method is finally validated using alternative TD solutions.

The crosshole electromagnetic (EM) method is used in reservoir development monitoring and evaluation. It reflects the resistivity distribution between wells in the form of EM response changes and describes the spatial distribution of pore fluids in subsurface reservoirs based on the correlation between resistivity and pore fluids. This technique has been used to describe reservoirs, monitor steam and brine flooding to improve oil recovery, optimize the design of infilled wells, and verify the effectiveness of reservoir numerical simulations. However, due to the complexity of the electrical distribution of underground reservoirs and the limitations of the crosswell EM response range, there is still a lack of practical and effective crosswell EM imaging methods. This article presents a three-dimensional EM inversion scheme for interpreting crosswell data in the frequency domain with general measures. For the forward modeling, the equation for the secondary electric field was discretized using the staggered-grid finite difference scheme and was solved using the Krylov subspace iterative method. For the inversion problem, the general measure of the data misfit and regularization constraints were integrated using the Gauss–Newton minimization method to form an objective function. By selecting appropriate parameters and regularization constraints, the sharp boundaries and blocky features of the inverted target were recovered. The sensitivity was calculated using the reciprocity relationship, and the method was found to be beneficial to determining appropriate initial values of regularization coefficients. Two synthetic data sets and a field data inversion of a crosswell configuration demonstrate the feasibility of this scheme.

A Yb3+:KBaY(MoO4)3 (Yb3+:KBYM) crystal with dimensions of 51 mm × 27 mm × 10 mm was successfully grown by the TSSG method. The characteristics of the crystal structure and probability of good optical properties were analyzed. The absorption and emission spectra of Yb3+:KBYM crystal exhibit broadened bands, with the maximum absorption cross-sections of 1.17 × 10-20, 1.44 ×10-20 and 1.37 × 10−20 cm2 at 976 nm for X-, Y- and Z-polarizations, respectively. The corresponding absorption FWHMs are as wide as 77, 46 and 55 nm. The well-known re-absorption effect of Yb3+ in the crystal is discussed. Two methods, the Fuchtbauer-Ladenburg method (FL) and reciprocity method (RM) were adopted to compute the emission cross-sections and results show a certain discrepancy but the errors are allowable. The laser potentiality of the Yb3+:KBYM crystal was also evaluated by calculations of minimum inversion fraction β min , saturation pump intensity I sat , the minimum pump intensity I min and gain cross-sections spectra. Laser experiment was carried out and Watt-level continuous wave laser has been realized. Results indicate that the Yb3+:KBYM crystal with a disordered structure may be a potential laser media that can be used to generate tunable and ultrashort pulse laser emissions with high quality beam.

A passive method of realizing nonreciprocal wave propagation in a two-dimensional (2D) lattice is proposed, using bilinear springs combined with the necessary spatial asymmetry to provide a stable and strong departure from reciprocity. The bilinear property is unique among nonlinear mechanisms in that it is independent of amplitude but sensitive to the sign of the wave motion; the 2D setup allows the flexibility of generating spatial asymmetry at both small and large scales. The starting point is a linear 2D monatomic spring-mass lattice with strong directionally dependent wave propagation. The source and receiver are aligned so that there is virtually no direct wave transmission between them. Adding a region of bilinearity combined with spatial asymmetry that is not in the direct path between the source and receiver causes signal transmission via nonreciprocal scattering. A variety of spatially asymmetric bilinear configurations are considered, ranging from compact modulations confined within the unit cell to extended ones over the whole section, to obtain different dynamic nonreciprocal effects. Simulations illustrate how the combination of bilinearity and spatial asymmetry ensures a passive amplitude-independent nonreciprocal 2D system for a variety of different excitations.

Wave frequency is a critical parameter for applications ranging from human hearing, acoustic non-reciprocity, medical imaging to quantum of energy in matter. Frequency alteration holds the promise of breaking limits imposed by the physics laws such as Rayleigh’s criterion and Planck–Einstein relation. We introduce a linear mechanism to convert the wave frequency to any value at will by creating a digitally pre-defined, time-varying material property. The device is based on an electromagnetic diaphragm with a MOSFET-controlled shunt circuit. The measured ratio of acoustic impedance modulation is up to 45, much higher than nonlinearity-based techniques. A significant portion of the incoming source frequency is scattered to sidebands. We demonstrate the conversion of audible sounds to infrasound and ultrasound, respectively, and a monochromatic tone to white noise by a randomized MOSFET time sequence, raising the prospect of applications such as super-resolution imaging, deep sub-wavelength energy flow control, and encrypted underwater communication. Temporal modulation materials have been attracting attention thanks to their ability to break wave reciprocity, i.e., waves traveling from point A to B are identical to waves propagating from B to A. The authors present a linear temporal modulation device with a giant acoustic impedance modulation ratio and ability to linearly change wave frequency, operating in two quantized states when a shunt circuit is connected and disconnected by a MOSFET.

Calibration methods and facilities have been employed to directly obtain sensitivities of an underwater acoustic vector receiver using two methods based on laser Doppler vibrometry. The vector receiver was first calibrated in a standing wave tube over the frequency range 20 Hz to 2 kHz, where the oscillatory velocity of the water-air interface was measured to determine the sound particle velocity at the position of vector receiver based on waveguide theory. In the frequency range 2.5-10 kHz, the vector receiver was calibrated in an anechoic vessel with dimensions of 1.2 m diameter × 1.8 m length using wideband signals, with a laser Doppler vibrometer used to detect the oscillatory motion of a plastic pellicle, which was sufficiently thin to follow the acoustic particle motion. The uncertainties of the calibration using the optical method were estimated to be 0.7-0.8 dB at 95% confidence interval. The calibration results were compared with those obtained using a reciprocity method in a 50 m × 15 m × 10 m water tank and using a comparison method in a standing wave tube, and the largest deviation did not exceed 1.0 dB over the frequency range 20 Hz to 10 kHz.

In this article, an ultra-wideband and wide-angle insensitive absorber is proposed. The unit cell of the proposed structure consists of a tightly coupled dipole array (TCDA2) under another TCDA (TCDA1) that is twice the height of TCDA2 (TCDA-under-TCDA structure). TCDA1 of the unit cell acts as either a lossless (or lossy) antenna when the frequency is out of (or in) the operating frequency range of TCDA2. Reciprocity is applied to design TCDA1 as an absorber when the frequency is out of the operating frequency range of TCDA2 (lossless antenna region). On the other hand, the multisection impedance matching technique is applied for TCDA1 to be an absorber when the frequency is in the operating region of TCDA2 (lossy antenna region and reciprocity cannot be applied). In addition, a metasurface (MS) and vertical metal strip (VMS) are employed to develop the wide-angle insensitivity absorber. A −10 dB reflection bandwidth of 0.63–6.55 (10.4:1) is achieved with a $0.126\lambda _{\mathrm {low}}$ at the lowest operating frequency under normal incidence. The bandwidth is moderately reduced to 0.69–6.75 (9.78:1) with a $0.138\lambda _{\mathrm {low}}$ for the TE mode and 0.75–6.22 (8.29:1) with a $0.150\lambda _{\mathrm {low}}$ for the TM mode under 45° oblique incidence. The measured results of the fabricated absorber using the transverse electromagnetic (TEM) cell are in good agreement with the simulated results.

Organic-inorganic hybrid perovskites hold great potential for various optoelectronic devices with exceptional properties. Although the direct generation of circularly polarized emission from perovskites would enable various compact devices, achieving a large degree of circular polarization (DCP) at room temperature still remains challenging. Herein, we demonstrate that DCP can be strongly enhanced at the narrow mode position of chiral Fano resonances. In our design, a perovskite film is spin-coated on a symmetry-broken structure with a relatively large feature size. A large DCP of more than 0.5 is achieved at room temperature without the direct patterning of the perovskite layer. Reciprocity calculation reveals that chiral field enhancement enables the emission of opposite helicity to couple into counter-propagating slab modes and leads to a large DCP. Our design is very general and scalable. Our work may lead to circularly polarized light sources based on various perovskite materials.

The tensor product of $${\mathbb {A}}^1$$ -invariant sheaves with transfers introduced by Voevodsky is generalized to reciprocity sheaves via the theory of modulus presheaves with transfers. We prove several general properties of this construction and compute it in some cases. In particular we obtain new (motivic) presentations of the absolute Kahler differentials and the first infinitesimal neighborhood of the diagonal.

Seismic interferometry is widely applied to retrieve wavefields propagating between receivers. Another version of seismic interferometry, called inter-source interferometry, uses the principles of seismic reciprocity and expands interferometric applications to retrieve waves that propagate between two seismic sources. Previous studies of inter-source interferometry usually involve surface-wave and coda-wave estimations. We use inter-source interferometry to estimate the P-waves propagating between two sources rather than the estimation of surface waves and coda waves. We show that the recovered arrival times are dependent on the accuracy of the earthquake catalog of the two sources. Using inter-source interferometry, one can recover the waveform of the direct body waves and potentially reconstruct the waveform of coda waves, depending on the source-receiver geometry. The retrieval of these waveforms is accurate only when the wavefield is sampled with approximately 4 receivers per wavelength in the stationary phase zone. We show that using only receivers inside the stationary phase region for inter-source interferometry introduces the phase error of approximately 0.3 radians. In our study, we show an example of the P-wavefield reconstruction between two earthquakes using the seismic records from an array along San Andreas Fault. The retrieved P waves give a qualitative estimation of the thickness of the low-velocity zone of San Andreas Fault of approximately 4 km.

A study is performed of the configuration of the mutual reflection of elastic waves in crystals where an additional acoustic wave propagates toward one of two reflected waves. It is shown that the reflection of an additional wave induces two waves, one of which is opposite the direction of the original incident wave, and the second has its own direction. All characteristics of elastic waves in the described scheme are calculated including directions, polarizations, walkoff angles, and coefficients of reflection. It is shown that despite the nonreciprocal geometry of reflection in an anisotropicedium, the condition of reciprocity for the energy coefficients of reflection is valid.

A non-reciprocal self-mixing receive antenna array is presented. First, the principle of the self-mixing concept is explained and it is found that self-mixing receivers achieve a large gain over a wide angular range, which is in contrast to reciprocity. In the second part, the design of a 4×2 antenna array operating from 34 GHz to 39 GHz including the receive amplifier and mixer is introduced. Measurements in an anechoic chamber verify the simulation results, showing promising results for future applications of self-mixing arrays with a wide angular receiving range.

This paper details the implementation of a new time-domain boundary element analysis for solving wave propagation problems inside the half-space. Initially, by developing a new set of half-plane fundamental solutions and implementing them into the dual reciprocity boundary element analysis (DRBEM), the discretization of the ground surface boundaries were eliminated. To convert DRBEM inertia domain integrals into the boundary integrals, a set of Fourier series was selected as the displacement field and required fundamental solutions were obtained. The series displacement field, then was implemented into the 2-dimensional elastodynamic equilibrium Equations and the time-dependent series coefficients were calculated using an algorithm called TSBEM (Time Series Boundary Element Method). The accuracy and efficiency of the presented method were tested compared to the available analytical solutions by modelling several examples. The Results showed that, the method can be sufficiently used for analyzing wave propagation and also any other dynamic problems.

In this paper, a direct Boundary Element Method (BEM) solution without load domain integrals for Reissner's plates subjected to higher-order polynomial loads is derived. To this end, the Multiple Reciprocity Method (MRM), which consists to transform original domain integrals into a series of equivalent boundary integrals using Green's second identity in a recursive way, is used. Moreover, higher-order fundamental solutions of thick plates in bending, which are essential in MRM technique, are also derived and presented in an explicit form for all terms of the series. Despite this present approach deals directly with higher-order polynomial distribution load, this boundary element solution can be also applied to other load distribution functions, since it is possible to expand them in a polynomial series. Numerical results are presented for differing cases of boundary conditions and load functions, such as linear, double quadratic, exponential, and double sinusoidal distributions. The BEM results are compared to analytical solutions showing good agreement among them.

The authors describe a meshless method for solving three-dimensional nonstationary heat conduction problems in anisotropic materials. A combination of dual reciprocity method using anisotropic radial basis function and method of fundamental solutions is used to solve the boundary-value problem. The method of fundamental solutions is used to obtain the homogenous part of the solution; the dual reciprocity method with the use of anisotropic radial basis functions allows obtaining a partial solution. The article shows the results of numerical solutions of two benchmark problems obtained by the developed numerical method; average relative, average absolute, and maximum errors are calculated.

When sound interacts with geometrically asymmetric structures, it experiences coupling between pressure and particle velocity, known as Willis coupling. While in most instances this phenomenon is perturbative in nature, tailored asymmetries combined with resonances can largely enhance it, enabling exotic acoustic phenomena. In these systems, Willis coupling obeys reciprocity, imposing an even symmetry of the Willis coefficients with respect to time reversal and the impinging wave vector, which translates into stringent constraints on the overall scattering response. In this work, we introduce and experimentally observe a dual form of acoustic Willis coupling, arising in geometrically symmetric structures when time-reversal symmetry is broken, for which the pressure-velocity coupling is purely odd-symmetric. We derive the conditions to maximize this effect, we experimentally verify it in a symmetric subwavelength scatterer biased by angular momentum, and we demonstrate the opportunities for sound scattering enabled by odd Willis coupling. Our study opens directions for acoustic metamaterials, with direct implications for sound control, non-reciprocal scattering, wavefront shaping and signal routing, of broad interest also for nano-optics, photonics, elasto-dynamics, and mechanics. Exploiting Willis coupling in acoustic metamaterials with designed geometrical asymmetries opens up new opportunities related to sound control and manipulation. Here, the authors report a dual form of Willis coupling in geometrically symmetric acoustic scatterers.

Structural health monitoring problems are studied numerically with the time reversal method (TR). The dynamic output of the structure is applied, time reversed, as an external loading and its propagation within the deformable medium is followed backwards in time. Unknown loading sources or damages can be discovered by means of this method, focused by the reversed signal. The method is theoretically justified by the time-reversibility of the wave equation. Damage identification problems relevant to structural health monitoring for truss and frame structures are studied here. Beam structures are used for the demonstration of the concept, by means of numerical experiments. The influence of the signal-to-noise ratio (SNR) on the results was investigated, since this quantity influences the applicability of the method in real-life cases. The method is promising, in view of the increasing availability of distributed intelligent sensors and actuators.

This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition. We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number. In the first part of this paper, adequate preparations for the main uniqueness result are made. We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves. Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method. Finally, the a priori estimates of solutions to the general transmission problem with boundary data in Lp (∂Ω) (1 < p < 2) are proven by the boundary integral equation method. In the second part of this paper, we give a novel proof on the uniqueness of the inverse conductive scattering problem.

A mixed initial-boundary value problem is formulated for linear thermo-elastic relaxed micromorphic continuum with asymmetric micro-distortion tensor, micro-dislocation tensor and temperature field...

As electronic products become increasingly more complicated, multiple noise sources are likely to simultaneously interfere with the radio frequency (RF) receiver. It will be very helpful if the dominant noise source can be identified when solving the RF interference issue in a complex system. This article proposes a method to separately calculate the contributions from multiple noise sources at their overlapped frequencies so that the worse noise source could be identified even when multiple sources radiate simultaneously. The proposed method creatively employs the decomposition method based on the reciprocity theory to calculate the interference contribution from different sources. Furthermore, in the interest of reducing the near-field scanning time and complexity, the magnetic field only scanning method is developed by using the finite-element method (FEM). In the proposed method, Huygens's surface is established for each source. The tangential magnetic near fields on each Huygens's surface were then applied to solve the corresponding tangential electric fields by the FEM. Subsequently, the sources are removed while the corresponding Huygens's surfaces are maintained. The victim structure is excited under these conditions to obtain the tangential magnetic fields on Huygens's surfaces, and a novel FEM procedure is applied to obtain the tangential electric fields. Finally, based on the electric and magnetic fields, the interference from each noise source can be separately estimated based on the reciprocity theory. This method is validated by a numerical example and measurement. This approach can assist engineers in identifying the contribution of coupling from different sources and in efficiently resolving electromagnetic interference issues.

This paper applies a semi-analytical boundary collocation method, the singular boundary method (SBM), in conjunction with the dual reciprocity method (DRM) and Laplace transformation technique to solve anomalous heat conduction problems under functionally graded materials (FGMs). In this study, transient heat conduction equation with Caputo time fractional derivative is considered to describe anomalous heat conduction phenomena. In the present numerical implementation, Laplace transformation and numerical inverse Laplace transformation are used to deal with the Caputo time fractional derivative, which avoid the effect of time step on the computational efficiency of the time fractional derivation approximation. The SBM in conjunction with the DRM is employed to obtain the high accurate results in the solution of Laplace-transformed time-independent nonhomogeneous problems. To demonstrate the effectiveness of the proposed method for anomalous heat conduction analysis under functionally graded materials, three numerical examples are considered and the present results are compared with known analytical solutions and COMSOL simulation.

In the present paper, a variational principle is derived for the recently introduced higher order time-fractional four-phase-lag generalized thermoelastic diffusion model for a linear, isotropic an...

The conductivity in the 2D Rayleigh model (isotropic matrix with a periodic distribution of circular inclusions) is considered for the critical concentration (percolation threshold). The effective conductivity of the model with the metal–ideal conductor phase transition is calculated using the binary approximation. The corresponding effective conductivity for an alternative model with a metal–insulator transition is determined from the Keller–Dykhne reciprocity relation.

In this paper, a new time-domain (TD) solution is proposed for analyzing the diffraction of ultra wideband (UWB) signals in three dimensional (3-D) scenarios. In this sense, the solution is based on uniform theory of diffraction (UTD) where the diffraction has been considered by obstacles like 3-D wedge and building. The TD solution is derived with the help of frequency-domain (FD) diffraction coefficient existing in the literature that can be used for arbitrary positions of transmitter (Tx) and receiver (Rx). Considering soft and hard polarizations, the TD expressions are obtained for both amplitude diffraction (i.e., single diffraction) and slope diffraction (i.e., double diffraction). The accuracy of the proposed solution is confirmed by comparing the TD results with the rigorous Maliuzhinets solution and also with the numerical inverse fast Fourier transform (IFFT) of the corresponding FD results. The results are shown for diffraction by objects made up of perfectly electrical conducing (PEC) and dielectric materials. It is obserevd that the TD solution exhibits symetery and reciprocity property and thus can predict the diffracted field for any arbitrary position of Tx and Rx. The generalized behavior of the TD solution is confirmed by employing different kinds of excitation pulses at the Tx. Channel impulse response (CIR) is also studied to analyze the pulse shape distortion. Finally it is shown that the proposed TD solution is computationally more efficient than the FD solution.

The matrix form of the reciprocity relationship for the ABCD matrix of a general distributed microwave circuit featuring multiple ports is revisited. The correct reciprocity relationship is used to identify mistakes previously made in the derivation of key relations in the vector-short-open-calibration (VSOC) deembedding methodology, which is commonly used for removing the effect of port discontinuities in the Method-of-Moments-based electronic design automation (EDA) models of microwave circuits, digital interconnects, and other structures. Numerical results demonstrating the impact of the incorrect reciprocity relation on the accuracy of VSOC deembedding are provided.

Pulsed electromagnetic field coupling to a transmission line (TL) located over two mutually orthogonal, perfect ground planes is described analytically. It is demonstrated that the effect of an additional ground plane can be readily accounted for by extending the existing formulas applying to the configuration with the single ground plane. The thus obtained closed-form time-domain (TD) formulas specifying the equivalent Thevenin circuits at the terminals of the TL are subsequently applied to calculating the plane-wave induced voltage across a general terminal load. Some special (limiting) cases concerning a relatively short line located close to the conducting reference planes are discussed. The novel analytical results are validated with the help of a three-dimensional computational tool by analyzing the TD response of a thin, conducting planar strip above two mutually orthogonal reference planes.

We define a reciprocity gap functional for electromagnetic scattering in chiral media. We assume that a perfectly conducting scatterer is embedded in a piecewise homogeneous isotropic background ch...

In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In this paper, we thus derive the representation theorem for viscoelastic waves in a medium with a non-symmetric stiffness matrix. The representation theorem expresses the wave field at a receiver, situated inside a subset of the definition volume of the viscoelastodynamic equation, in terms of the volume integral over the subset and the surface integral over the boundary of the subset. For the given medium, we define the complementary medium corresponding to the transposed stiffness matrix. We define the frequency-domain complementary Green function as the frequency-domain Green function in the complementary medium. We then derive the provisional representation theorem as the relation between the frequency-domain wave field in the given medium and the frequency-domain complementary Green function. This provisional representation theorem yields the reciprocity relation between the frequency-domain Green function and the frequency-domain complementary Green function. The final version of the representation theorem is then obtained by inserting the reciprocity relation into the provisional representation theorem.

Graphical abstract, Highlights • The 3D variable-order time fractional variable-order time fractional diffusion is generated. • An efficient meshless method is proposed for numerical solution of the new problem. • The proposed approach is established upon the singular boundary method. • The method accuracy is examined by some numerical examples on various geometries. • The method can be extended for other types of variable-order fractional problems., Introduction This study describes a novel meshless technique for solving one of common problem within cell biology, computer graphics, image processing and fluid flow. The diffusion mechanism has extremely depended on the properties of the structure. Objectives The present paper studies why diffusion processes not following integer-order differential equations, and present novel meshless method for solving. diffusion problem on surface numerically. Methods The variable- order time fractional diffusion equation (VO-TFDE) is developed along with sense of the Caputo derivative for (0

Solutions to a nonlinear parabolic convection–diffusion equation are constructed in the form of a diffusion wave that propagates over a zero background at a finite velocity. The theorem of existence and uniqueness of the solution is proven. The solution is constructed in the form of a characteristic series whose coefficients are determined using a recurrent procedure. Exact solutions of the considered type and their characteristics, including the domain of existence, are determined, and the behavior of these solutions on the boundaries of this domain of existence is studied. The boundary element method and the dual reciprocity method are used to develop, implement, and test an algorithm for constructing approximate solutions.

The widely applied Structure-Preserving Reduced-order Interconnect Macromodeling (SPRIM) algorithm cannot retain the reciprocity or the block structure of the circuit matrices of the original system, being inherent to RCL circuits; and consequently it is harder to synthesize a Passive Reduced-order Interconnect Macromodeling Algorithms (PRIMA) model into a practical circuit. In order to overcome this deficiency, this paper proposes an improved SPRIM algorithm to maintain the structure features of the input-output correlation matrix. Firstly, the algorithm in this paper reorders the modified nodal analysis (MNA) equations. An Input-Output structure Preserving Order Reduction (IOPOR) technique applicable to SPRIM is then proposed. Also, one combines the IOPOR technique with the conventional SPRIM algorithm to obtain a new projection matrix that can maintain the input and output correlation matrix of the original system. The feasibility and effectiveness of the proposed algorithm are verified through numerical analysis and calculation of typical problems.

This paper introduces analytical solutions to gap waveguide slot antenna structures. The reciprocity method is used for the analysis by exploiting Green’s function of a bed of nails structure employing a homogenized plane-wave spectral-domain approach. Green’s function is found using parallel plate waveguide and surface admittance concepts. The spectral surface admittance of the pin structure is calculated using asymptotic boundary condition (ABC), and the unknown antenna slot currents are solved using moment methods. The structure is designed to have a cutoff frequency of 10–15 GHz, and the central operating frequency of the slot is 12.5 GHz. This approach is applied to the specific geometry of a propagating ridge gap waveguide single transverse broad wall slot antenna structure. The equivalent series impedance and far zone fields and patterns are calculated, and the results are compared with a full-wave commercial software, and they are proved to be accurate.

A closed mathematical formulation of plane non-stationary contact problems for rigid dies and an elastic half-space with deepened cavities is constructed. Using the dynamic theorem of reciprocity of works, a system of resolving equations is obtained. It includes the basic boundary integral equation arising from the principle of reciprocity and boundary conditions, as well as the equations of translational and rotational motion of the die. The fundamental and singular solutions for the elastic plane are the cores of the main resolving equation. They determine displacements and stresses in the elastic plane from the applied single instantaneous concentrated force. An original solution algorithm based on the method of boundary integrals with an additional iterative procedure that allows one to take into account the partial separation of the boundary surfaces of the die and the half-space in the contact area has been developed and implemented on a computer. In this case, at each moment of time in the half-space, there is a region that is in a perturbed state and outside of which there are no perturbations. The integral operators of the resolving system of equations are replaced by discrete analogs in the spatial variable and in time. A parametric study of the process of unsteady contact of an absolutely rigid rectangular die with a half-space having a recessed cavity is carried out. Analysis of the calculation results revealed the manifestation of a significant effect of the cavity on the process of non-stationary contact interaction. The influence of the cavity begins to show itself from the moment the reflected waves arrive from its boundary. In this case, the nature of the unsteady stress-strain state and displacements changes significantly. The developed calculation algorithm can be used in engineering practice by design and research organizations in the process of designing and calculating buildings and structures under the influence of natural and man-made vibrations propagating in the soil.

A bidirectional Monte Carlo (BDMC) method based on reversibility of bundle trajectory and reciprocity of thermal radiative energy exchange was developed to solve radiative heat transfer in absorbing and scattering medium. Two types of sampling models were introduced into the Monte Carlo (MC) simulation, namely the equivalent sampling and the weight sampling, respectively. Mathematical formula for the sampling models and the statistical calculation of sampling bundles were derived. Furthermore, the reciprocity error correlation of radiative exchange factors between the BDMC method and the traditional Monte Carlo (TMC) method were demonstrated and analyzed. Radiative heat transfer in a two-dimensional rectangular domain with absorbing and scattering media was solved by using both the BDMC method and the TMC method. Radiative exchange factors and radiative equilibrium temperature profiles predicted by the BDMC method were compared with those predicted by the TMC method. The performance parameter P, defined to evaluate the performance of MC methods, was computed and compared between the BDMC and the TMC methods. The results showed the superiority of BDMC method compared with the TMC method for radiative heat transfer, in addition, the weight sampling was proved to be more flexible than the equivalent sampling in the BDMC method.

One of the attractive and practical techniques to transform the domain integrals to equivalent boundary integrals is the dual reciprocity method (DRM). The success of DRM relies on the proper treatment of the non-homogeneous term in the governing differential equation. For this purpose, radial basis functions (RBFs) interpolations are performed to approximate the non-homogeneous term accurately. Moreover, when the interpolation points are large, the global RBFs produced dense and ill-conditioned interpolation matrix, which poses severe stability and computational issues. Fortunately, there exist interpolation functions with local support known as compactly supported radial basis functions (CSRBFs). These functions produce a sparse and well-conditioned interpolation matrix, especially for large-scale problems. Therefore, this paper aims to apply DRM based on multiquadrics (MQ) RBFs and CSRBFs for evaluation of the Poisson equation, especially for large-scale problems. Furthermore, the convergence analysis of DRM with MQ and CSRBFs is performed, along with error estimate and stability analysis. Several experiments are performed to ensure the well-conditioned, efficient, and accurate behavior of the CSRBFs compared to the MQ-RBFs, especially for large-scale interpolation points.

This paper presents the acoustic and structure characteristics of chambers with elastic/rigid baffles and elastic walls using a novel formulation. The acoustic fluid is assumed to be compressible and inviscid, and the effect of mean flow is neglected. The acoustic field is formulated based on the dual reciprocity boundary element method (DRBEM), and the finite element method (FEM) is used to model the structural dynamics of elastic walls. The reduced-order model (ROM) of the coupled system is derived based on modal analysis of the acoustic field with rigid boundaries and the structure in a vacuum. Numerical examples are presented, and the acoustic modes and frequencies of the chambers are determined by analysis of eigenvalues of the coupled governing equations. The accuracy of the introduced model, which is based on the reduced-order DRBEM-FEM formulation, is examined by comparing the results with analytical and numerical predictions reported in the literature, and good agreements are achieved. Besides, the effects of baffles are studied for different configurations and the elasticity of a wall in a combustion chamber is investigated.

In this work, we have studied the asymptotic behavior of Green's function and the reciprocity relation of the far-field pattern in the stratified ocean waveguide. Moreover, two direct sampling meth...

Due to the near monopoly held by nonlinear energy sinks in the study of targeted energy transfer, little research has been done on the flow of mechanical energy between oscillators with comparable mass. The goal of the present paper is to investigate the flow of mechanical energy between two nonlinearly coupled oscillators with comparable mass that arise due to the breaking of dynamic reciprocity. The first oscillator represents the prototypical linear oscillator (LO), whereas the second oscillator represents a nonlinear oscillator (NO) that is nonlinearly coupled to the LO only. By breaking dynamic reciprocity, one-way energy propagation is achieved in the system, such that energy can only be irreversibly transferred from the NO to the LO. As such, the NO is isolated from the LO for physically reasonable energies whenever it is not directly excited. Moreover, when the NO is directly excited, there exist regimes where the LO, despite being linear and of comparable mass to the NO, behaves like a nonlinear energy sink and parasitically and irreversibly absorbs energy from the NO. The theoretical portion of this works employs direct numerical simulation of the structure to explore the strongly nonreciprocal dynamics and resulting energy transfers. The theoretical results are then verified through experimental measurements of a comparable structure. The present study promotes a new paradigm for investigating energy transfer in mechanical structures and opens the way for passively controlling the flow of energy in complex mechanical systems.

Reciprocity is an underlying symmetry within a physical system that dates back to the work of Green in electrostatics in 1828 [1] . Later on, through the works of Helmholtz, Rayleigh, and Lorentz, reciprocity theorems were developed in different fields, such as optics, acoustics, elastodynamics, and electromagnetics [2] , [3] . The electromagnetic reciprocity theorem states that, for a system with symmetrical permittivity and permeability tensors, which is passive, linear, and time invariant, the transmission and reception between two points in space are identical in opposite directions regardless of any spatial asymmetry within the channel between them.

We present a new numerical algorithm combining the dual reciprocity method with the dual interpolation boundary face method for solving the two-dimensional Poisson equations. In this new combined approach, the boundary physical variables and particular solutions are approximated by dual interpolation elements which include source and virtual points. Additionally, this algorithm is implemented by employing the augmented thin plate spline interpolation function to approximate non-homogeneous term and the Hermite-type moving-least-square approximation to approximate physical variables for virtual nodes. Compared with the traditional dual reciprocity boundary element method, this combined method possesses higher accuracy and efficiency and is better suited for structures with small feature sizes. Several numerical examples are given to illustrate the superiority of the proposed method for solving Poisson equations.

Owing to an inconsistent load demand, hydraulic turbines are often operated under off-load range. Resultant flow instabilities comprise low-frequency pressure fluctuations, which are dependent on the operating condition and unavoidable high-frequency fluctuations evolving from the interactional design concept of hydrofoils. Through the analysis of averaged flow parameters within the runner, this article investigates the mechanism of reciprocity in flow instabilities between draft tube and upstream components. Two recommended operating conditions are used to approximate harmless traveling disturbances, and two part-load discharges are discussed accordingly. The CFD commercial code ANSYS CFX has been used for unsteady flow simulation, where the Shear Stress Transport (SST) turbulence model has been adopted. The used numerical scheme has been validated through experiments in terms of pressure pulsation characteristics, and findings display a good agreement. It has been found that low-frequency disturbances, as instabilities taking source from the fluid structure itself, can override strong flow gradients and exert a higher backward influence farther than high-frequency perturbations. The low-frequency component and its harmonic strengthened by the wall impact feedback are less sensitive to the backward damping. The blade passing frequency dominates the draft tube inlet to influence the local pressure recovery; but it is rapidly diffused and tapped by the low-frequency core instability.

This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform $L^{p}_{\alpha }\ (1< p\leq 2)$ L α p ( 1 < p ≤ 2 ) estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable structure can be uniquely identified by means of the scattered field measured only above the structure induced by a countably infinite number of quasi-periodic incident plane waves.

The main goal of the present paper was to obtain some new uniqueness results for the anisotropic thermoelastic bodies with double porosity structure. There are obtained some auxiliary results based on the Betti reciprocity relation that involve some thermoelastic processes.

The article deals with problems on determining the effective moduli of porous piezoceramic materials with substances that have extreme properties and are deposited on the pore boundaries. The argumentation for the method of effective moduli is given. The reciprocity relation, from which the properties of effective moduli that are similar to known ones for moduli of piezoelectric materials can be obtained, is proved. It is noted that for homogenization of porous piezoelectric composites with rigid or electrode pore boundaries, it is necessary to use models for materials having extremely large moduli that are located on the pore boundaries. Using numerical calculations, anomalous properties of various effective piezoelectric moduli that are promising for practical applications of the investigated piezocomposites have been revealed.

Rayleigh surface wave motion in a homogeneous orthotropic elastic solid half-space under time-harmonic sources is theoretically investigated. In this article, closed-form expressions of the Rayleigh wave field as a result of a time-harmonic concentrated line load are simply determined by using reciprocity theorems. For the verification purpose, analytical predictions are also obtained through Fourier transform technique with the aid of the residue theorem. The solutions found by the two approaches are shown to be mathematically the same. As an example of calculation, surface waves due to a set of buried loadings in the orthotropic half-plane are then examined in detail. A discussion of these results is presented to explore the influence of the loading types on the displacement amplitudes of the generated wave fields.

Single-well imaging (SWI) is a borehole measurement technique for detecting geologic structures outside a borehole by using arrays of receivers to record the waves reflected from these structures. The asymptotic solutions of P-P, SV-SV, and SH-SH waves in SWI have been obtained, but the P-SV and SV-P waves have been ignored in previous studies. It is necessary to know when these conversion waves are large and to estimate these waves when they are not ignorable. The analytical solutions of P-SV and SV-P waves are first derived using reciprocity relations between virtual concentrated forces and acoustic sources. The analytical results agree well with finite-difference solutions for monopole and dipole sources. We have found that, for a given source-receiver offset, the detected converted waves first increase and then decrease with the increase of the source-reflector distance. The relative amplitudes of converted waves to reflected waves are larger than 20% and cannot be ignored when the ratio of source-reflector distance to source-receiver offset is smaller than four. However, when the source-reflector distance is 10 or more times the source-receiver offset and the dip angle of the reflector is smaller than 10°, the amplitudes of the converted waves are smaller than 5% of the reflected waves. Furthermore, the relative amplitudes of converted waves increase with the dip angle of the reflector. The analytical solutions of converted waves are useful for simulating SWI wavefields and checking the inversion results in field logging.