Wave Propagation Phenomena Research Articles

A concurrent two‐scale coupling for wave propagation using direct solution schemes with explicit time integration

AbstractThis article proposes an efficient concurrent coupling of two different material scales—a macroscale and a microscale—in a direct solution scheme based on explicit time integration. Both scales may be discretized with different element sizes and the microdomain may exhibit a heterogeneous structure. A surface coupling is described, which imposes the macrovelocities at the interfaces on the microscale. Using an averaged stress state of several elements on the microscale within a bounded volume, forces are derived which transfer the micromaterial response back to the macroscale. Whereas established surface couplings based on Lagrange multipliers achieve an exact solution of the interface problem, the proposed coupling is based on a weak staggered scheme. The advantage is that no common global system of equations has to be solved and the approach preserves the efficiency of direct solution schemes almost completely. It is therefore well applicable to the simulation of wave propagation phenomena in heterogeneous materials with complex constitutive models and suitable for massive parallelization. Example simulations demonstrate the capabilities and current limitations.

Fractional Derivative Modification of Drude Model.

A novel, two-parameter modification of a Drude model, based on fractional time derivatives, is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing good agreement between theoretical description and numerical results. The absorption coefficient and wave vector are shown to follow a power law in the frequency domain, which is a common phenomenon in electromagnetic and acoustic wave propagation in complex media such as biological tissues. The main novelty of the proposal is the introduction of two separate parameters that provide a more flexible model than most other approaches found in the literature. Moreover, an efficient numerical implementation of the model is presented and its accuracy and stability are examined. Finally, the model is applied to an exemplary soft tissue, confirming its flexibility and usefulness in the context of medical biosensors.

Abundant traveling wave solutions to an intrinsic fractional discrete nonlinear electrical transmission line

The main idea of this paper is to search for all traveling wave solutions to an intrinsic fractional discrete nonlinear electrical transmission line, which plays a essential role in obtaining the new insights in nonlinear voltage dynamics. We first give a brief introduction how to transform the discrete system into a continuous one, which is described by a fractional-order partial differential equation. After that, this equation is handled by conformable fractional transformation and the complete discrimination system for polynomial method (CDSPM). By applying the advanced method, the whole of the exact traveling wave solutions emerged in existing articles are obtained, especially we obtain the solitary wave solutions and elliptic functions solutions which are hardly founded by other methods. Notably, the elliptic functions solutions in rational form are discovered for the first time. Finally, the electrical characteristics and the fractional nature are revealed via graphical represents. By the depicted graphs, we intuitively observe the existence of the phenomena for periodic wave and solitary wave, and the time-fractional derivative is proved do has important influence on the behaviors of the solutions. Considering the significance of the nonlinear electrical transmission line, the acquired results would have wide application in electrical engineering and nonlinear voltage dynamics, liking analyzing and predicting the complex voltage wave propagation phenomenon in realistic electrical transmission system.

A homogenized damping model for the propagation of elastic wave in a porous solid

This paper develops an averaging technique based on the combination of the eigenfunction expansion method and the collaboration method to investigate the multiple scattering effect of the SH wave propagation in a porous medium. The semi-analytical averaging technique is conducted using Monto Carlo method to understand the macroscopic dispersion and attenuation phenomena of the stress wave propagation in a porous solid due to multiple scattering effects. The averaging technique is verified by finite element analysis. Finally, a simple homogenized elastic model with structural damping is proposed to describe the macroscopic attenuation effect of SH waves in a porous medium.

SHM system for anomaly detection of bolted joints in engineering structures

In this article, the elastic wave propagation phenomenon is applied as the basis for a system designed to detect anomalies in the pre-tensioned connections of engineering structures. A series of laboratory tests were carried out on a steel frame. This approach, where the connection is a fragment of the complex structure, and not an isolated part, enabled us to analyse behaviours similar to those in real engineering structures. The problem of the similarity of signals corresponding to different types of anomalies was considered. Thanks to the application of principal component analysis and a procedure employing a combination of artificial neural networks, the extraction of the most significant features of the registered signals was possible. The proposed procedure proved to be very sensitive and accurate for the proper detection of anomalies, as well as for the determination of their location and type, even if the loosening of bolts was very slight (i.e., invisible to the naked eye). The most important element of the presented approach is the fact that the combination of the assessment of the condition of local parts along with the application of artificial intelligence techniques can result in a Structural Health Monitoring (SHM) system that allows for the global assessment of structural integrity.

Deep-Learning-Driven Full-Waveform Inversion for Ultrasound Breast Imaging.

Ultrasound breast imaging is a promising alternative to conventional mammography because it does not expose women to harmful ionising radiation and it can successfully image dense breast tissue. However, conventional ultrasound imaging only provides morphological information with limited diagnostic value. Ultrasound computed tomography (USCT) uses energy in both transmission and reflection when imaging the breast to provide more diagnostically relevant quantitative tissue properties, but it is often based on time-of-flight tomography or similar ray approximations of the wave equation, resulting in reconstructed images with low resolution. Full-waveform inversion (FWI) is based on a more accurate approximation of wave-propagation phenomena and can consequently produce very high resolution images using frequencies below 1 megahertz. These low frequencies, however, are not available in most USCT acquisition systems, as they use transducers with central frequencies well above those required in FWI. To circumvent this problem, we designed, trained, and implemented a two-dimensional convolutional neural network to artificially generate missing low frequencies in USCT data. Our results show that FWI reconstructions using experiment data after the application of the proposed method successfully converged, showing good agreement with X-ray CT and reflection ultrasound-tomography images.

Noise induced suppression of spiral waves in a hybrid FitzHugh-Nagumo neuron with discontinuous resetting.

A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated, and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A N×N network of the neuron model is constructed to study the wave propagation and wave re-entry phenomena. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed, but for such values of the flux coupling, the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term, we showed that when noise is introduced for the entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely.

Seismic wave modeling in vertically varying viscoelastic media with general anisotropy

Seismic anisotropy, wave attenuation, and dispersion are critical phenomena of wave propagation in real media. Full-wavefield modeling of wave behavior in such media plays an important role in investigating dynamic features of the earth’s interior and in full-waveform inversion of anisotropic parameters and velocity dispersion. We have developed a numerical scheme to model the full-waveform response from a point source in a vertically varying viscoelastic medium of arbitrary anisotropy. The method is implemented in the frequency domain, so the complexity of anelasticity and anisotropy can be described by a complex elastic stiffness matrix and frequency-dependent moduli can also be readily incorporated. In our scheme, we solve the elastodynamic equations for general anisotropy through finite-element method in the frequency-wavenumber domain and we use the stiffness reduction method to suppress reflections from artificial boundaries along the depth direction. A nonuniform 2D Fourier transform strategy is developed to reconstruct the spatial-domain counterparts from the wavenumber-domain solutions. The time-domain responses are then obtained by taking inverse fast Fourier transform with respect to frequency. We validate the method by comparing the numerical results with the exact solutions for a homogeneous transversely isotropic model and a two-layered model. In the application example, we further proved the feasibility and generality of the scheme using an attenuative, dispersive model with velocity and attenuation anisotropy. Our scheme enjoys significant advantages in incorporating various viscoelastic/dispersive behaviors and general anisotropy, and thus provides a useful tool for numerical simulation of dynamic responses in practical application.

Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

Fractional residual series for conformable time‐fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations of seventh order

The purpose of the present work is to analyze and investigate the analytical solution of the seventh‐order fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations under the conformable derivatives. Using the residual series expansion algorithm, the posed fractional models are studied analytically and numerically. Simultaneously, convergence analysis and error estimation are performed for the proposed technique. For this purpose, an advanced numerical algorithm is designed to handle the complexity of nonlinear fractional terms. Some experiments are provided to support theoretical analysis in a one‐dimensional finite compact regime in light of the conformable sense. Eventually, numerical comparison is performed with other existing techniques along with some two‐ and three‐dimensional representative graphs. Physical interpretation of the solution behaviors is discussed as well for various α values in an adequate time duration. Comparative results indicate the superiority and great flexibility of the presented method for fractional evolution systems arising in nonlinear wave propagation phenomena.

Significance of Bloch impedance over wave impedance in photonic crystal waveguides

The impedance of a medium carrying electromagnetic waves had been one of the important metrics for designing devices. However, the conclusions of wave impedance in periodic media like photonic crystal (PhC) waveguides fail to describe different wave propagation phenomena. Instead, Bloch impedance fits more appropriately in such a case. However, the existing definition of Bloch impedance by Boscolo et al. [J. Lightwave Technol. 20, 304 (2002)JLTEDG0733-872410.1109/50.983245] is also unable to encounter some typical characteristics of wave propagation. This work brings out these discrepancies by providing a detailed comparison between the wave impedance, and the said Bloch impedance in rods-in-air-type and holes-in-dielectric-type PhC (hole-type) structures. The theoretical analysis shows that the nature of wave propagation in a rods-in-air-type PhC waveguide can be successfully described by this Bloch impedance in the whole band, whereas the wave impedance fails in it at and beyond the point of transition (from positive to negative) in group velocity. Conversely, this Bloch impedance is unable to characterize the wave propagation at the point of transition in group velocity within a hole-type PhC. Thereby, a procedural change in the calculation of Bloch impedance is proposed, and the supremacy of this proposed calculation over existing ones has been established for both the types of PhC waveguides. Moreover, the unexplored odd mode of the hole-type PhC waveguide has also been examined along with its even band in order to signify the importance of Bloch impedance over wave impedance.

Effects of Nonlinear Soil Behavior on Kappa (κ): Observations from the KiK-Net Database

ABSTRACTSoil nonlinear behavior is often triggered in soft sedimentary deposits subjected to strong ground shaking and has led to catastrophic damage to civil infrastructure in many past earthquakes. Nonlinear behavior in soils is associated with large shear strains, increased material damping ratio, and reduced stiffness. However, most investigations of the high-frequency spectral decay parameter κ, which captures attenuation, have focused on low-intensity ground motions inducing only small shear strains. Because studies of the applicability of the κ model when larger deformations are induced are limited, this article investigates the behavior of κ (both κr per record and site-specific κ0 estimates) beyond the linear-elastic regime. About 20 stations from the Kiban–Kyoshin network database, with time-average shear-wave velocities in the upper 30 m between 213 and 626 m/s, are used in this study. We find that the classification scheme used to identify ground motions that trigger soil nonlinear behavior biases estimates of κ0 in the linear and nonlinear regimes. A hybrid method to overcome such bias is proposed considering proxies for in situ deformation (via the shear-strain index) and ground shaking intensity (via peak ground acceleration). Our findings show that soil nonlinearity affects κr and κ0 estimates, but this influence is station dependent. Most κ0 at our sites had a 5%–20% increase at the onset of soil nonlinear behavior. Velocity gradients and impedance contrasts influence the degree of soil nonlinearity and its effects on κr and κ0. Moreover, we observe that other complexities in the wave propagation phenomenon (e.g., scattering and amplifications in the high-frequency range) impose challenges to the application of the κ0 model, including the estimation of negative values of κr.

Cable reverberations during wireline distributed acoustic sensing measurements: their nature and methods for elimination

ABSTRACTThe application of distributed acoustic sensing in borehole measurements allows for the use of fibre optic cables to measure strain. This is more efficient in terms of time and costs compared with the deploying of conventional borehole seismometers. Nevertheless, one known drawback for temporary deployment is represented by the freely hanging wireline cable slapping and ringing inside the casing, which introduces additional coherent coupling noise to the data. The present study proposes an explanation for the mechanism of noise generation and draws an analogy with similar wave propagation processes and phenomena, such as ghost waves in marine seismics. This observation allows to derive a ringing noise filter function, to study its behaviour and to consider known effects of the gauge length filter. After examining existing methods aimed at eliminating ringing noise and results of their application, we propose a two‐step approach: (1) developing a denoising method based on a matching pursuit decomposition with Gabor atoms and (2) subtracting the noise model for imaging improvement. The matching pursuit method focuses on decomposing the original input signal into a weighted sum of Gabor functions. Analysing Gabor atoms properties for frequency, amplitude and position in time provides the opportunity to distinguish parts of the original signal denoting noise caused by the vibrating cable. The matching pursuit decomposition applied to the distributed acoustic sensing‐vertical seismic profiling data at the geothermal test site Groß Schönebeck provides a versatile processing instrument for noise suppression.

Modified Morris–Lecar neuron model: effects of very low frequency electric fields and of magnetic fields on the local and network dynamics of an excitable media

A Morris–Lecar neuron model is considered with electric and magnetic field effects where the electric field is a time-varying sinusoid and magnetic field is simulated using an exponential flux memristor. We have shown that the exposure to electric and magnetic fields have significant effects on the neurons and has exhibited complex oscillations. The neurons exhibit a frequency-locked state for the periodic electric field and different ratios of frequency-locked states with respect to the electric field frequency is also presented. To show the impact of the electric and magnetic fields on network of neurons, we have constructed different types of network and have shown the network wave propagation phenomenon. Interestingly, the nodes exposed to both electric and magnetic fields exhibit more stable spiral waves compared to the nodes exhibited only to the magnetic fields. Also, when the number of layers is increased, the range of electric field frequency for which the layers exhibit spiral waves also increases.

Mathematical Study on Traveling Waves Phenomena on Three Phase Transmission Lines – Part I: Fault-Launched Waves

A mathematical study on the traveling waves (TWs) propagation phenomena on three-phase power lines under fault conditions is presented in this article. This article is divided into two parts, and this part focuses on the analytical development of expressions that describe fault-launched TWs as functions of line and fault parameters. From the obtained mathematical representation of TWs launched by faults, TW-based applications can be designed in a more reliable way, justifying the relevance of the presented study.

Characterization of mechanical discontinuities based on data-driven classification of compressional-wave travel times

Wave propagation and diffusive transport phenomena are influenced by the mechanical discontinuities in material. This study shows that certain bulk properties of the network of low-velocity mechanical discontinuities (e.g. air-filled cracks) in a material can be characterized by processing compressional-wave travel times using traditional data-driven classification techniques. To that end, we perform three tasks in chronological order: (1) use the discrete fracture network (DFN) method to create two-dimensional (2D) numerical models of crack-bearing material embedded with various types of low-velocity mechanical discontinuities, (2) use the fast marching method (FMM) to simulate the propagation of the wave/diffusion front from a single source through the 2D crack-bearing material to multiple receivers placed on the boundary of the material, and (3) train 9 data-driven classifiers to characterize the crack-bearing materials (i.e. bulk properties of the network of mechanical discontinuities in the crack-bearing material) by learning from the simulations of travel times detected by multiple receivers placed around the crack-bearing material. The classifiers identified the orientation, spatial distribution, and dispersion of the low-velocity mechanical discontinuities. Voting classifier performs the best among the 9 classifiers. For the characterization of bulk dispersion and distribution of discontinuities, the sensors located on the adjacent boundaries are more important; whereas for the characterization of bulk orientation of discontinuities, the sensors located on the opposite side are more important.

Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media.

Network performance of neurons plays a vital role in determining the behavior of many physiological systems. In this paper, we discuss the wave propagation phenomenon in a network of neurons considering obstacles in the network. Numerous studies have shown the disastrous effects caused by the heterogeneity induced by the obstacles, but these studies have been mainly discussing the orientation effects. Hence, we are interested in investigating the effects of both the size and orientation of the obstacles in the wave re-entry and spiral wave formation in the network. For this analysis, we have considered two types of neuron models and a pancreatic beta cell model. In the first neuron model, we use the well-known differential equation-based neuron models, and in the second type, we used the hybrid neuron models with the resetting phenomenon. We have shown that the size of the obstacle decides the spiral wave formation in the network and horizontally placed obstacles will have a lesser impact on the wave re-entry than the vertically placed obstacles.

The nonlinear thermo-hyperelasticity wave propagation analysis of near-incompressible functionally graded medium under mechanical and thermal loadings

This article presents a non-Fourier thermo-hyperelastic model to investigate thermal and stress wave propagation phenomenon in a near-incompressible functionally graded medium (FGM) for various thermal and mechanical boundary conditions. A strain energy function is chosen to modify FGM’s hyperelastic equations considering the coupling effects of mechanical and thermal terms. By switching the strain tensor's invariants, equations are developed to estimate a near-incompressible model for rubber. The rubber is characterized by a gradual variation in the longitudinal direction. Therefore, the material properties of rubber mainly depend on coordinates in through an exponential function. The nonlinear governing equations are derived from the large displacement approach using Finite Strain Theory. To find an acceptable solution of nonlinear time-dependent thermo-hyperelastic equations, Newmark's time integration process and a nonlinear Hermitian finite element algorithm are employed. The final system’s responses to different boundary conditions such as input surface traction, heat flux and variable material properties are described schematically, and their influence on the wave propagation is calculated. It is shown that the amplitude of oscillation in a functionally graded hyperelastic medium is less than that of a medium with constant properties. The results also show that the wave travels through the medium faster than the FGM. Moreover, the modified Fourier law of heat conduction is applied and the impact of enhanced heat conduction model on the thermo-hyperelastic responses is discussed.

Evaluation of Pressure Resonance Phenomena in DCT Actuation Circuits

The paper investigates hydraulic wave propagation phenomena through hydraulic circuits of power transmission systems by means of numerical approaches. The actuation circuit of a Dual-Clutch Transmission (DCT) power transmission system supplied by a Gerotor pump is analyzed. A steady state approach is adopted to detect resonance phenomena due to Gerotor design parameters and circuit lengths, while one-dimensional numerical models are implemented to predict the pressure oscillations through the hydraulic ducts for the whole pump operating domain. CFD-1D pipelines are adopted to address the pressure oscillation behavior through the hydraulic pipeline, while spectral maps and order tracking techniques are used to evaluate their fluctuation intensity in function of the pump speed rate. The numerical models are validated with experimental tests performed on an ad hoc test rig for power transmission systems and a good match is found between the numerical and the experimental results. Pump design parameters as well as hydraulic accumulators and resonators are numerically investigated to quantitatively evaluate their improvement on the circuits’ hydro-dynamic behavior. Furthermore, simplified numerical models are implemented to investigate the frequency response behavior of the hydraulic circuits by means of linear analysis. This approach resulted to be particularly effective for the prediction of the resonance frequencies location, and it can be adopted as an optimization tool since significant simulation time can be saved. Finally, the performance of the circuits operating with an eco-friendly fluid is evaluated numerically and the results are compared with the ones obtained with a traditional petroleum-based oil.

Characteristics of Quantum Plasmonic Waves Guided by a Symmetric Metal–Gap–Dielectric Nano-system

The guiding properties of a symmetric conductor–gap–dielectric system consists of a metal film symmetrically surrounded by media of two dielectrics, and is theoretically analyzed by using the quantum hydrodynamic model and Maxwell’s equations. We found that the quantum effects, including the Fermi pressure and the Bohm potential, facilitate the propagation of the hybrid surface waves at higher values of the wavenumber. The results show that the permittivity of the surrounding dielectric mediums and the geometric effects (namely, the thickness of the metal film and gap layers) significantly modify the basic behaviors of the hybrid surface waves. Our results provide a good understanding of the basic features of the wave propagation phenomenon in hybrid waveguide systems.