Inhomogeneous Wave Research Articles

Effect of wave inhomogeneity on fatigue damage of mooring lines of a side-anchored floating bridge

Mooring systems are important structural components of very long floating bridges. They effectively limit the transverse motions of the bridge under environmental loads. They also add viscous hydrodynamic damping to the entire system. The safe and economical design of mooring systems is thus important but also challenging especially when the wave conditions are inhomogeneous. In this paper, a computational study is carried out to investigate the responses of the mooring lines for a 4.6 km long fjord crossing floating bridge accounting for inhomogeneous wave conditions. Based on the structural responses, this study also attempts to evaluate the fatigue damage in the mooring lines by using different fatigue analysis methods. The accuracy of the spectral methods is examined by comparison with the conventional rainflow cycle counting algorithm. Numerical studies are conducted to obtain an indication of the effect of various wave inhomogeneities on the fatigue damage in the mooring lines.

Collisionally Inhomogeneous Bose-Einstein Condensates with a Linear Interaction Gradient.

We study the evolution of a collisionally inhomogeneous matter wave in a spatial gradient of the interaction strength. Starting with a Bose-Einstein condensate with weak repulsive interactions in quasi-one-dimensional geometry, we monitor the evolution of a matter wave that simultaneously extends into spatial regions with attractive and repulsive interactions. We observe the formation and the decay of solitonlike density peaks, counterpropagating self-interfering wave packets, and the creation of cascades of solitons. The matter-wave dynamics is well reproduced in numerical simulations based on the nonpolynomial Schrödinger equation with three-body loss, allowing us to better understand the underlying behavior based on a wavelet transformation. Our analysis provides new understanding of collapse processes for solitons, and opens interesting connections to other nonlinear instabilities.

Complete phenomenon of reflection at the plane boundary of a dissipative anisotropic elastic medium

SUMMARYA complex slowness vector governs the 3-D propagation of harmonic plane waves in a dissipative elastic medium with general anisotropy. In any sagittal plane, this dual vector is specified with phase direction, propagation velocity and coefficients for attenuation. A generalized reflection phenomenon is illustrated for incidence of inhomogeneous waves at the stress free boundary of the medium. Each reflected wave at the boundary is characterized by its propagation direction, propagation velocity, inhomogeneity, amplitude ratio, phase shift and energy flux. These propagation characteristics are exhibited graphically for a numerical example of anisotropic viscoelastic medium.

Fraunhofer Diffraction Description In The Approximation Of The Light Field Theory

The wavelength is that natural scale that determines the applicability domains of the ray approximation and the wave approximation of light. If the change of the radiation power spatial density is significant at the wavelength scale, then we deal with the light diffraction phenomenon, which is a subject to the wave optics. Consider the diffraction phenomenon at the diaphragm. It is possible to distinguish the near zone with significant wave inhomogeneities (i.e. the Fresnel zone) and the far Fraunhofer diffraction zone, in which the wave becomes close to homogeneous (the so-called quasi-homogeneous) and the ray approximation is possible. The problem is that there is no explicit relationship between the radiance of the rays before and after diaphragm. Method for determining the boundary conditions for the radiance in the Fraunhofer zone through the radiance of the incident radiation is proposed in the paper. This approach for computing the radiance field in the Fraunhofer zone can be generalized to other problems of optics, thereby providing the possibility of using computationally efficient ray-approximation-based methods to determine the light fields.

Electromagnetic Scattering of Inhomogeneous Plane Wave by Ensemble of Cylinders

The interaction between an ensemble of cylinders and an inhomogeneous plane wave is introduced and is determined, in the present paper, through a rigorous theoretical approach. Scattered electromagnetic field generated by an indefinite number of infinite circular cylinders is analyzed by the application of the generalized vector cylinder harmonics (VCH) expansion. The exact mathematical model relied upon to represent this scenario considers the so-called complex-angle formalism reaching a superposition of vectorial cylindrical-harmonics and Foldy-Lax Multiple scattering equations (FLMSE) to account for the multiscattering process between the cylinders. The method was validated by comparing the numerical results obtained with the use of the finite element method and a homemade Matlab code

Correct procedure to study reflection in orthotropic thermoelastic medium: Inhomogeneous propagation of waves

Any study on reflection in anisotropic thermoelastic media, as available in literature, is either incorrect or incomplete. At the best, the earlier studies on this topic avoided the incidence of inhomogeneous waves. On the other hand, in recent times, each study is found to be forcing the isotropic elastic Snell’s law to define the anisotropic propagation of inhomogeneous reflected waves. To illustrate the common mistakes committed, this study revisits and corrects a previous work on reflection at the boundary of an orthotropic thermoelastic medium. For chosen directions of propagation with attenuation, a real finite parameter represents the inhomogeneity. A complex slowness vector is specified to define the propagation of inhomogeneous incident wave. In this incidence, horizontal slowness determines the slowness vectors for all reflected waves. For each reflected wave, the corresponding slowness vector is resolved to define its phase direction, phase velocity and attenuation coefficients. The slowness vectors of incident and reflected waves define the aggregate wave-field in thermoelastic medium. Appropriate boundary conditions on this wave-field determines the amplitude ratios and phase shifts for reflected waves relative to the incident wave. A square matrix of order four determines the partition of incident energy flux among the reflected waves.

Machine-Learning-Based Hybrid Method for the Multilevel Fast Multipole Algorithm

In this letter, a hybrid translation computation method for the multilevel fast multipole algorithm (MLFMA) is proposed based on machine learning. The hybrid method combines both generalized regression neural network (GRNN) and artificial neural network (ANN) to replace the traditional translation procedure during the solving process of the MLFMA. Based on the data corresponding to every one of the interaction list boxes at each level, the hybrid neural network is trained. Comparing with the previous machine learning method in this field, the proposed model is more general, and with lower complexity since it inherits the accuracy of the GRNN as well as the efficiency of the ANN. To the best of our knowledge, it is for the first time that the ANN is integrated into the MLFMA. Numerical examples are benchmarked to illustrate the reliability and capability, thus making it possible to solve similar problems during the fast inhomogeneous plane wave algorithm solving process in the multilayered medium.

Electromagnetic scattering between an elliptically inhomogeneous plane wave and a multilayered cylinder

The interaction of a stratified cylinder with an elliptically inhomogeneous plane wave is introduced and also determined through a rigorous theoretical approach. The scattered electromagnetic field by a multilayered cylinder is investigated through an application of the generalized Vector Cylinder Harmonics (VCH) expansion. The exact mathematical model to represent this scenario considers the so-called complex-angle formalism reaching a superposition of Vectorial Cylindrical-Harmonics and the T-matrix formulation to contemplate the multi-scattering process between the cylinders. The validation of the procedure was accomplished with a comparison between the numerical results obtained with the Finite Element Method (FEM) in Comsol Multiphysics environment and a homemade Matlab code.

Permittivity Gradient Induced Depolarization: Electromagnetic Propagation With the Maxwell Vector Wave Equation

Recent interest in 3-D vectorial sensors requires the development of vectorial propagation methods, rather than scalar wave equation approaches. We derive a vector wave equation from Maxwell’s equations for a medium which has an inhomogeneous dielectric permittivity dominated by variation along one dimension. It is well known that the electric field components decouple for homogeneous media. However, 1-D permittivity variations yield an upper triangular system of scalar wave equations with the wave polarization component parallel to the inhomogeneous direction/axis acting as a forcing term for the orthogonal components. The main implication is that waves with polarization oriented parallel to the permittivity gradient will act as a forcing term and excite other polarization components and, thus, induce depolarization. Contemporary studies treat the permittivity as a constant when deriving a wave equation or paraxial approximation, and then re-introduce via inhomogeneous wave speed, variable permittivity, thus missing important terms and physical mechanisms in their resulting equations. Contemporary studies neglect the term in the Maxwell vector wave equation responsible for this effect. Application of the electromagnetic propagation depolarization effect is demonstrated numerically for an air–sea interface evaporation duct with a 500 MHz source.

Perfect Conversion of a TM Surface Wave Into a TM Leaky Wave by an Isotropic Periodic Metasurface Printed on a Grounded Dielectric Slab

This article presents an exact solution for a perfect conversion of a TM-polarized surface wave (SW) into a TM-polarized leaky wave (LW) using a reciprocal and lossless penetrable metasurface (MTS) characterized by a scalar sheet impedance, located on a grounded slab. On contrary to the known realizations of LW antennas, the optimal surface reactance modulation which is found here ensures the absence of evanescent higher-order modes of the field Floquet-wave expansion near the radiating surface. Thus, all the energy carried by the SW is used for launching the single inhomogeneous plane wave into space without accumulation of reactive energy in the higher-order modes. It is shown that the resulting penetrable MTS exhibits variation from an inductive to a capacitive reactance passing through a resonance. The present formulation complements a previous article of the authors, in which a perfect conversion from TM-polarized SW to TE-polarized LW was found for impenetrable boundary conditions. Here, the solution takes into account the grounded slab dispersion, and it is convenient for practical implementation.

Prediction of exotic magnetic states in the alkali-metal quasi-one-dimensional iron selenide compound Na2FeSe2

The magnetic and electronic phase diagram of a model for the quasi-one-dimensional alkali metal iron selenide compound Na$_2$FeSe$_2$ is presented. The novelty of this material is that the valence of iron is Fe$^{2+}$ contrary to most other iron-chain compounds with valence Fe$^{3+}$. Using first-principles techniques, we developed a three-orbital tight-binding model that reproduces the {\it ab initio} band structure near the Fermi level. Including Hubbard and Hund couplings and studying the model via the density matrix renormalization group and Lanczos methods, we constructed the ground state phase diagram. A robust region where the block state $\uparrow \uparrow \downarrow \downarrow \uparrow \uparrow \downarrow \downarrow$ is stabilized was unveiled. The analog state in iron ladders, employing 2$\times$2 ferromagnetic blocks, is by now well-established, but in chains a block magnetic order has not been observed yet in real materials. The phase diagram also contains a large region of canonical staggered spin order $\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow \uparrow$ at very large Hubbard repulsion. At the block to staggered transition region, a novel phase is stabilized with a mixture of both states: an inhomogeneous orbital-selective charge density wave with the exotic spin configuration $\uparrow \uparrow \downarrow \uparrow \downarrow \downarrow \uparrow \downarrow$. Our predictions for Na$_2$FeSe$_2$ may guide crystal growers and neutron scattering experimentalists towards the realization of block states in one-dimensional iron-selenide chain materials.

Scattering of ion cyclotron range of frequency waves by filaments and ELMs

The scattering of ion cyclotron range of frequency (ICRF) waves by filaments and ELMs has been comprehensively studied via modeling. The influence of filaments on the propagation of ICRF waves is studied by building a 2D COMSOL model which solves the wave equation. It is benchmarked against the Mie scattering theoretical model. Cases either with perfect matching layer boundary condition or with poloidal periodic boundary condition are considered. Parameter scans, including the filament density, the filament radius, the number of filaments as well as the distance between filaments, are performed. Then, the influence of ELMs on the propagation of ICRF waves in realistic geometry is studied by importing density distributions calculated by 3D non-linear MHD code JOREK into the 3D antenna code RAPLICASOL. The evolution of density and wave fields during an ELM is analyzed for cases with a low and high scrape-off layer density, respectively. Both the COMSOL simulation and the realistic simulation with JOREK and RAPLICASOL show that the wave fields and Poynting flux can be significantly and globally modified by the ELM filaments. Due to the mutual influence of many density filaments, radially elongated and poloidally distributed stripe structures of the wave fields develop, leading to poloidally inhomogeneous wave fields. Furthermore, the influence of ELMs on the antenna power and antenna coupling resistance is investigated with experimental results in ASDEX Upgrade.

The inhomogeneous wave equation with $L^p$ data

We prove existence and uniqueness of $L^2$ solutions to the inhomogeneous wave equation on $\mathbb{R}^{n-1}\times\mathbb{R}$ under the assumption that the inhomogeneous data lies in $L^p(\mathbb{R}^n)$ for $p=2n/(n+4)$. We also require the Fourier transform of the inhomogeneous data to vanish on an infinite cone where the solution could become singular. Subsequently, we show sharpness of the exponent $p$. This extends work of Michael Goldberg, in which similar Fourier-analytic techniques were used to study the inhomogeneous Helmholtz equation.

Elastic waves at the plane interface of swelling porous half-space and viscoelastic half-space with voids

Reflection/ refraction phenomena of inhomogeneous plane waves at a plane interface with a swelling porous elastic solid consisting of three constituents - an elastic solid, viscous liquid, inviscid gas on one side and a viscoelastic solid with voids on the other side have been studied. This model has been considered in the spirit of a gas and oil/ water reservoir containing the porous solid skeleton that swells up due to the shear response of the viscous liquid present in the pores and natural gas; trapped beneath the Earth’s crust containing minerals rocks. We have considered two problems: (i) Incident wave strikes the interface from the swelling porous half-space; (ii) Incident wave strikes the interface from the viscoelastic solid half-space with voids. Assuming the pores of the swelling porous medium at the interface to be sealed, appropriate boundary conditions have been formulated and the amplitude ratios corresponding to various reflected/ refracted waves have been presented. While conducting the numerical simulation for the specific model, the variations of energy ratios against the angle of incidence and frequency parameter have been thoroughly studied and are illustrated graphically. Attention has been paid to analyze the effects of voids of the viscoelastic half-space and swelling of the porous half-space on the energy ratios corresponding to various propagating waves in the two media. It is concluded that during reflection/ refraction phenomena, the sum of the energy ratios carried along various reflected and refracted waves is equal to unity at each angle of incidence only if the interactional energy ratios are included.

Infrared Propagating Electromagnetic Surface Waves Excited by Induction

AbstractPropagating inhomogeneous electromagnetic waves called surface plasmon polaritons (SPPs) can be excited by free-space beams on corrugated conducting surfaces at resonance angles determined by corrugation period, permittivity, and optical frequency. SPPs are coupled to and co-propagate with surface charge displacements. Complete electrical isolation of individual conducting corrugations prevents the charge displacement necessary to sustain an SPP, such that excitation resonances of traveling SPPs are absent. However, SPPs can be excited via electric induction if a smooth conducting surface exists below and nearby the isolated conducting corrugations. The dependence of SPP excitation resonances on that separation is experimentally investigated here at long-wave infrared wavelengths. We find that excitation resonances for traveling SPPs broaden and disappear as the dielectric’s physical thickness is increased beyond ~1% of the free-space wavelength. The resonance line width increases with refractive index and optical thickness of the dielectric.

Effect of local fluid flow on the reflection and transmission of elastic waves at an interface between an elastic solid and a double-porosity medium

We have studied the reflection and transmission of elastic waves incident on an interface separating an elastic solid and a double-porosity medium described by the Biot-Rayleigh model that considers the effect of local fluid flow (LFF). The P1- and SV-wave incidence generates two reflected elastic waves in the elastic solid and four transmitted inhomogeneous waves in the double-porosity medium, represented by Helmholtz potential functions. The reflection and transmission coefficients are derived in closed form based on the boundary conditions at the interface. Energy ratios are then derived, and energy conservation at the interface is verified. The contribution of fluid flow to the three transmitted longitudinal waves in the double-porosity medium is expressed as a function of frequency, the transmission coefficient, and the corresponding slowness vector. Numerical examples indicate that LFF predicts significant compressional-wave velocity dispersion in the seismic band, and frequency-dependent reflection and transmission coefficients. For the case in which the incidence angle is larger than the critical angle, the transmitted P1-wave shows a nonzero energy flux in the vertical direction, whereas it does not if LFF is absent.

Internal Observability, Controllability and Stabilization of the Inhomogeneous and Anisotropic Elastic Wave Equation

In this paper, we consider the inhomogeneous and anisotropic elastic wave equation on bounded domain. We prove the internal observability, controllability and stabilization of the elastic wave equation under a suitable condition of inhomogeneous and anisotropic medias. The main methods are multiplier methods and compactness-uniqueness arguments.

Modification to the Fresnel formulas for amplified or attenuated internal reflection

The present study addresses the question of total internal reflection of a plane wave from an amplifying or attenuating medium. Inspection on the expressions for the modal gain or loss of an asymmetric planar waveguide having an amplifying or attenuating cladding has led us to the coefficients for amplified or attenuated internal reflection. The derived formulas suggest an interpretation that the refracted inhomogeneous plane wave undergoes amplification or attenuation while it travels a distance equal to the Goos–Hänchen shift along the boundary plane before going back into the high-index medium. Furthermore, the evanescent wave in the low-index medium is discussed. Unlike the transparent case, the Poynting vector is shown to have a nonvanishing time-averaged component perpendicular to the boundary plane.

Q values and wave inhomogeneity parameters of reflected inhomogeneous P and S waves at the free surface of an effective Biot solid

SUMMARYIn this study, new methods are developed to estimate the dissipation factors, inhomogeneity parameters and phase velocities of the reflected waves at the free surface of a poro-viscoelastic solid in which the seismic wave propagation is described by effective Biot theory. The Christoffel equations of an effective Biot medium are solved for a general harmonic plane wave and the three complex velocities obtained corresponding to the shear wave (SV), fast-P wave and slow-P wave, together with their polarizations. Based on the complex form of the energy balance equation in an effective Biot material, expressions are derived for the energy ratios at the free surface. Moreover, the equations for the inhomogeneity parameters are derived as functions of the complex slowness or the unit polarization vectors. Based on the implicit and the explicit dissipation factor expressions, two methods are developed to obtain the dissipation factors, the inhomogeneity parameters and the phase velocities of mode-converted waves. These methods are illustrated by numerical examples which show that the dissipation factors, inhomogeneity parameters and phase velocities of reflected waves can strongly depend on the incidence angle (also reflected angle), the incident wave inhomogeneity parameter and the wave frequency. Ignoring these dependencies and using dissipation factors only valid for homogeneous waves can cause discrepancies in computed phase velocities and dissipation factors for interface generated (reflected/transmitted) inhomogeneous waves.

SeismicQof inhomogeneous plane waves in porous media

Seismic waves in an attenuative porous medium are generally inhomogeneous waves, which have different directions of propagation and attenuation. The dissipation factors (1/ Q) of inhomogeneous waves are strongly dependent on the degree of wave inhomogeneity and cannot be expressed correctly with the usual 1/ Q expressions valid only for homogeneous waves. We have used the differing definitions of 1/ Q for inhomogeneous waves (i.e., the ratio of the time-averaged dissipated energy density to the time-averaged strain energy density or time-averaged total energy density) and the complex form of the energy balance equations of poroviscoelastic media to derive concise and explicit expressions for the dissipation factors. They are given as simple functions of the material parameters and the wave inhomogeneity parameter for inhomogeneous SV-waves and fast and slow P-waves. The isotropic, poroviscoelastic medium under consideration is upscaled from effective Biot theory for a double-porosity solid, which is the most general theory to describe wave propagation in a reservoir. We find that, if the inhomogeneity parameter is infinite (i.e., the inhomogeneity angle is 90°) for all three Biot waves, then the dissipation factors only depend on the ratio of the imaginary to the real part of the complex shear modulus. Our explicit expressions for the dissipation factors of poroviscoelastic materials also are reduced to obtain their counterparts for viscoelastic media as a special case. The inhomogeneous waves in an example poroviscoelastic material are used to demonstrate that the 1/ Q values of the three Biot waves strongly depend on the inhomogeneity parameters and furthermore the different definitions may cause significant differences of 1/ Q values. We find that the dissipation factor of fast P-waves may decrease with the increasing degree of inhomogeneity, which contradicts previously published results.