Description Of Wave Propagation Research Articles

Controllable excitations of rogue waves and breathers in an inhomogeneous erbium doped fiber system

We study the generalized nonlinear Schrödinger Maxwell–Bloch equation describing wave propagation in erbium-doped nonlinear fibers and derive the analytical bright and dark rogue wave and breather solutions under certain parametric conditions. We display the propagation properties of the attained solutions by modulating the relation between maximum effective propagation distance ζm and the parameter ζ0 relating to the excitation type of nonlinear waves. Their controllable behaviors such as fast appearance, postponement, sustainment and annihilation for exponentially dispersion decreasing fiber system have been demonstrated. Additionally, we delineate the longitudinal control of rogue waves. Our results may be useful in understanding and enriching the manipulation of rogue waves in resonant erbium-doped optical fibers.

Influence of a delamination on Lamb wave excitation by a nearby piezoelectric transducer

This article presents the results of theoretical and experimental investigations of characteristic changes of Lamb wave excitation and scattering by a strip-like horizontal delamination in a layered elastic waveguide for Lamb waves induced by a piezoelectric wafer active sensor. The boundary integral equation method is used to describe wave propagation in an infinite layered waveguide with a delamination, while the frequency domain spectral element method is employed to model the dynamic behaviour of the piezoelectric wafer active sensor, which allows to simulate debonding between the piezoelectric wafer active sensor and the waveguide. Experimental investigations of the dynamic interaction of the piezoelectric wafer active sensor with a layered plate containing a horizontal delamination is conducted for several damage scenarios, showing a good agreement with the results obtained using the developed mathematical model. The obtained mathematical model is employed to analyse alteration of the piezo-induced Lamb waves including modes’ decomposition due to delamination. The conversion and/or conservation of the Lamb waves on account of a delamination is investigated. The electro-mechanical impedance of the piezoelectric transducer and the stress intensity factors of a delamination are analysed in dependence on the delamination location.

Equations and fundamental characteristics of transverse waves propagating in fluid-saturated porous materials

The main purpose of the paper is to present an extended analysis of the coupled system of linear equations describing wave propagation in fluid-saturated porous materials used for the determination of their fundamental characteristics. The present paper is the first part, mainly devoted to the analysis of the system of equations describing transverse wave propagation. The analysis of equations for compressional waves will be presented in a separate paper. The starting point of considerations are nonlinear equations describing the dynamic behavior of the medium formulated in the spirit of the theory of interacting continua in which parameters of isotropic pore space structure are explicitly present in the model, and constitutive equations are formulated for each physical component separately. They contain all fundamental mechanical couplings between components of this medium in the general nonlinear form and of clear physical meaning. Linear equations of this theory for barotropic fluid and hyperelastic skeleton are the subject of the analysis performed in the paper. They are equivalent to Biot's model, widely used in the description and analysis of wave propagation in saturated porous materials and wave interaction with the boundary of such media. A new method of analysis is proposed in the paper, based on spectral decomposition of the system of equations in the two-dimensional vector space of rotations of solid and fluid particles. It is shown that each choice of the base in this vector space defines the division of the medium into two new components and transforms the system of equation to the form describing the dynamic behavior of these components, and the requirement of the basic dynamic properties of the medium to be invariant in each chosen base uniquely determines the mass densities and bulk modules of the new components. Such an approach enabled decomposition of the system of equations for particle rotations to two uncoupled scalar equations, the only one of which describes propagation of the transverse wave. This also allowed obtaining expressions characterizing transverse wave propagation in fluid-saturated porous materials: velocity, effective mass densities and wave impedance of the medium associated with this wave and its frequency characteristics: phase velocity and attenuation coefficient. It is shown that both frequency characteristics are fully defined by the effective mass densities of both components associated with the transverse wave, the tortuosity of the pore space, and the coefficient characterizing the viscous interaction of the fluid with the skeleton.

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.

Solitary waves in the resonant nonlinear Schrödinger equation: Stability and dynamical properties

The stability and dynamical properties of the so-called resonant nonlinear Schrödinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schrödinger (NLS) equation with the addition of a perturbation used to describe wave propagation in cold collisionless plasmas. We first examine the modulational stability of plane waves in the RNLS model, identifying the modifications of the associated conditions from the NLS case. We then move to the study of solitary waves with vanishing and nonzero boundary conditions. Interestingly the RNLS, much like the usual NLS, exhibits both dark and bright soliton solutions depending on the relative signs of dispersion and nonlinearity. The corresponding existence, stability and dynamics of these solutions are studied systematically in this work.

SOUND TRANSMISSION LOSS ACROSS A FINITE CLAMPED DOUBLE-LAMINATED COMPOSITE PLATE WITH POROELASTIC MATERIAL

A theoretical study of sound transmission loss across a clamped double-laminated composite plate filled with poroelastic material is formulated. Biot’s theory is employed to describe wave propagation in elastic porous media. The two face composite plates are modeled as classical thin plates. By using the modal superposition theory, a double series solution for the sound transmission loss of the structure is obtained with the help of the Galerkin method. The analytical model is validated against previous experimental results of a single sound wave under normal incidence. The numerical results suggest that the density of poroelastic material, the type of composite materials and the composite plies arrangement have significant effects on the sound transmission loss of considered structure.

SOUND TRANSMISSION LOSS ACROSS A FINITE CLAMPED DOUBLE-LAMINATED COMPOSITE PLATE WITH POROELASTIC MATERIAL

A theoretical study of sound transmission loss across a clamped double-laminated composite plate filled with poroelastic material is formulated. Biot’s theory is employed to describe wave propagation in elastic porous media. The two face composite plates are modeled as classical thin plates. By using the modal superposition theory, a double series solution for the sound transmission loss of the structure is obtained with the help of the Galerkin method. The analytical model is validated against previous experimental results of a single sound wave under normal incidence. The numerical results suggest that the density of poroelastic material, the type of composite materials and the composite plies arrangement have significant effects on the sound transmission loss of considered structure.

Next-generation neural mass and field modeling.

The Wilson-Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson-Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson-Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

Effective spring boundary conditions modelling wave scattering by an interface with a random distribution of aligned interface rectangular cracks

In the present study frequency-dependent effective spring boundary conditions are introduced to describe wave propagation through an interface between two elastic isotropic media with a distribution of rectangular aligned micro-cracks. The explicit analytic formulae are obtained for stiffnesses in effective spring boundary conditions modelling the distribution of rectangular cracks employing the boundary integral equation method, the ensemble averaging technique and Boström–Wickham approach. Three diagonal components of the introduced stiffness matrix are expressed in terms of the elastic properties of materials, the frequency, and dimensions of rectangular cracks. The analysis of the derived relations for stiffnesses shows the low influence of density on stiffnesses. If the area of rectangular cracks is constant, but the elongation of rectangular cracks increases then stiffnesses become larger. On the other hand, stiffnesses get smaller if one side is constant and the second side of rectangular crack increases. Examples demonstrating the influence of material properties and the elongation of rectangular cracks on three components of the stiffness matrix are provided. Effective stiffnesses for the distribution of square cracks are nearly proportional to the corresponding stiffnesses obtained for the distribution of circular cracks.

Extra-wide-angle parabolic equation for wave propagation in inhomogeneous media

To describe wave propagation at large angles with respect to a nominal direction, wide-angle parabolic equations (WAPEs) have been widely used in atmospheric and ocean acoustics, geophysics, electromagnetic wave propagation, and other fields of physics. This paper considers an application of an extra-wide-angle parabolic equation (EWAPE) for such problems. For small variations of the refractive index of a medium, the EWAPE describes wave propagation up to 90 deg with respect to the nominal direction and is more general than the WAPEs used in the literature. The EWAPE can be written in an integral form or as a pseudo-differential equation and may be solved by a split-step spectral algorithm or the Padé series expansions of the pseudo-differential operators. The EWAPE is also generalized to large variations in the refractive index, sound propagation above an impedance boundary, and a moving medium with small or large Mach numbers. For sound propagation in a moving medium, the EWAPE enables derivation of new WAPEs which are accurate and simpler to implement than those currently available in the literature. Numerical examples illustrating the application of these new WAPEs to sound propagation in a moving atmosphere are presented.

Numerical analysis of buried trench in screening surface vibration

In practical engineering, open trenches would be covered by soil or plate for greenery and safety reasons, which inevitably turns them into buried trenches. It is necessary to reassess the screening efficiency of these buried trenches. A plane strain model is then established to describe wave propagation in ground. The influences of geometrical parameters normalized by Rayleigh wavelength (LR) are investigated, followed by a simplified design formula to estimate the screening capacity of buried trenches. Results show that the buried depth and trench depth play dominant roles in screening effect whereas the influence of trench width is small. Furthermore, four kinds of extending plates mounted on top of buried trenches are considered. It can be found that extending plates would significantly increase the screening performance of the barrier system. The source- and receiver-oriented extending plate are found to be the more effective measures and make a more contribution to wave screening when buried depth is around 0.2–0.3LR.

Two-breather solutions for the class I infinitely extended nonlinear Schrödinger equation and their special cases

We derive the two-breather solution of the class I infinitely extended nonlinear Schrodinger equation (NLSE). We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free parameters of the two breather components. Particular cases of this solution include rogue wave triplets, and special cases of breather-to-soliton and rogue wave-to-soliton transformations. The presence of many parameters in the solution allows one to describe wave propagation problems with higher accuracy than with the use of the basic NLSE.

Continuum modelling of frequency dependent acoustic beam focussing and steering in hexagonal lattices

Wave propagation in hexagonal lattices is characterised by a transition from isotropic to anisotropic regime as the frequency increases. This feature cannot be observed when the lattice material is modelled within the framework of classic Cauchy theory of elasticity, except when the real geometry of the microstructure is explicitly described. Homogenized equivalent continua can capture the onset of this anisotropy only if tensors involved in the constitutive law are at least of order six. This requirement is met in the case of Strain-Gradient Elasticity (SGE). In this work the SGE model is calibrated to quantitatively describe wave propagation within hexagonal lattices in a sufficiently large region of the dispersion diagram, by fitting the dispersion relations obtained from a Bloch-Floquet analysis on the unit cell. It is then shown that focussing and beam steering effects can be obtained by acting only on the local material orientation of the hexagonal lattice. This is achieved by computing the Poynting vector in the SGE model and optimising the distribution of material orientation.

Distributed-order fractional constitutive stress–strain relation in wave propagation modeling

Distributed order fractional model of viscoelastic body is used in order to describe wave propagation in infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem, corresponding to fractional wave equation, is studied. The explicit form of fundamental solution is calculated, and wave propagation speed, arising from solution's support, is found to be connected with the material properties at initial time instant. Existence and uniqueness of the fundamental solutions to the fractional wave equations corresponding to four thermodynamically acceptable classes of linear fractional constitutive models, as well as to power type distributed order model, are established and explicit forms of the corresponding fundamental solutions are obtained.

Nondegenerate Solitons in Manakov System.

It is known that the Manakov equation which describes wave propagation in two mode optical fibers, photorefractive materials, etc., can admit solitons which allow energy redistribution between the modes on collision that also leads to logical computing. In this Letter, we point out that the Manakov system can admit a more general type of nondegenerate fundamental solitons corresponding to different wave numbers, which undergo collisions without any energy redistribution. The previously known class of solitons which allows energy redistribution among the modes turns out to be a special case corresponding to solitary waves with identical wave numbers in both the modes and traveling with the same velocity. We trace out the reason behind such a possibility and analyze the physical consequences.

Next-generation neural field model: The evolution of synchrony within patterns and waves.

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of θ-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatiotemporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.

The role of material and geometric nonlinearities in acoustoelasticity

Wave propagation in prestressed and prestrained continua can be modelled by the theory of acoustoelasticity, which typically includes different assumptions. These are third or fourth order expressions of hyperelastic strain energy, as well as finite initial strains and a formulation of balance equations in the current configuration. In this paper, we use a model describing wave propagation in a three dimensional elastically prestrained continuum to clarify the role of different mechanical aspects taken into account in the classical hypotheses of the theory. We consider different states of prestress: hydrostatic, biaxial and uniaxial. Changes in shear and longitudinal wave speeds and their polarization as a function of the initial prestress are described for all directions of propagation. The role of the strain energy power order in changes of speed is elucidated. Moreover, material and geometric nonlinearities are shown to affect changes with the opposite sign, depending also on the direction of propagation.

Waves Along Fractal Coastlines: From Fractal Arithmetic to Wave Equations

Beginning with addition and multiplication which are intrinsic to a Koch-type curve, I formulate and solve a wave equation that describes wave propagation along a fractal coastline. As opposed to the examples known from the literature I do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve.

Multiple Waves Propagate in Random Particulate Materials

For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterized by a single effective wavenumber. Here, however, we show that there exist many effective wavenumbers, each contributing to the effective transmitted wave field. Most of these contributions rapidly attenuate away from boundaries, but they make a significant contribution to the reflected and total transmitted field beyond the low-frequency regime. In some cases at least two effective wavenumbers have the same order of attenuation. In these cases a single effective wavenumber does not accurately describe wave propagation even far away from boundaries. We develop an efficient method to calculate all of the contributions to the wave field for the scalar wave equation in two spatial dimensions, and then compare results with numerical finite-difference calculations. This new method is, to the best of the authors' knowledge, the first of its kind to give such accurate predictions across a broad frequency range and for general particle volume fractions.

Complex Fractional Zener Model of Wave Propagation in ℝ

Abstract The classical wave equation is generalized within fractional framework, by using fractional derivatives of real and complex order in the constitutive equation, so that it describes wave propagation in one dimensional infinite viscoelastic rod. We analyze existence, uniqueness and properties of solutions to the corresponding initial-boundary value problem for generalized wave equation. Also, we provide a comparative analysis with the case of the same equation but considered on a bounded or half-bounded spatial domain. We conclude our investigation with a numerical example that illustrates obtained results.