通过边界积分方程方法研究在不均一有裂纹的统一体中的波衍射(英文)

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Simple method for obtaining electron scattering phase shifts from energies of an atom in a cavity

We present a simple method for obtaining elastic scattering phase shifts and cross sections from precise ab initio many-body perturbation theory energies of atoms in variable cavities. This method does not require calculations of wave functions of continuum states, can be generalized to many atoms and ions, and is extremely convenient because existing codes developed for energy calculations can be used without modification. The high precision of the method and close agreement with experiment are illustrated on examples of e-Ar and e-Kr scattering. Correlations as well as relativistic corrections are systematically considered.     

Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

Analysis of Laser-generated Rayleigh wave on viscoelastic materials

In order to understand the viscoelasticity of material, this research has been conducted to study the propagation characteristics of viscoelastic Rayleigh wave theoretically. A model is presented for the pulsed laser generation of ultrasound on viscoelastic medium surface. Referred to the Kelvin model, the frequency equation and the normal displacement of viscoelastic Rayleigh wave were derived, the influence of the viscoelastic modulus on dispersion and attenuation was discussed. From the theoretical calculation, it is shown that the effect of viscoelasticity on the attenuation of Rayleigh wave is more than that on its dispersion. In the case of a weak viscosity, the attenuation of viscoelastic Rayleigh wave is directly proportional to viscosity modulus; the effect of shear viscosity on the attenuation is much more than that of bulk viscosity. The transient response of viscoelastic Rayleigh wave was also simulated using Laplace and Hankel inversion transform, which are showed in good agreement with the theoretic predictions. The model provides a useful tool for the determination of viscoelastic parameters of medium.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

The multiple scattering of non-homogeneous shear waves from two cavities in functionally graded materials

The propagation and multiple scattering of non-homogeneous shear waves resulting from two cavities embedded in exponential functional graded materials (FGMs) were investigated, and the dynamic stress around the two cavities derived. The non-homogeneous scattering fields of shear waves around the cavities are analytically expressed by using the wave function expansion method. The interaction of non-homogeneous scattering fields between the two cavities is described accurately. The dynamic stresses around the cavities under different geometrical and physical parameters are graphically illustrated and analyzed. Analysis shows that the non-homogeneous properties of FGMs exhibit a significant effect on the dynamic stress around the cavities. The effect of the non-homogeneous properties of FGMs on the dynamic stress is also dependent on the gradation direction, the distance between the two cavities, the relative position of the two cavities and the incident frequency of waves. A comparison with other existing studies in the literature is also presented.     

The scattering of guided waves in partly embedded cylindrical structures

The scattering of ultrasonic guided waves at a point where a free cylindrical waveguide enters an embedding material is investigated. A modal solution that is valid when the guided waves are incident from the free section of the waveguide is developed. It is shown that in this case it is valid to consider only the modal fields over the cross section of the waveguide, neglecting the fields in the embedding material. As an application, the scattering of the lowest-order longitudinal mode in a cylindrical waveguide, L(0,1), is examined in detail. As well as considering epoxy resin as an embedding material, the case where the embedding material is replaced by a perfectly rigid boundary is discussed. The latter gives some insight into the role of nonpropagating and inhomogeneous waveguide modes in the scattering process. The results from the modal solution are validated using Finite Element modeling, very good agreement being obtained.     

Modeling of high-frequency propagation in inhomogeneous background random media

When a high-frequency electromagnetic wave propagates in a complicated scattering environment, the contribution at the observer is usually composed of a number of field species arriving along different ray trajectories. In order to describe each contribution separately the parabolic extension along an isolated ray trajectory in an inhomogeneous background medium was performed. This leads to the parabolic wave equation along a deterministic ray trajectory in a randomly perturbed medium with the possibility of presenting the solution of the high-frequency field and the higher-order coherence functions in the functional path-integral form. It is shown that uncertainty considerations play an important role in relating the path-integral solutions to the approximate asymptotic solutions. The solutions for the high-frequency propagators derived in this work preserve the random information accumulated along the propagation path and therefore can be applied to the analysis of double-passage effects where the correlation between the forward-backward propagating fields has to be accounted for. This results in double-passage algorithms, which have been applied to analyze the resolution of two point scatterers. Under strong scattering conditions, the backscattering effects cannot be neglected and the ray trajectories cannot be treated separately. The final part is devoted to the generalized parabolic extension method applied to the scalar Helmholtz's equation, and possible approximations for obtaining numerically manageable solutions in the presence of random media.     

Nonstationary two-flux model of radiation transport for optical tomography of scattering media

A nonstationary two-flux model is formulated for the transport of radiation in an inhomogeneous scattering medium and is applied to the situation where such a medium is irradiated by the narrow beam of a pulsed laser. It is shown that when the time distribution of the transmitted photons is measured it is possible simultaneously to reconstruct the two spatial functions (the coefficients of absorption coefficient and of scattering of the radiation by the medium) by means of an inverse Radon transformation and the solution of a system of nonlinear differential equations on the projection lines. An analytic solution is obtained in quadratures for these differential equations. The results constitute a method of solving problems in optical tomography in an inhomogeneous scattering medium Zh. Tekh. Fiz. 67, 61–65 (May 1997)     

冲击波作用下铝的等效剪切模量

提出了冲击波作用下通过测量沿着准弹性卸载过程纵波波速与体波波速得到等效剪切模量的方法,应用该方法对LY12铝在20—70 GPa冲击压力下的等效剪切模量进行了测量.实验结果表明,等效剪切模量随应力线性减少直至反向屈服时为零,而初始卸载时的等效剪切模量可以由修正的Steinberg-Cochran-Guinan模型进行描述.应用得到的等效剪切模量进行了初步数值模拟,计算结果与实验测量的粒子速度剖面符合很好,重现了准弹性卸载到塑性卸载的光滑过渡. 关键词： 等效剪切模量 波速 准弹性卸载 冲击波 铝     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Acoustic properties of a dielectric with cavities in a polarizing electric field

The effect of an external polarizing electric field on the shear wave propagation in a centrosymmetric crystal with electrostriction, whose body is penetrated with parallel cylindrical cavities (pores), is considered. The cavities are distributed throughout the crystal at random and with a low density. The waves are assumed to be polarized along the cavity generatrices, and the wave propagation occurs in the elastic isotropy plane, which is orthogonal to the cavity axes. The external field is assumed to be axial. Possibility of controlling the propagation of shear waves by the polarizing field is demonstrated for the case of metallized cavity surfaces.     

On reflection from a suddenly created plasma half-space: transientsolution

The reflection by a suddenly created plasma half-space of a time-harmonic plane electromagnetic wave propagating in free space is considered. The problem involves a temporal discontinuity, a spatial discontinuity, and a dispersive medium. The steady-state solution is obtained by considering the basic features of the scattering processes due to each of the discontinuities in terms of analogous transmission-line models. The electric field of the reflected wave consists of two components. One component (called component A) is of the same frequency as the incident wave frequency and is due to the spatial discontinuity. The other component (called component B) is of a different frequency and arises because of the temporal discontinuity. The B component is damped out even if the plasma is only slightly lossy. The damping rate of the B component is calculated. The transient solution is obtained through the use of Laplace transforms. The solution is given in terms of Bessel-like functions. The limiting value of this solution is shown to agree with the steady-state solution. Numerical results illustrating the transient effects are for two typical cases     

One-dimensional acoustic waves in retarding structures with propagation velocity tending to zero

A retarding structure that allows the effective admittance of a tube wall to increase smoothly along the tube axis is considered. The sound velocity gradually decreases along a finite segment of the tube and finally vanishes at some cross section. The time of the sound propagation along this segment is infinitely long. A wave incident on the input cross section cannot reach the other end of the tube within a finite time, and, hence, it is not reflected from it. The wave is completely absorbed, the absorption being caused by the energy accumulation in the cross section where the velocity of sound vanishes, rather than by the energy transformation to heat, as in common sound absorbers. A differential equation is obtained to describe the sound propagation in a one-dimensional waveguide with a varying cross section and varying acoustic admittance of the walls. The solutions to this equation are analyzed in the WKB approximation. An exact solution is determined for the case of some specific functions describing the variations of the cross section and admittance. Calculated results for the input admittance of the waveguide are presented. A possible similarity to the problem of shear waves in sea sediments is pointed out.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber

In the framework of surface elasticity theory, the scattering of plane compressional and shear waves by a single nano-sized coated fiber embedded in an elastic matrix is studied using the method of eigenfunction expansion. The dynamic stress concentration factors along the interface between the coated fiber and the matrix induced by the plane elastic wave and scattering cross section are derived and numerically evaluated. The interface stress, inhomogeneous material constants and thickness of the coated layer on the scattering of the elastic wave become much more important when the radius of the coated-fiber is reduced to the nanometer scale. These were confirmed by the use of numerical results. Our results can aid in understanding the dynamic mechanical properties of nano-composites. The proposed method has potential applications in the characterization of the interfacial layer that links reinforced fibers to their matrix.     

Multiscale modeling of the effect of carbon nanotube orientation on the shear deformation properties of reinforced polymer-based composites

A combination of molecular dynamics (MD), continuum elasticity and FEM is used to predict the effect of CNT orientation on the shear modulus of SWCNT-polymer nanocomposites. We first develop a transverse-isotropic elastic model of SWCNTs based on the continuum elasticity and MD to compute the transverse-isotropic elastic constants of SWCNTs. These constants are then used in an FEM-based simulation to investigate the effect of SWCNT alignment on the shear modulus of nanocomposites. Furthermore, shear stress distributions along the nanotube axis and over its cross-sectional area are investigated to study the effect of CNT orientation on the shear load transfer.     

Scattering of waves by irregularities in periodic discrete lattice spaces. I. Reduction of problem to quadratures on a discrete model of the Schrödinger equation

The scattering of plane waves and of point source pulses by irregularities in a discrete lattice model of the Schrödinger equation is considered. Closed form expressions are derived for the scattered wave function in terms of lattice Green's functions in the case that a finite number of lattice points or “bonds” are defective. The scattered wave function appears in the form of the ratio of two determinants. While in continuum scattering theory the scatterer must have some symmetry, perhaps spherical, cylindrical or elliptical, in order to allow separation of variables in the basic scattering differential equation, such symmetries are not necessary for the construction of scattered wave functions on discrete lattices. When the number of irregularities becomes large, the determinants in the solution of the scattering problem become large.     

Viscoelastic micropolar continuum and viscoelastic waves

Generalized Kelvin model is applied to isotropic viscoelastic micropolar continuum. Constitutive equations in integral and differential form, generalized Lamé equations, and wave equations for displacement and microrotation are derived for this model. For damped viscoelastic waves, which are realized in the continuum under examination, the wave vectors and vectors of decay are explicitly given as functions of elastic moduli, viscosity coefficients, angular frequency, density, and microinertia coefficient. Analogous relations are derived for further eleven simpler mass models. Results are compared for three models in current use. For two of them (classical elastic and micropolar elastic medium) are the derived results in agreement with the ones usually used, for the third model (viscoelastic continuum) are the usual formulas a limiting case of the relations derived in this paper.