Acceleration waves in elastic dielectrics with polarization gradient effects

In this paper the propagation of acceleration waves arbitrary form propagating into a deformed eleastic dielectric with polarization effect is investigated. An acceleration wave is defined as a second order propagating surface of discontinuity on which the position vector, the polarization vector and Maxwell potential, and their first order derivatives with respect to time and space coordinates are continuous while the second order derivatives of these quantities may suffer jumps but are continuous everywhere else. By computing the jumps of the balance equations on the singular surface, implicit equations for wave speeds corresponding to non-zero amplitudes of the acceleration wave are obtained. It is noteworthy that the second order derivatives of Maxwell potential are also continuous across the acceleration wave.The same equation for wave speeds are also derived for isotropic elastic dielectrics. The wave speeds for longitudinal and transverse waves are obtained in explicit forms and the conditions of existence for real wave speeds are investigated.     

A thermodynamic analysis of rigid heat conductors

A thermodynamic approach to rigid heat conductors is proposed: it introduces the heat flux vector as independent variable while its temporal evolution is governed by a first order differential equation. The form of the second law is that proposed by Müller wherein the entropy flux and the entropy source are not given a priori but determined through constitutive equations. Restrictions on the constitutive equations are placed by the second law. Some properties, valid in the vicinity of equilibrium are established. In particular, it is shown that the present theory leads to a hyperbolic heat conduction equation, allowing for the propagation of heat as a thermal wave with a finite velocity. The concept of thermodynamic forces and fluxes is also introduced. The latter are seen to derive from a potential function plus an additional term. Finally, it is established under which conditions symmetry relations are satisfied.     

Contributions of higher order terms to nonlinear waves in fluid-filled elastic tubes: strongly dispersive case

In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid, and then utilizing the modified reductive perturbation technique presented by us [15] the amplitude modulation of weakly nonlinear waves is examined. It is shown that the first order term in the perturbation expansion is governed by a nonlinear Schrödinger equation and the second order term is governed by the linearized Schrödinger equation with a nonhomogeneous term. In the longwave limit a travelling wave type of solution to these equations are also given.     

Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations

The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.     

An Efficiency Study of Transient Wave Generation in a Thermoelastic Layer with a Pulsed Laser

The efficiency of transient wave generation in a thermoelastic silicon layer excited by a pulsed laser is considered. First a principle-based transfer matrix formulation with relaxation effect, also referred to as the generalized dynamic theory of linear thermoelasticity, is used in obtaining transfer functions between the input heat field and the elements of the thermoelastic state vector. The second sound effect, through this relaxation time term, is included to eliminate the thermal wave travelling with infinite velocity as predicted by the diffusion heat transfer model. By employing the fast Fourier transform (FFT) algorithm, the transient response of a silicon thermoelastic layer under a thermal excitation (by a pulsed laser) is investigated to quantify the conversion efficiency from thermal to mechanical energy. The transient acceleration, stress, heat, temperature, and mechanical power flux responses are presented. The pulse duration of the laser excitation is submicrosecond level and, consequently, a large number of modes of motion are excited. Rigid body singularities are eliminated by considering the higher order time derivatives of the state variables. A layer made of bulk silicon under this laser excitation is considered and it is found that the amplitude ratio of the applied heat field to the propagating heat flux at the data points is in the order of 10°. The ratio of the applied power (heat flux) to the generated mechanical power flux is in the order of 10°. The resulting rigid body motion of the layer due to the laser excitation is excluded in calculating the mechanical power.     

Interface waves along an anisotropic imperfect interface between anisotropic solids

First and second order asymptotic boundary conditions are introduced to model a thin anisotropic layer between two generally anisotropic solids. Such boundary conditions can be used to describe wave interaction with a solid-solid imperfect anisotropic interface. The wave solutions for the second order boundary conditions satisfy energy balance and give zero scattering from a homogeneous substrate/layer/substrate system. They couple the in-plane and out-of-plane stresses and displacements on the interface even for isotropic substrates. Interface imperfections are modeled by an interfacial multiphase orthotropic layer with effective elastic properties. This model determines the transfer matrix which includes interfacial stiffness and inertial and coupling terms. The present results are a generalization of previous work valid for either an isotropic viscoelastic layer or an orthotropic layer with a plane of symmetry coinciding with the wave incident plane. The problem of localization of interface waves is considered. It is shown that the conditions for the existence of such interface waves are less restrictive than those for Stoneley waves. The results are illustrated by calculation of the interface wave velocity as a function of normalized layer thickness and angle of propagation. The applicability of the asymptotic boundary conditions is analyzed by comparison with an exact solution for an interfacial anisotropic layer. It is shown that the asymptotic boundary conditions are applicable not only for small thickness-to-wavelength ratios, but for much broader frequency ranges than one might expect. The existence of symmetric and SH-type interface waves is also discussed.     

Geometric view of adaptive optics control

The objective of an astronomical adaptive optics control system is to minimize the residual wave-front error remaining on the science-object wave fronts after being compensated for atmospheric turbulence and telescope aberrations. Minimizing the mean square wave-front residual maximizes the Strehl ratio and the encircled energy in pointlike images and maximizes the contrast and resolution of extended images. We prove the separation principle of optimal control for application to adaptive optics so as to minimize the mean square wave-front residual. This shows that the residual wave-front error attributable to the control system can be decomposed into three independent terms that can be treated separately in design. The first term depends on the geometry of the wave-front sensor(s), the second term depends on the geometry of the deformable mirror(s), and the third term is a stochastic term that depends on the signal-to-noise ratio. The geometric view comes from understanding that the underlying quantity of interest, the wave-front phase surface, is really an infinite-dimensional vector within a Hilbert space and that this vector space is projected into subspaces we can control and measure by the deformable mirrors and wave-front sensors, respectively. When the control and estimation algorithms are optimal, the residual wave front is in a subspace that is the union of subspaces orthogonal to both of these projections. The method is general in that it applies both to conventional (on-axis, ground-layer conjugate) adaptive optics architectures and to more complicated multi-guide-star- and multiconjugate-layer architectures envisaged for future giant telescopes. We illustrate the approach by using a simple example that has been worked out previously [J. Opt. Soc. Am. A 73, 1171 (1983)] for a single-conjugate, static atmosphere case and follow up with a discussion of how it is extendable to general adaptive optics architectures.     

Second order stress gradient plasticity with an application to thin foil bending

The continuum theory of dislocations is applied to formulate the problem of a double ended dislocation pileup under quadratic applied stress. Accordingly, a second order stress gradient plasticity model is presented to address the contribution of the first and the second stress gradients in the effect interpretation. The model is employed to predict the initial strengthening and subsequent hardening in curved and straight thin foils under pure bending within the continuum framework. It is shown that the so-called stress gradient plasticity model that ignores the second stress gradient may not give sound interpretations of the size effects. The plastic response of thin foils is affected by both the first and second stress gradients, yet their interaction strongly depends upon the length scale parameter. The larger the length scale parameter, the quadratic term contribution would be important and the predictions of the first and second order models deviate significantly from each other.     

Simulation of wind velocity time histories on long span structures modeled as non-Gaussian stochastic waves

A methodology is proposed for efficient and accurate modeling and simulation of correlated non-Gaussian wind velocity time histories along long-span structures at an arbitrarily large number of points. Currently, the most common approach is to model wind velocities as discrete components of a stochastic vector process, characterized by a Cross-Spectral Density Matrix (CSDM). To generate sample functions of the vector process, the Spectral Representation Method is one of the most commonly used, involving a Cholesky decomposition of the CSDM. However, it is a well-documented problem that as the length of the structure – and consequently the size of the vector process – increases, this Cholesky decomposition breaks down numerically. This paper extends a methodology introduced by the second and fourth authors to model wind velocities as a Gaussian stochastic wave (continuous in both space and time) by considering the stochastic wave to be non-Gaussian. The non-Gaussian wave is characterized by its frequency–wavenumber (FK) spectrum and marginal probability density function (PDF). This allows the non-Gaussian wind velocities to be modeled at a virtually infinite number of points along the length of the structure. The compatibility of the FK spectrum and marginal PDF according to translation process theory is secured using an extension of the Iterative Translation Approximation Method introduced by the second and third authors, where the underlying Gaussian FK spectrum is upgraded iteratively using the directly computed (through translation process theory) non-Gaussian FK spectrum. After a small number of computationally extremely efficient iterations, the underlying Gaussian FK spectrum is established and generation of non-Gaussian sample functions of the stochastic wave is straightforward without the need of iterations. Numerical examples are provided demonstrating that the simulated non-Gaussian wave samples exhibit the desired spectral and marginal PDF characteristics.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part II. Incoherent and coherent scattered fields

A theoretical model for ultrasonic wave scattering for geometrically irregular and imperfectly bonded interfaces is presented. Part I presents the stochastic interface characterization and a model for its mechanical response based on a micromechanics model of asperity contact. Part II uses this interface representation to write the well used quasi-static boundary conditions for scattering from a.flat imperfect interface¹ directly on the irregular interface profile. The boundary conditions are then expanded in an asymptotic series in the roughness parameter (standard deviation of the surface height) which is small compared to wavelength. The slope of the profile must also be everywhere small. These equations are solved exactly for the zero-th and second order terms, which are the flat coherent solution and its' first coherent correction, and the first order term, which is the first term in the expansion for the incoherently scattered solution. Results for obliquely incident longitudinal and shear waves show a strong dependence on the roughness in both the coherent and incoherent reflected fields, but little if any dependence on the roughness in the transmitted fields. In particular, the reflected coherent fields show markedly increasing attenuation compared to the flat compliant interface with increasing roughness and increasing ultrasonic frequency, the latter result being in qualitative agreement with results for scattering from an inhomogeneous array of individual scatterers.² There is evidence in the incoherent reflected fields for the existence of an incoherent leaky interface disturbance which manifests itself as a bulk incoherent shear wave at a scattering angle equal to the critical longitudinal angle. A coherent true interface wave is also supported by the rough interface which is shown to further attenuate the coherent reflected fields compared to the flat compliant interface solution.     

A hard-sphere model of the helium film

A quantum hard-sphere system bounded by two parallel rigid walls is studied at absolute zero as a model of a helium film. A variational wave function is constructed which is of the Bijl-Dingle-Jastrow type modified by a one-body term which vanishes at the walls; Monte Carlo quadrature is used. We focus our attention particularly on the behavior of the single-particle density function and the condensed-state wave function, i.e., the order parameter. Both show significantly different behavior from that predicted by the Hartree theory. The healing length is calculated, we believe for the first time, and is rather small. The average condensate as a function of distance between two walls is also investigated. The calculation serves as a special probe for approximations to the ground-state wave function in a uniform system.This work has been supported by the U.S. Atomic Energy Commission under contract # AT(11-1)-3077 and Grant No. GH-36457 with National Science Foundation.     

Theoretical aspects of nonlinear echo image system

In order to develop the nonlinear echo image system to diagnose pathological changes in biological tissue , a simple physical model to analyse the character of nonlinear reflected wave in biological medium is postulated. The propagation of large amplitude plane sound wave in layered biological media is analysed for the one dimensional case by the method of successive approximation and the expression for the second order wave reflected from any interface of layered biological media is obtained. The relations between the second order reflection coefficients and the nonlinear parameters of medium below the interface are studied in three layers interfaces. Finally, the second order reflection coefficients of four layered media are calculated numerically. The results indicate that the nonlinear parameter B/A of each layer of biological media can be determined by the reflection method.     

Holographic quantum eraser experiment reveals polarization structure of depolarized light

It is shown that a holographic setup for real-time interferometry can be used to realize a quantum eraser (QE) experiment. Circular polarized light is used to distinguish between the photons of the reconstructed image of the object and the direct object wave consisting of scattered photons from the illuminated flat object. To erase the "which path information," a linear polarizer is used. The experimental results show that polarized light, after depolarizing reflection from a dielectric surface, contains an internal polarization structure, which can be described extending the well-known Jones vector formalism.     

Compact schemes for anisotropic reaction–diffusion equations with adaptive time step

Many problems in biology and engineering are governed by anisotropic reaction–diffusion equations with a very rapidly varying reaction term. These characteristics of the system imply the use of very fine meshes and small time steps in order to accurately capture the propagating wave avoiding the appearance of spurious oscillations in the wave front. This work develops a fourth‐order compact scheme for anisotropic reaction–diffusion equations with stiff reactive terms. As mentioned, the scheme accounts for the anisotropy of the media and incorporates an adaptive time step for handling the stiff reactive term. The high‐order scheme allows working with coarser meshes without compromising numerical accuracy rendering a more efficient numerical algorithm by reducing the total computation time and memory requirements. The order of convergence of the method has been demonstrated on an analytical solution with Neumann boundary conditions. The scheme has also been implemented for the solution of anisotropic electrophysiology problems. Anisotropic square samples of normal and ischemic cardiac tissue have been simulated by means of the monodomain model with the reactive term defined by Luo–Rudy II dynamics. The simulations proved the effectiveness of the method in handling anisotropic heterogeneous non‐linear reaction–diffusion problems. Bidimensional tests also indicate that the fourth‐order scheme requires meshes about 45% coarser than the standard second‐order method in order to achieve the same accuracy of the results. Copyright © 2009 John Wiley & Sons, Ltd.     

Acceleration waves in condensing gases

Summary The flow of a condensing gas is treated as a two-phase-flow, in which the size of the condensate-droplets may vary due to transfer of mass, momentum, and heat; the formation of new droplets is disregarded. An ordinary differential equation for the temporal variation of the amplitude of a one-dimensional acceleration wave is deduced, which holds along the path of the wave. Especially, if the wave propagates into a mixture at rest with spatial variation of the volume fraction of the droplets, the variation of the amplitude is given by the sum of three terms, one of which is quadratic in the amplitude and the others are linear. The quadratic term is solely determined by nonlinear effects in the pure gas and leads to a growth. The first linear term is given by the dissipative effect of the velocity relaxation; this term is the same as for the flow of a mixture of a gas and small solid particles. The second linear term is determined by the combined dissipative effects of the temperature relaxation and the mass transfer; both linear terms lead to a decay. Further, conditions are discussed, on which shock waves are formed.With 6 Figures     

低频矢量声场建模及其应用研究

浅海近距离矢量声场携带了丰富的信息可以用来识别目标。采用射线理论对浅海低频矢量声场进行建模,并且分析了该模型在浅海或深海低频时的适用性。经过与波动理论的比较,说明该模型仅是矢量声场传播损失的简单近似。通过分析浅海声压场的特性,提出了一种目标运动参数估计的方法,海试数据分析说明了其有效性。近距离目标辐射的低频宽带噪声通过浅海声场后,在LOFAR图上形成双曲线干涉条纹。运用图像处理中边缘提取的常用方法——Hough变换,提取双曲线参数,可以得到运动目标的航速、航深及距离的信息。     

Evolution equation for nonlinear Scholte waves

The evolution equations for nonlinear Scholte waves (finite amplitude elastic waves propagating along liquid/solid interface), which account for the second order nonlinearity of a liquid, are derived for the first time. For mathematical simplicity the nonlinearity of the solid, which influence is expected to be weak in the case of weak localization of the Scholte wave, is not taken into consideration. The analysis of these equations demonstrates that the nonlinear processes contributing to the evolution of the Scholte wave can be divided into two groups. The first group includes nonlinear processes leading to wave spectrum broadening which are common to bulk pressure waves in liquids and gases. The second group includes the nonlinear processes which are active only in the frequency down-conversion (leading to wave spectrum conservation or narrowing), which are specific to the confined nature of the interface wave. It is demonstrated that the nonlinear parameters, which characterize the efficiency of various nonlinear processes in the interface wave, strongly depend on the relative properties of the contacting liquid and solid (or, in other words, on the deviation of the Scholte wave velocity from the velocities of sound in liquid and in solid). In particular, the sign of the nonlinear parameter responsible for the second harmonic generation can differ from the sign of the nonlinear acoustic parameter of the liquid. It is also verified that there are particular liquid/solid combinations where the nonlinear processes, which are inactive in the frequency up-conversion, dominate in the evolution of the Scholte wave. In this case distortionless propagation of the finite amplitude harmonic interface wave is possible. The proposed theory should find applications in nonlinear acoustics, geophysics, and nondestructive testing.     

支架结构建模中设计参数的修正与优化

为降低某支架有限元建模的参数设置误差。根据有限元模态和实验模态结果,建立模态频率残差向量。应用灵敏度分析法,从结构12个设计参数中选取了3个弹性模量和3个密度参数作为修正量。以模态频率残差向量和参数修正量构建目标函数,并采用优化算法行求解。修正后的有限元模态与实验模态具有高度的一致性,表明修正后的支架有限元模型能够准确地反映结构特性,同时也验证设计参数修正方法的有效性和可行性。     

A comparison of methods for the statistics of slow-drift oscillations

A probabilistic model for the slowly varying horizontal motion of a moored floating structure, excited by nonlinear, second order wave forces is derived. The model consists of a coupled system of three white-noise excited stochastic differential equations that govern a continuous vector Markov process. Different methods are applied for the investigation of the first passage time probabilities of the displacement of the marine structure. The methods include time history simulation estimation of the first four moments, time history simulation of the first passage problem, and finite element solution of the backward Kolmogorov equation governing the first passage time distribution. The impact of non-Gaussian aspects of the response on extreme value statistics is demonstrated.