Nonstationary doppler effect and frequency-phase methods of investigation and control

A general theory of the nonstationary Doppler effect, which originates during wave passage through a medium whose properties vary in time, is elucidated. Relations are obtained for the frequency shift and phase difference, and numerical estimates are made in an example of ultrasonic oscillations. The advantages of methods of investigation and control based on the effect under consideration are shown.     

Some results on finite amplitude elastic waves propagating in rotating media

Summary. Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity provides such a framework for incompressible solids. Second: how can finite amplitude exact solutions be generated? It is seen that for some finite amplitude transverse waves in rotating incompressible elastic solids with general shear response the solutions are obtained by reduction of the equations of motion to a system of ordinary differential equations equivalent to the system governing the central motion problem of classical mechanics. In the special case of circularly-polarized harmonic progressive waves, the dispersion equation is solved in closed form for a variety of shear responses, including nonlinear models for rubberlike and soft biological tissues. A fruitful analogy with the motion of a nonlinear string is pointed out.     

Thermoelasticity of nonhomogeneous media

A system of equations is derived for the coupled thermoelasticity of an anisotropic nonhomogeneous body, taking into account the generalized law of heat conduction, by the method of systems identification and with the aid of the Clausius-Duhem inequality.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 6, pp. 1111–1114, June, 1980.     

Wave fronts in nonhomogeneous elastic media

This paper deals with the propagation of acceleration wave fronts in nonhomogeneous isotropic media undergoing plane elastodynamic motions. The partial differential equations governing the evolution of such waves are solved using the method of Charpit. A number of examples based on special choices of the nonhomogeneity and the initial data are treated. In particular, interesting examples arise in connection with (i) a radially symmetric nonhomogeneity, and (ii) a problem corresponding to a time dependent disturbance of a given region.     

A method for predicting crack growth in nonhomogeneous viscoelastic media

Equations are developed for predicting crack growth in the opening mode for quite general situations, including many quasi-static and dynamic problems involving moisture and temperature gradients in monolithic and composite materials. Except for the small zone of failing material at the crack tip, the body is assumed to be linearly viscoelastic. A method for obtaining viscoelastic stresses and displacements from elastic solutions is first described. The traction boundary condition for the crack faces is not in general satisfied by these results. However, it is shown by modifying the failure zone in the elastic problem this condition can be met, and an integral equation for the stress in the modified failure zone is derived. Approximate analysis similar to that used previously by the author in stress analysis is then employed to solve the integral equation and develop relatively simple equations for predicting crack speed; these equations relate crack speed in the viscoelastic material to stress intensity factors in a suitably defined elastic body.

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Résumé Des équations ont été développées pour prédire la croissance de la fissure suivant un mode d'ouverture pour des situations tout à fait générales incluant plusieurs problèmes quasi-statiques et dynamiques comportant de l'humidité et des gradients de tempèrature dans des matériaux monolitiques et dans des matériaux composites. A l'exception de la petite zône de matière située à la pointe de la fissure, le corps est supposé être linéairement visco-élastique. Une méthode pour obtenir les contraintes et les déplacements visco-élastiques à partir des équations élastiques est en premier lieu décrite. La condition de frontière à la traction pour les faces de la fissure n'est en général pas satisfaite par ces résultats. Toutefois, on montre qu'en modifiant la zône de rupture dans le problème élastique, cette condition peut être atteinte et une équation intégrale pour la contrainte dans la zône de rupture modifiée est dérivée. Une analyse approximative similaire à celle utilisée précédemment par l'auteur dans l'analyse des tensions est ensuite utilisée pour résoudre l'équation intégrale et développer des équations relativement simples pour prédire la vitesse de fissuration. Ces équations mettent en relation la vitesse de fissuration dans le matériau visco-élastique aux facteurs d'intensité des contraintes dans uns corps élastique défini de manière appropriée.

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Sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, grant No. 74-2697. Presented at the Environmental Degradation of Engineering Materials conference, October 10–12, 1977. Virginia Polytechnic Institute, Blacksburg, Va.     

A fundamental solution for transversely isotropic and nonhomogeneous media

The purpose of this paper is to consider the concept of a ring of sources or forces using the integral transform techniques to derive the axisymmetric fundamental solution for nonhomogeneous transversely isotropic elastic media. Firstly, the formulation of the problem in homogeneous media to derive the fundamental solutions is shown. In the case of a nonhomogeneous medium, the shear modulus of the material varies with the z-coordinate exponentially.     

An advanced boundary element method for elasticity problems in nonhomogeneous media

Summary This paper presents a new boundary element method formulation and numerical implementation of elasticity problems in nonhomogeneous media. The fundamental solutions for elasticity in homogeneous media are employed and the nonsingular formulation is derived. A physically and mathematically meaningful elimination of internal degrees of freedom is proposed. The solution at an arbitrary point is expressed in terms of boundary displacements and tractions. The rank of the system matrix (for computation of relevant unknowns) is dependent only on the discretization of the boundary.     

Hamiltonian formulation for solitary waves propagating on a variable background

Solitary waves propagating on a variable background are conventionally described by the variable-coefficient Korteweg-de Vries equation. However, the underlying physical system is often Hamiltonian, with a conserved energy functional. Recent studies for water waves and interfacial waves have shown that an alternative approach to deriving an appropriate evolution equation, which asymptotically approximates the Hamiltonian, leads to an alternative variable-coefficient Korteweg-de Vries equation, which conserves the underlying Hamiltonian structure more explicitly. This paper examines the relationship between these two evolution equations, which are asymptotically equivalent, by first discussing the conservation laws for each equation, and then constructing asymptotically a slowly-varying solitary wave.     

Plane-disturbance propagation in elastic nonhomogeneous media. General solution

This paper deals with the problem of uniaxial propagation of disturbances in continuous axiallynonhomogeneous media. The general mathematical solution obtained is applicable to physical problems dealing with media with longitudinally-variable parameters.Solution of the resulting differential equations is based on symmetry of their space and time variables. This symmetry leads to transformation of boundary problems into their initial and terminal counterparts. By working out a special version of Fourier's transform, a law for uniaxial propagation in nonhomogeneous media is derived. It is shown that D'Alembert's well-known solution for propagation in a homogeneous thin bar or string is a particular case of this law.The significance of such a general theory lies in the fact that most dynamic phenomena in nature occur in nonhomogeneous media, and the solution presented here may contribute to their physical evaluation. As an example, we solve the propagation of a pulse in a heated thin bar.     

Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves

The arbitrary control of electromagnetic waves is a key aim of photonic research. Although, for example, the control of freely propagating waves (PWs) and surface waves (SWs) has separately become possible using transformation optics and metamaterials, a bridge linking both propagation types has not yet been found. Such a device has particular relevance given the many schemes of controlling electromagnetic waves at surfaces and interfaces, leading to trapped rainbows, lensing, beam bending, deflection, and even anomalous reflection/refraction. Here, we demonstrate theoretically and experimentally that a specific gradient-index meta-surface can convert a PW to a SW with nearly 100% efficiency. Distinct from conventional devices such as prism or grating couplers, the momentum mismatch between PW and SW is compensated by the reflection-phase gradient of the meta-surface, and a nearly perfect PW-SW conversion can happen for any incidence angle larger than a critical value. Experiments in the microwave region, including both far-field and near-field characterizations, are in excellent agreement with full-wave simulations. Our findings may pave the way for many applications, including high-efficiency surface plasmon couplers, anti-reflection surfaces, light absorbers, and so on.     

Conversion of evanescent waves into propagating waves by vibrating knife edge

Using plane wave spectrum methods, we analyze the propagation and mutual conversion of plane and evanescent waves generated by a one-dimensional object partially obscured by a vibrating knife edge. We show that subwavelength details of the object may be detected in each part of the transmitted plane wave spectrum, upon scanning the knife edge across the object. We discuss the implications for near-field scanning optical microscopy (NSOM) and compare some aspects of conventional NSOM (physical aperture), and vibrating knife edge (electronic aperture) approaches to the sampling of optical fields. © 1996 John Wiley & Sons, Inc.     

The apparent additional mass effect and waves in poroelastic layered media

The effect of the apparent additional mass of fluid in case of propagation of elastic waves in porous saturated media is considered. There are various points of view about this term. Some authors suggest to consider this term equal to zero, and the others nonzero. Here, the type of wave motion is established in which nonzero apparent additional masses lead to essential effect on some frequences.     

Semi-analytical Monte Carlo simulation for time-resolved light propagating in multilayered turbid media

In this study, a Monte Carlo (MC) method for time-resolved light scattering from multilayered turbid media (SMCML) has been developed. This method is particularly suitable for simulating light backscattering from layered media and receiving the time-resolved signal in a finite sensor area, such as ocean detection, photomedicine and photobiology. The classical semi-analytical MC method requires the scattering events to be located in a single-layer medium. To address the multilayer problem, the energy loss mechanism of photons propagating in tissue was analyzed in this study. According to the energy contribution to the detector, only photons that contribute significantly were considered. Simulations were conducted for stochastic turbid media with different optical parameters. Temporal profiles of the echo signal were obtained with a satisfactory convergence. Compared to the classical MC method, the SMCML method can dramatically reduce the computation time by more than two orders of magnitude.     

Polarization discrimination of coherently propagating light in turbid media

We describe the use of degree of polarization to discriminate unscattered and weakly scattered light from multiply scattered light in an optically turbid material. We use spatially resolved measurements of the degree of polarization to compare how well linearly and circularly polarized light survives in a sample. Experiments were performed on common tissue phantoms consisting of polystyrene and Intralipid microsphere suspensions and on adipose and arterial tissue. The results indicate that polarization is maintained even after unpolarized irradiance through each sample has been extinguished by several orders of magnitude. The results also show that polarized light propagation in common tissue phantoms is distinctly different from polarized light propagation in the two tissues investigated. Further, these experiments illustrate when polarization is an effective discrimination criterion and when it is not. The potential of a polarization-based discrimination scheme to image through the biological and nonbiological samples investigated here is also discussed.     

Seismic waves in random media

Earthquake waves travel in a medium that is naturally stochastic. Stochasticity is manifested by introducing uncertainties into the model as well as reductions in the mean field and mean amplitudes through random mode coupling and physical scattering from the random irregularities. This survey shows the effect of the stochasticity in wave amplitudes, in standard deviations for defining reliability limits, summarizes various perturbation schemes, and draws attention to the differences between media with random values and stochastic media.     

The effect of solid conversion on travelling combustion waves in porous media

A system of nonlinear partial differential equations, which describe the combustion of a gas passing through a porous medium, is examined. This model provides a bridge between recent porous-medium combustion studies and more classical combustion models. In particular, the effect of solid conversion on the downstream temperature is determined for travelling-wave solutions to the system. In cases for which the solid matrix is a perfect catalyst, solely enhancing the exothermic chemical reaction, with zero mass exchange, it is proved that the downstream temperature must always exceed the upstream temperature. However, when the solid is allowed to react with the gas, travelling-wave solutions for which the up- and down-stream temperatures are equal may be realised. A key result of this work is then the investigation of physical processes and related parameter ranges that give rise to travelling wave solutions with equal up- and down-stream temperatures. Specifically, two critical wavespeeds c_i with 0 < c₁ < c₂ are identified. For c < c₁ the downstream temperature always exceeds that upstream, whilst for c > c₂ no bounded travelling-wave solutions exist. Behaviour in the region c₁ < c < c₂ is new: here solutions having equal up- and down-stream temperatures are realised. The two factors upon which this result depends are the inclusion into the model of solid conversion effects and the distinction between solid and gas temperatures. Thus the inclusion of a new physical process, that of heat storage in the solid varying as the reaction proceeds, allows the existence of a new type of travelling-wave solution. Further phenomena studied include the appearance of nonunique solutions (which are of a type that may be related to ignition processes) and degenerate solutions which terminate precisely when all the solid and gaseous fuel is used up. Parameter regimes for the existence of these various types of solutions are found and the stability of such solutions discussed.     

Surface acoustic waves propagating over a rotating piezoelectric half-space

Surface acoustic waves (SAW) propagating over a piezoelectric half-space rotating at a constant angular rate about a fixed axis are analyzed using the linear theory of piezoelectricity, including Coriolis and centrifugal forces. Rotation sensitivity, the rotation induced change of wave speed, is studied. The dependence of the rotation sensitivity on the orientation of the rotation axis and the orientation of the material is examined. Numerical results for polarized ceramics PZT-5H are presented to show the detailed characteristics of the rotation sensitivity. The implications of the numerical results are discussed for different applications     

Relativistic doppler effect in quantum communication

Abstract

When an electromagnetic signal propagates in vacuo, a polarization detector cannot be rigorously perpendicular to the wave-vector because of diffraction effects. The vacuum behaves as a noisy channel, even if the detectors are perfect. The ‘noise’ can, however, be reduced and nearly cancelled by a relative motion of the observer towards the source. The standard definition of a reduced density matrix fails for photon polarization, because the transversality condition behaves like a superselection rule. We can, however, define an effective reduced density matrix which corresponds to a restricted class of positive operator-valued measures. There are no pure photon qubits and no exactly orthogonal qubit states.