Elastic Energy and Elastic Interaction Ordering of Binary Solid Solutions

A theory in the framework of continuum elasticity has been developed to calculate the totalcontribution of "atomic size effect" or "strain energy effect" to free energy of binary solidsolutions. It is found that elastic free energy consists of two parts f elastic self energy (ESE),and elastic interaction energy(EIE). The former is a function of composition alone, the latter isalso a function of atomic configuration. Minimization of total elastic free energy with respect toatomic arrangement resuIts in an ordered arrangement of atoms, which is caIIed elastic interactionordering (EIO), as it originates from elastic interaction among atoms. EIO is a kind of localordering within a "characteristic range", and it is found to be important in determining the Stateof solid solutions and structures of superlattices. The present theory also gives good explanationto the coexistence of ordering and decomposition which can not be understood in conventionaltheories.     

Attenuation of coupled waves in antiferromagnetic elastic conductors in weak magnetic fields

Following along the same line of approach as in a previous paper in which dissipative mechanisms were ignored, the present paper discusses the attenuation of coupled magnetoelastic oscillations in a simple deformable antiferromagnet of which the material symmetry has been broken by a relatively weak bias magnetic field. The linearized equations needed in the analysis are deduced from a fully dynamical nonlinear, rotationally invariant and thermodynamically admissible theory of deformable antiferromagnets. Three types of dissipative mechanisms are taken into account: viscosity, Spin-lattice relaxation and electrical conduction. While all these mechanisms affect to a greater or lesser degree the propagation of essentially transverse elastic modes outside resonance regions, electrical conduction modifies the absorption of spin waves due to spin-lattice relaxation and both viscosity and spin-lattice relaxation are shown to contribute, collaboratively and equally, to the damping of mixed elastic-spin modes in the two magnetoacoustic resonance regions which correspond to the interaction of left-circularly polarized transverse elastic waves and an upper spin-wave branch and right-circularly polarized transverse elastic waves and a lower spin-wave branch, respectively. The analytical discussion of the resulting dispersive and attenuated coupled modes is achieved in terms of characteristically small parameters in a quasi-magnetostatic approximation. The phenomenon of heat conduction, important as it may be, is left out of the analysis.     

Controlled chaotic microwave generation under conditions of four-wave parametric interaction of surface spin waves

Controlled chaotic microwave generation under the conditions of four-wave parametric interaction of the surface spin waves has been experimentally studied in active resonance rings based on tangentially magnetized ferromagnetic films. It is shown that the chaotic microwave signal parameters can be effectively controlled.     

Direct observation and mapping of spin waves emitted by spin-torque nano-oscillators

Dynamics induced by spin-transfer torque is a quickly developing topic in modern magnetism, which has initiated several new approaches to magnetic nanodevices. It is now well established that a spin-polarized electric current injected into a ferromagnetic layer through a nanocontact exerts a torque on the magnetization, leading to microwave-frequency precession detectable through the magnetoresistance effect. This phenomenon provides a way for the realization of tunable nanometre-size microwave oscillators, the so-called spin-torque nano-oscillators (STNOs). Present theories of STNOs are mainly based on pioneering works predicting emission of spin waves due to the spin torque. Despite intense experimental studies, until now this spin-wave emission has not been observed. Here, we report the first experimental observation and two-dimensional mapping of spin waves emitted by STNOs. We demonstrate that the emission is strongly directional, and the direction of the spin-wave propagation is steerable by the magnetic field. The information about the emitted spin waves obtained in our measurements is of key importance for the understanding of the physics of STNOs, and for the implementation of coupling between individual oscillators mediated by spin waves. Analysis shows that the observed directional emission is a general property inherent to any dynamical system with strongly anisotropic dispersion.     

Generation of dissipative structures in self-oscillating ring systems upon parametric interaction of spin waves

A quasi-periodic sequence of pulses in a self-oscillating ring system with a resonant amplifier and a ferromagnetic film has been generated upon three-wave parametric interaction of spin waves. It is established that the generated pulses are analogs of dissipative bright solitons, which are formed as a result of competition between amplification and loss, as well as between time dispersion and nonlinearity. To describe the mechanism of formation of these structures, we have proposed a model in the form of three parametrically coupled differential equations with amplification and a differential equation of linear oscillator. Under certain assumptions, this model has analytical solutions in time in the form of structures with a profile similar to that of bright solitons.     

Wave propagation in micropolar mixture of porous media

This paper is concerned with the possible propagation of waves in an infinite porous continuum consisting of a micropolar elastic solid and a micropolar viscous fluid. Micropolar mixture theory of porous media developed by Eringen [A.C. Eringen, Micropolar mixture theory of porous media, J. Appl. Phys. 94 (2003) 4184–4190] is employed. It is found that there exist four coupled longitudinal waves (two coupled longitudinal displacement waves and two coupled longitudinal microrotational waves) and six coupled transverse waves in a continuum of this micropolar mixture. All the waves are found to attenuate and dispersive in nature. A problem of reflection of coupled longitudinal waves from a free boundary surface of a half-space consisting the mixture of a micropolar elastic solid and Newtonian liquid, is investigated. The expressions of various amplitude ratios and surface responses are derived. Numerical computations are performed to find out the phase velocity and attenuation of the waves. The variation of amplitude ratios, energy ratios and surface responses are also computed for a specific model. All the numerical results are depicted graphically. Some limiting cases have also been discussed.     

铁磁超细颗粒的低温磁化及磁振子的微波吸收理论

根据铁磁自旋波理论及自旋波与微波辐射的相互作用量子理论，得到计入量子尺寸效应时铁磁超细颗粒的低温磁化强度及磁振子的微波吸收函数。     

The propagation of plane waves in bilevel anisotropic elastic solids with nonlocal polar constitution

In analyzing problems involving material behavior from the standpoint of generalized continuum mechanics, one is often faced with different forms of anisotropy at different levels of microscopic and macroscopic aggregates within the same material. In this article, a continuum theory incorporating nonlocal effects within the microstructure of anisotropic solids is developed. In order to illustrate the mathematical development of the theory in practical applications, the theory is applied to the case of materials possessing orthotropy on the nonlocal micropolar level and transverse isotropy on the local micropolar level. This case may apply to materials such as wood and wood composites. The resulting field equations are solved for the propagation of plane waves in a bilevel, anisotropic, nonlocal, micropolar elastic solid.     

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.     

On the nonlocal aspects of the propagation of Love waves

Propagation of Love waves in an isotropic homogeneous elastic medium is analyzed in the context of the linear theory of nonlocal continuum mechanics. The dispersion equation, obtained for the plane transverse horizontally polarized waves in an infinite space, is compared with the corresponding equation given by the atomic lattice dynamics in order to determine a nonlocal modulus. It is found that the lower bound for the speed of Love waves predicted by the nonlocal theory agrees better with the seismological observations of such waves than its counterpart furnished by the conventional theory.     

Dispersion relations and normal modes for magnetoelastic waves in ferromagnetic insulators

The dispersion relation and the normal modes for magnetoelastic waves in ferromagnetic insulator crystals are calculated when the interaction between magnetization and strains is approximated to a bilinear form of creation and annihilation boson operators. Numerical results are obtained for YIG.     

Interaction of shear waves with a griffith crack situated in an infinitely long elastic strip

This paper deals with the propagation of shear waves in a wave guide which is in the form of an infinite elastic strip with free lateral surfaces. This strip contains a Griffith crack. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic elastic material. This method reduces the problem into an integral equation. It has been observed that only shear waves with frequencies less than a parameter-value, depending on the width of the wave guide, can propagate. The integral equation is solved numerically for a range of values of wave frequency and the width of the strip. These solutions are used to calculate the dynamic stress intensity factor, displacement on the surface of the crack and crack energy. The results are shown graphically.     

Investigation on the Nonlinear Excitation in an Array of Spin Valve Pillars During the propagation of Electromagnetic Wave

We have investigated the nonlinear excitations in an array of spin valve pillars during the propagation of an electromagnetic wave. The flowing electrons exhibit spins transportation effect due to the torque experienced by the spin magnetization. From the Hamiltonian which models the spin interaction in a spin valve array, we have studied the effect of perturbation using multiple scale expansion and Reduction Perturbation method. The Landau–Lifshitz–Gilbert equation of magnetization, which models the evolution of magnetization of the ferromagnetic layer, is studied along with Maxwell’s equation for the electromagnetic waves. It is found that the system of equations reduce to the celebrated modified KdV equation. The solution of the spin excitations are localized solitons. The physically interesting solitons can be harnessed to the increase in density of memory devices.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

Elastodynamic analysis of nonplanar cracks in a half-space

Summary The interaction of time harmonic antiplane shear waves with nonplanar cracks embedded in an elastic half-space is studied. Based on the qualitatively similar features of crack and dislocation, with the aid of image method, the problem can be formulated in terms of a system of singular integral equations for the density functions and phase lags of vibrating screw dislocations. The integral equations, with the dominant singular part of Hadamard's type, can be solved by Galerkin's numerical scheme. Resonance vibrations of the layer between the cracks and the free surface are observed, which substantially give rise to high elevation of local stresses. The calculations show that near-field stresses due to scattering by a single crack and two cracks are quite different. The interaction between two cracks is discussed in detail. Furthermore, by assuming one of the crack tips to be nearly in contact with the free surface, the problem can be regarded as the diffraction of elastic waves by edge cracks. Numerical results are presented for the elastodynamic stress intensity factors as a function of the wave number, the incident angle, and the relative position of the cracks and the free surface.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

A note on energy flux in micropolar elastic waves

The expressions for the time average power per unit area, the kinetic energy per unit volume, strain energy per unit volume and velocity of energy flux are derived for the case of a plane time harmonic micropolar elastic waves and it has been shown that the time-average energy density is equally divided between the time-averages of the kinetic and strain energy densities. The energy ratios of reflected micropolar elastic waves with the angle of emergence of incident longitudinal displacement wave have been shown graphically.     

Influence of dislocations on magnon-phonon couplings: A phenomenological approach

On the basis of a nonlinear theory of finitely deformable elastoviscoplastic ferromagnetic crystals developed in a companion paper, the present work presents an attempt at a phenomenological study of the influence of dislocations and viscoplastic flow on the behavior of spin waves (the collective modes of oscillations typical of ferromagnetism). This is achieved by linearizing the above mentioned nonlinear theory about a fundamental ferromagnetic phase with a practically vanishing viscoplastic threshold. The main results obtained after a study of wave modes and asymptotic evaluations in terms of a piezomagnetic coupling parameter are the evidence of a magnetoacoustic resonance between spin waves and left circularly polarized transverse elastoviscoplastic disturbances, a slight shift towards higher wave numbers of the corresponding critical wave number as compared to the perfectly elastic-crystal case and the fact that spin waves suffer a damping which is directly proportional to the piezomagnetic coupling parameter and to the reciprocal primary relaxation time (the relaxation time associated with the viscosity processes inherent in viscoplasticity, in the absence of restoring effects.     

Kinematics of failure waves in glasses

A new method for observation of the failure waves in glasses is proposed which allows this phenomenon to be reliably and reproducibly monitored, the failure wave propagation velocity to be measured, and an increase in the longitudinal stress to be determined. Using this method, the stresses produced by an elastic shock compression pulse propagating from the entrance of a stack of glass plates to the exit from this stack were experimentally measured. The compression wave exhibits splitting at each interface between adjacent glass plates in the stack, which leads to the formation of transmitted and reflected failure waves and is accompanied by decreasing stress in the leading elastic wave.     

The effect of viscosity on the transient free-surface waves in a two-dimensional tank

The paper attempts to develop some understanding of the interaction between viscous flow and a free surface by analysing the unsteady flow in an idealised two-dimensional rectangular tank. The mathematical model used is based on the linearized Navier-Stokes equations which are solved by use of the Laplace transform. Various results are provided to show the effect of viscosity on the free surface waves.