Interaction of a shear wave with a moving domain wall in a ferromagnetic crystal with allowance for the external magnetic field

The boundary-value problem of the magnetoelastic wave interaction with a moving domain wall in a ferromagnetic crystal is solved in the nonexchange magnetostatic approximation with allowance for the external magnetic field. It is shown that the difference introduced by magnetic field between the ferromagnetic resonance frequencies of the domains does not cause any noticeably departure of the refraction characteristics of reflected and transmitted waves from those observed at zero frequency mismatch. By contrast, the magnitudes of the transmission and reflection coefficients strongly depend on the external magnetic field and on the mobility of the domain wall. The dependence of the magnitude of the reflection coefficient on the external magnetic field at a fixed angle of shear wave incidence is found to possess two ferromagnetic resonance peaks. The positions and heights of the peaks may vary depending on the mobility of the domain wall.     

Shear Surface Wave on a Moving Bloch Wall

Using Galileo's transformation for moving to the rest frame of the Bloch wall in the exchange-free magnetostatic approximation, we obtain the dispersion relation for a shear surface wave guided by a moving 180-degree domain boundary of a ferromagnetic crystal. It is found that the motion of the domain boundary has the orienting action on the wave normal of the shear surface wave and significantly changes the spectrum of forward-propagating waves in the frequency band below the scattered-field ferromagnetic resonance.     

On the interaction of a shear wave with a moving domain wall in a nonlinear response of the spin subsystem

A solution of the problem of parametric interaction between a plane monochromatic shear wave and a uniformly moving 180°-domain wall of a garnet-ferrite crystal is obtained in the exchangeless magnetostatic approximation by using the perturbation method under the conditions of a nonlinear response of the spin subsystem. It is shown that in a ferromagnetic resonance with magnetostatic oscillation of stray fields, the nonlinearity of the spin subsystem leads to the excitation of shear waves of triple frequency, which may have amplitudes comparable with that of the incident wave for oscillations doubly localized by a domain wall.     

A trapped wave in a ferroelectric with a moving strip domain

The existence of a shear homogeneous plane wave trapped by a strip domain moving uniformly in a tetragonal ferroelectric crystal is demonstrated. Using the nonrelativistic quasistatic approximation and a change to the moving frame of reference, the solution is obtained and the dispersion relation is derived for the spatial spectrum of the trapped wave. The uniqueness of the solution is established in the case of the multiple degeneracy of the roots of the characteristic equation when the trapped wave contains an attached wave in the strip domain. The trapped wave is shown to correspond to the antisymmetric mode of the electroacoustic wave of the strip domain at the initial point of the spectrum branch. The specific features of the spatial resonance of the trapped wave with a shear wave obliquely incident on the strip domain are considered.     

Nonlinear magnetoacoustic interactions in weak ferromagnets

The pinning and interaction of a single domain wall with normal magnetoelastic waves excited during its motion in a single-crystal yttrium orthoferrite plate, were discovered and investigated by a method based on the magneto-optical Faraday effect. The dependences of the bending wave amplitude and the spectra of shear waves, which can be excited by a moving domain wall, were calculated. The results obtained are interpreted with allowance for the interactions of excited oscillations in both the magnetic and elastic subsystems of the orthoferrite.     

Excitation spectrum and thermodynamics of domain walls in the biaxial ferromagnet

The problem on spectrum of linear excitations in the presence of a moving domain wall in 1D Heisenberg ferromagnet with orthorhombic anisotropy is exactly solved. The explicit expressions for spin waves scattering on the domain wall are obtained. The phase shift of a spin wave, as the result of collision of spin wave with a moving wall, is exactly determined. The change in magnon density of states is calculated from this scattering data, and the contribution of domain walls to the classical low-temperature thermodynamics is found.     

Mode spectrum of noncollinear electroacoustic boundary-guided waves in a ferroelectric with a moving strip domain

The mode spectrum of electroacoustic boundary waves guided by a strip domain uniformly moving in a 4-mm ferroelectric is considered in the quasi-static approximation. The motion of the strip domain is found to cause the wave vector of the electroacoustic wave to be noncollinear with the guiding boundaries. The frequency dependences of the phase velocity are presented for the symmetric and antisymmetric modes of the electroacoustic wave. These dependences are compared in the reference system fixed to the strip domain and in the laboratory reference system. It is shown that, at low and moderate frequencies, the symmetric mode of the electroacoustic wave is more efficiently localized by a moving strip domain than by a single domain wall.     

Reflection of antiferromagnetic vortices on a supersonic domain wall in yttrium orthoferrite

Reflection of solitary flexural waves propagating in a supersonic domain wall of yttrium orthoferrite from the domain wall part moving with the transverse-sound velocity is observed experimentally. This observation confirms that such a reflection of a solitary flexural wave leads to a change in the sign of the topological charge of the antiferromagnetic vortex accompanied by this wave, which proves a direct relationship between these two objects.     

Spectral properties of electroacoustic waves in a ferroelectric with a moving periodic domain structure

The propagation of shear waves in a tetragonal ferroelectric with a moving superlattice of 180° domain walls (DW) is considered in a quasistatic approximation. It is found that the spectrum of shear waves consists of alternating allowed and forbidden bands in both cases of static and moving superlattices. It is shown that, due to the Doppler shift in the wave eigenfrequencies, the motion of the DW superlattice causes the degenerate roots of the dispersion equation to split and the splitting increases with the vibration mode number. The acoustic nonreciprocity induced by the moving DW superlattice in the ferroelectric is discussed.     

Suboptimal control of wall turbulence with arrayed dimple actuators for drag reduction

Direct numerical simulation of a turbulent channel flow with moving dimples at the bottom wall is carried out using the pseudo-spectral method and the curvilinear coordinate system. Suboptimal control based on the spanwise wall shear stress is applied for skin-friction drag reduction, and is implemented by the finite-size sensor-actuator system. The control law is realised in physical space by using a cross-shaped truncation of the wall shear stress information, which can be measured by the sensor. Only the information of wall shear stress inside the sensor area is utilised and that outside the sensor area is obtained by a linear reconstruction from the averaged value over the sensor. To effectively intervene the near-wall coherent structures, low-pass filtering of the spanwise wall shear stress is additionally implemented to eliminate the extra disturbances induced by the presence of dimple actuators, and the filtered stress is used as the control input. Numerical tests on the present control strategy show that the pressure form drag caused by the presence of dimples is reduced significantly as compared with the original suboptimal control, and the reduction of total drag is comparable with that of the opposition control. The underlying mechanism is further analysed by looking into the interaction between the moving dimples and the near-wall coherent structures.     

Interaction of a moving domain wall with surface magnetoelastic waves in yttrium orthoferrite

The amplitude-frequency characteristics of magnetoelastic surface waves excited by moving domain walls in a lamellar yttrium orthoferrite samples are discovered and measured. The results of analysis of the effect of magnetoelastic surface waves on the dynamics of domain walls in this orthoferrite are considered. The nonlinear interaction between magnetoelastic surface waves accompanying a moving domain wall is analyzed.     

Zakharov-Benney resonance as a mechanism for generating extremely short pulses in uniaxial crystals

The possibility of generating an extremely short (without high-frequency filling) pulse of an extraordinary wave in a uniaxial crystal by means of nonlinear interaction with a quasi-monochromatic ordinary wave in the regime of Zakharov-Benney resonance is discussed. It is shown that the appropriate conditions can be created in crystals with positive birefringence, and stable extremely short extraordinary solitons can be created in the spectral range of normal dispersion at the threshold intensity of input pulse on the order of 10¹³–10¹⁴ W/cm².     

Efficiency of shear surface wave transformation by the motion of the confining domain wall

The transformation of a shear surface magnetoelastic wave by the motion of the 180° confining domain wall in a ferromagnet is considered. Changes in the wave spectrum due to the motion of the wall are correlated with the variations of the energies of the elastic and magnetic subsystems. The efficiency of surface wave transformation by the domain wall motion is estimated in terms of energy. The frequency dependences of the mean energy density of the wave are found. It is shown that the energy density grows with wall velocity.     

Localization of a transverse elastic wave in a semibounded acoustic superlattice of ferrimagnetic and superconducting layers: 3. Leaky surface modes and associated resonances

In terms of the effective medium method, conditions for the existence of leaky shear surface acoustic waves in a semibounded fine-layered magnetic superlattice consisting of ferrimagnetic and superconducting layers are determined. On this basis, the possibility of a resonance interaction between a surface elastic SH wave propagating in the magnetic superlattice and a shear bulk wave propagating in the adjacent nonmagnetic medium is investigated.     

Phase velocities and attenuations of shear, Lamb, and Rayleigh waves in plate-like tissues submerged in a fluid (L)

In the past several decades, the fields of ultrasound and magnetic resonance elastography have shown promising results in noninvasive estimates of mechanical properties of soft tissues. These techniques often rely on measuring shear wave velocity due to an external or internal source of force and relating the velocity to viscoelasticity of the tissue. The mathematical relationship between the measured velocity and material properties of the myocardial wall, arteries, and other organs with non-negligible boundary conditions is often complicated and computationally expensive. A simple relationship between the Lamb-Rayleigh dispersion and the shear wave dispersion is derived for both the velocity and attenuation. The relationship shows that the shear wave velocity is around 20% higher than the Lamb-Rayleigh velocity and that the shear wave attenuation is about 20% lower than the Lamb-Rayleigh attenuation. Results of numerical simulations in the frequency range 0-500 Hz are presented.     

Resonance interaction of an edge-dislocation wall with a traveling sound wave

The dynamics of an infinite edge-dislocation wall and fragments of this wall in their interaction with a monochromatic sound wave with a nonzero wave vector has been investigated taking into account the mass of dislocations. It has been shown that the drift velocities of the wall fragments significantly increase when the sound wave frequency approaches the natural frequencies of small-amplitude vibrations, including zero frequency. For the infinite wall, a similar increase in the drift velocity is observed for low frequencies and for frequencies close to half the maximum frequency of small-amplitude vibrations of the edge-dislocation wall. The resonance increase in the drift velocity at low frequencies of the sound wave can be important for practical applications.     

Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium

Peristaltic transport of an incompressible viscous fluid in an inclined asymmetric channel through a porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The analytical solution has been obtained in the form of a stream function from which the axial velocity and pressure gradient have been derived. The results for the pressure drop and shear stress have also been computed numerically. The effects of various physical parameters are discussed through graphs and the phenomenon of trapping is also discussed. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Shear elasticity of fluids at low-frequent shear influence

The visco-elastic properties of liquids have been investigated using acoustical resonance method. Piezoquatrz performed tangential oscillations on the main resonance frequency of 74 kHz contacts by the one end of horizontal surface with the studied liquid layer covered by quartz cover-plate. So the stagnant shear waves are installed in layer. The solution of interaction of piezoquartz-liquid layer-cover-plate gives three methods of determination of the real shear modulus (G) and the tangent of mechanical loss angle (tan theta) of liquid. The first method is realized at smaller thickness of liquid layer then the length of shear wave. Liquids of different classes have been studied using this method: polymer liquids, oils, glycols and alcohols. The second method is connected with the propagation of shear wave in liquid layer, parameters of which are determined the G and tan theta. And the third method is based on the determination of limit shift of resonance frequencies at completes damping of shear wave in thick layer of liquid. All these three methods give satisfactory agreement of results.     

Two-dimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data

The crawling wave experiment was developed to capture a shear wave induced moving interference pattern that is created by two harmonic vibration sources oscillating at different but almost the same frequencies. Using the vibration sonoelastography technique, the spectral variance image reveals a moving interference pattern. It has been shown that the speed of the moving interference pattern, i.e., the crawling wave speed, is proportional to the shear wave speed with a nonlinear factor. This factor can generate high-speed artifacts in the crawling wave speed images that do not actually correspond to increased stiffness. In this paper, an inverse algorithm is developed to reconstruct both the crawling wave speed and the shear wave speed using the phases of the crawling wave and the shear wave. The feature for the data is the application to in vitro prostate data, while the features for the algorithm include the following: (1) A directional filter is implemented to obtain a wave moving in only one direction; and (2) an L(1) minimization technique with physics inspired constraints is employed to calculate the phase of the crawling wave and to eliminate jump discontinuities from the phase of the shear wave. The algorithm is tested on in vitro prostate data measured at the Rochester Center for Biomedical Ultrasound and University of Rochester. Each aspect of the algorithm is shown to yield image improvement. The results demonstrate that the shear wave speed images can have less artifacts than the crawling wave images. Examples are presented where the shear wave speed recoveries have excellent agreement with histology results on the size, shape, and location of cancerous tissues in the glands.     

Nonlinear phenomena accompanying the development of oscillations excited in a layer of a linear dissipative medium by finite displacements of its boundary

A method of describing oscillations in resonators on the basis of evolution equations is proposed. The latter are obtained by simplifying the functional equations under the assumption that the distortions of travelling waves within the resonator length are small, that the Mach number for the moving boundary oscillations is small, and that the frequency is close to one of the natural frequencies of the resonator. The problems of nonstationary oscillations of a layer with a moving boundary are solved. The law that should govern the wall oscillations to provide the development of steady-state linear resonance oscillations is determined. The shape of the resonance curve formed in the presence of a boundary nonlinearity is calculated. The method of matching of asymptotics is applied to the singularly perturbed problem with small dissipation. It is shown that a boundary nonlinearity leads to a distortion of the temporal profile of the standing wave and to the generation of higher harmonics in the process of the development of steady-state oscillations. In contrast to the classical linear problems where the resonance occurs at the coincidence of the external force frequency with one of the natural frequencies, in the case under study the resonance behavior is observed in frequency bands, which are wider the higher the amplitude of the boundary oscillations is.