Quasi-transverse Research Articles

Reflection of plane waves in a functionally graded thermoelastic medium

In this paper, the reflection phenomenon of plane harmonic waves in a functionally graded thermoelastic medium is studied based on the generalized theory of thermoelasticity. The boundary is assumed to be stress free and thermally insulated. For the incidence of quasi-longitudinal (QL) wave or quasi-transverse (QT) type wave, there may exist three types of reflected waves. For each reflected wave, the corresponding slowness vector is resolved to define its phase speed and reflected angle. Further, the effect of the functionally graded factor on the phase speeds, reflected angles as well as the reflection coefficients for the incidence of QL or QT wave were investigated and shown graphically.

Effect of grain boundaries on elastic shock wave in graphene

Effect of grain boundaries (GBs) on elastic shock wave in graphene is investigated by molecular dynamics simulations. Bicrystal graphenes with symmetrical GB are shocked along directions perpendicular and parallel to GB. For perpendicular shock loadings, double elastic shock waves emerge in form of quasilongitudinal (QL) and quasitransverse (QT) waves, since the loading direction is neither zigzag nor armchair. GB attenuates the QL wave and gives rise to new QT waves propagating into grains. Transverse particle motion in the elastic shocks can induce small lattice rotations and different oriented regions, whose number increases upon the passage of waves through GB. Upon shock loadings along GB, transverse particle motions of opposite direction generate in the two grains, and change the pressure distribution right behind wavefront, and then result in deviation of shock wave from planar loading or “V” shaped wavefront turning at GB. The above phenomena are attributed to the turn of grain orientation at GB and transverse particle motions induced by lattice symmetry reduction upon shock compression.

Response of Two-Temperature on the Energy Ratios at Elastic-Piezothermoelastic Interface

In the present investigation the reflection and transmission phenomenon of plane waves between two half spaces elastic and orthotropic piezothermoelastic with two-temperature theory is discussed. A piezothermoelastic solid half space is assumed to be loaded with an elastic half space. Due to the phenomenon, four qausi waves are obtained; quasi longitudinal (qP) wave, quasi transverse (qS) wave, quasi thermal (qT) wave and electric potential wave (eP). It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the piezothermoelastic properties of media. The energy ratios are computed numerically using amplitude ratios for a particular model of graphite and cadmium selenide (CdSe). The variations of energy ratios with angle of incidence are shown graphically depicting the effect of two-temperature. The conservation of energy across the interface is justified. A particular case of interest is also deduced from the present investigation.

Reflection of plane waves on the stress-free and rigid boundary surfaces of pre-stressed piezoelectric-orthotropic substrate: A comparative approach

This study delves with the reflection phenomenon of plane-waves due to incidence of quasi-longitudinal (QL) wave at a semi-infinite structure comprising of pre-stressed piezoelectric-orthotropic substrate (POS) with stress-free (Case I) and rigid (Case II) bounding surfaces. The compact-form expressions of reflection-coefficients (RCs) of reflected QL wave, quasi-transverse (QT) wave and evanescent-electroacoustic (EA) wave for different cases of pre-stressed POS are deduced. To unravel effects of higher anisotropy in substrate, comparative analysis in pre-stressed transversely isotopic piezoelectric substrate (TIPS) medium with stress-free (Case III) and rigid (Case IV) boundaries is carried out. PVDF and ALN materials are considered for numerical computations. For validation, energy-partition and conditions of grazing incidence for all the undertaken cases are analyzed.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

Abstract The present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

Flare SOL2012-07-06: On the Origin of the Circular Polarization Reversal Between 17 GHz and 34 GHz

The new generations of multiwavelength radioheliographs with high spatial resolution will employ microwave imaging spectropolarimetry to recover flare topology and plasma parameters in the flare sources and along the wave propagation paths. The recorded polarization depends on the emission mechanism and emission regime (optically thick or thin), the emitting particle properties, and propagation effects. Here, we report an unusual flare, SOL2012-07-06T01:37, whose optically thin gyrosynchrotron emission of the main source displays an apparently ordinary mode sense of polarization in contrast to the classical theory that favors the extraordinary mode. This flare produced copious nonthermal emission in hard X-rays and in high-frequency microwaves up to 80 GHz. It is found that the main flare source corresponds to an interaction site of two loops with greatly different sizes. We have investigated the three possible known reasons of the circular polarization sense reversal - mode coupling, positron contribution, and the effect of beamed angular distribution. We excluded polarization reversal due to contribution of positrons because there was no relevant response in the X-ray emission. We find that a beam-like electron distribution can produce the observed polarization behavior, but the source thermal density must be much higher than the estimate from to the X-ray data. We conclude that the apparent ordinary wave emission in the optically thin mode is due to radio wave propagation across the quasi-transverse (QT) layer. The abnormally high transition frequency (above 35 GHz) can be achieved reasonably low in the corona where the magnetic field value is high and transverse to the line of sight. This places the microwave source below this QT layer, i.e. very low in the corona.

Plane wave propagation in transversely isotropic laser-excited solids

This paper concentrates on the study of body harmonic wave propagation in an anisotropic laser-excited solid in the context of the model based on coupled equations for the displacement and atomic defect concentration fields. The complex secular equations for transversely isotropic solids are derived and discussed. It is found, in general, four types of dispersive waves, namely a quasi-longitudinal (QL), two quasi-transverse (QT) and a quasi-defect wave (N-mode) can propagate in these types of crystals. The different characteristics of waves like phase velocity, attenuation coefficient are obtained and presented graphically. It is demonstrated that there is an appreciable variation in case of the QL mode as compared with QT and N-modes. Some particular cases have also been discussed.

Super-Gaussian conical refraction beam.

We demonstrate the transformation of Gaussian input beams into super-Gaussian beams with a quasi flat-top transverse profile by means of the conical refraction phenomenon by adjusting the ratio between the ring radius and the waist radius of the input beam to 0.445. We discuss the beam propagation of the super-Gaussian beam and show that it has a confocal parameter three times larger than the one that would be obtained from a Gaussian beam. The experiments performed with a KGd(WO4)2 biaxial crystal are in good agreement with the theoretical predictions.

Nonlinear elastic effects in graphite/epoxy: An analytical and numerical prediction of energy flux deviation

Manipulating acoustic wave propagation through a material have several interdisciplinary applications. Here we predict shift in energy flux deviation for acoustic waves propagating in unidirectional graphite/epoxy due to applied normal and shear stresses using both an analytical model, using acoustoelastic continuum theory, and a finite element discrete numerical model. The acoustoelastic theory predicts that the quasi-transverse (QT) wave exhibits larger shifts in energy flux deviation compared to quasi-longitudinal (QL) or the pure transverse (PT) due to an applied shear stress for fiber orientation angle ranging from 0° to 60°. Due to an applied shear stress the QT wave exhibits a shift in energy flux deviation at 0° fiber orientation angle as compared to normal stress case where the flux deviation and its load induced shift are both zero. A finite element model (FEM) is developed where equations of motion include the effect of nonlinear elastic coefficients. Element equations were integrated in time using Newmark’s method to determine the shift in energy flux deviations in graphite/epoxy for different loading cases. The energy flux shift of QT waves predicted by FEM for fiber orientation angles from 0° to 60° for applied shear stress case is in excellent agreement with acoustoelastic theory. Because energy shift magnitudes are not small, it is possible to experimentally measure these shifts and calibrate shifts with respect to load type (normal/shear) and magnitude.

Wave propagation in an initially stressed transversely isotropic thermoelastic solid half-space

The governing equations of thermoelasticity of transversely isotropic solid with initial stresses are formulated at uniform temperature. These equations are solved analytically in two-dimensions to show the existence of three plane quasi waves, namely, Quasi-Longitudinal (QL), Thermal (T-mode) and Quasi-Transverse (QT) waves. Reflection from a thermally insulated stress free surface of an initial stressed transversely isotropic thermoelastic solid half-space is studied. A particular model is chosen for the numerical computations of the propagation speeds, attenuation coefficients and reflection coefficients. Effects of initial stress parameter and thermal disturbances are observed on speeds of propagation, attenuation coefficients and reflection coefficients.

Plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic rotating half-spaces with two relaxation times

The present paper concentrates on the study of reflection and refraction characteristics of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic rotating half-spaces with different elastic and thermal properties. In this type of problem of orthotropic thermoelastic rotating medium, there are three types of plane waves quasi longitudinal (QL-) wave, quasi thermal (T-mode) wave and quasi transverse (QT-) wave, whose velocities depend on the angle of incidence, imperfection and rotation. The amplitude ratios of reflected waves to that of incident one in each case have been derived. Some special cases of boundaries, i.e. normal stiffness, transverse stiffness, thermal contact conductance, slip boundary and welded contact boundary have been deduced from an imperfect one. Effect of rotation on the amplitude ratios of different reflected and refracted waves with respect to incident QL-wave at different boundaries have been studied graphically. It is observed that thermal properties, imperfect boundary and rotation have significant effect on the propagation of waves.

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave ( T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave ( T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.

Reflection/transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half-spaces

The present study is concerned with the reflection and transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half-spaces with different elastic and thermal properties. The reflection and transmission coefficients of quasi longitudinal (QL-) wave, quasi thermal (T-mode) wave and quasi transverse (QT-) wave have been derived for different incident waves. The reflection and refraction coefficients of different reflected and transmitted waves have been compared for the two generalized theories, i.e. Lord–Shulman theory [H.W. Lord, Y. Shulman, J. Mech. Phys. Solids 15 (1967) 299–309] and Green–Lindsay theory [A.E. Green, K.A. Lindsay, J. Elasticity 2 (1) (1972) 1–7] with angle of incidence. Some special cases of boundaries, i.e. normal stiffness, transverse stiffness, thermal contact conductance, slip boundary and welded contact boundary have been deduced from an Imperfect one. It is observed that thermal properties and imperfect boundary have significant effect on the propagation of waves.

Coronal Magnetography of Solar Active Region 8365 with the SSRT and NoRH Radio Heliographs

Microwave maps of solar active region NOAA 8365 are used to derive the coronal magnetograms of this region. The technique is based on the fact that the circular polarization of a radio source is modified when microwaves pass through the coronal magnetic field transverse to the line of sight. The observations were taken with the Siberian Solar Radio Telescope (SSRT) on October 21 – 23 and with the Nobeyama Radio Heliograph (NoRH) on October 22 – 24, 1998. The known theory of wave mode coupling in quasi-transverse (QT) region is employed to evaluate the coronal magnetograms in the range of 10 – 30 G at the wavelength 5.2 cm and 50 – 110 G at 1.76 cm, taking the product of electron density and the scale of coronal field divergence to be constant of 1018 cm−2. The height of the QT-region is estimated from the force-free field extrapolations as 6.2 × 109 cm for the 20 G and 2.3 × 109 cm for 85 G levels. We find that on large spatial scale, the coronal magnetograms derived from the radio observations show similarity with the magnetic fields extrapolated from the photosphere.

Linearized approximations for phase velocities of elastic waves in weaklyanisotropic media

This paper focuses on the development of linearized formulae for the phasevelocities of quasi-longitudinal (QL) and quasi-transverse (QT) waves in weaklyanisotropic media. The formulae for quasi-transverse waves derived fromfirst-order perturbation theory possess the property of rotational invariance in aplane perpendicular to the wave normal. Based on this property, a planarcoordinate system, describing the possible polarization of the two degeneratetransverse waves, can be conveniently selected. The relationships between thefirst-order formulae and other related existing approximate expressions areclarified. For a symmetry plane of orthorhombic media, we extended Gassmann'sformula for the QL-wave phase velocity in transversely isotropic media to QLand QT waves. Three forms of phase velocity expressions are discussed. Fornon-symmetry planes of weakly orthorhombic media, we propose a unified formfor the QL-wave phase velocity and in a very simple way derive the linearizedThomsen- and Gassmannn-like formulae. Furthermore we suggest QT-wave phasevelocity expressions which are linear functions of the elastic constantsassuming that wave propagation has a slight deviation from a symmetry plane oforthorhombic media. Finally, numerical results in a symmetry plane show thatthe set of first-order approximate formulae performs best for weaklyanisotropic materials.

CORONAL MAGNETOGRAPHY OF AN ACTIVE REGION FROM MICROWAVE POLARIZATION INVERSION

The microwave circular polarization of the active region (AR) NOAA 7260 on 21 - 23 August 1992 is analyzed. Two-dimensional images at 1.76 cm with spatial resolution ofD 10 00 from the Nobeyama radioheliograph and one-dimensional scans at 9 wavelengths in the range of 1.81 - 3.43 cm andD 16:3 00 -3 1:1 00 from the radio telescope RATAN-600 were used. An inversion of the sense of circular polarization through the wavelength range was recorded on 22 August. It is shown that both the wavelength and the time dependence of the inversion are consistent with quasi-transverse (QT) propagation of the radiation in the solar corona. From this, the strength of the coronal magnetic field in the active region was found to be H D 20 - 65 G at a height of hD (5.7 -8 :7/ 10 9 cm above the photosphere on 22 and 30 August and 125 G at the lower height of (3.7 -6 .4)10 9 cm on 23 August. We present a new technique, based on the radio mapping (in both Stokes I and V ) of an AR undergoing circular polarization inversion; applying this method to the Nobeyama data we obtained, for the first time, a magnetogram of the coronal magnetic field. For AR 7260 we found values in the range of 70 - 100 G at heights of (4 - 6)10 9 cm on 23 August, adopting a constant value ofNL (whereN is the electron density andL is the scale of the coronal field divergence) of 2:5 10 18 cm 2 . We compare our results with force-free extrapolations of the photospheric magnetic field from a MSFC magnetogram obtained on 20 August.

Analysis of the multiple inversion of the circular polarization of sunspot-associated microwave sources

Solar observations with a new panoramic spectrum analyzer (PSA) of RATAN-600 showed the multiple inversion of the sense of circular polarization in microwave local sources (LSs). The polarization spectra of LSs are analyzed in terms of the theory of linear coupling of ordinary and extraordinary modes in the quasitransverse (QT) region. We consider the RATAN-600 radio observations of June 2, 1977, January 10, 1992, and May 9 and 10, 1992 for the LS, which demonstrated the inversion of polarization sense in the range 2.0–6.5 cm. The theory of QT propagation imposes a constraint on the degree of polarization of microwaves at wavelengths close to the inversion wavelength. The dependence of the multiple inversion on the wavelength due to multiple crossing of QT regions is verified. The LS polarization spectra are correlated with the spectra calculated for a varied multiplicity to determine more accurately the multiplicity of the inversion.

Unique cuspidal features in the group-velocity surface of barium sodium niobate and Rochelle salt

Crystals that have sufficient elastic anisotropy can exhibit cuspidal features in the group-velocity surface so that the group velocity is double- or triple-valued. In nonpiezoelectric crystals such cuspidal features occur only in the quasi-transverse (QT) modes when the wave vectors are restricted to the symmetry planes of the crystal. Sufficient piezoelectric stiffening of the elastic constants, however, can generate cuspidal features in other modes when the wave vectors are restricted to these same symmetry planes. In barium sodium niobate (BSN) there is insufficient elastic anisotropy to generate cuspidal features when piezoelectric stiffening is neglected. The addition of piezoelectric stiffening changes only the quasi-longitudinal (QL) and QT modes in the (100) and (010) planes, and changes only the pure transverse (T) mode in the (001) plane. There is sufficient piezoelectric stiffening, however, to generate small cuspidal features in the QL mode about the [001] and \([00\bar 1]\) axes in the (100) and (010) planes. In Rochelle salt, however, there is sufficient elastic anisotropy to generate cuspidal features in the QT modes about collinear axes along nonsymmetry directions in the (100) and (010) planes. The addition of piezoelectric stiffening changes only the T mode in the (100), (010) and (001) symmetry planes. This piezoelectric stiffening is large enough, however, to generate large cupsidal features in the T mode about new collinear axes along nonsymmetry directions in the (010) and (001) planes.

DETERMINATION OF THE ELASTIC CONSTANTS OF ANISOTROPIC SOLIDS FROM GROUP VELOCITIES MEASURED IN SYMMETRY DIRECTIONS

We present in this article a novel method of determining all three elastic constants of cubic crystals from a single broadband waveform propagating in the [001] direction. The method can be easily extended to media of orthorhombic symmetry whose symmetry plane quasitransverse (QT) group velocity sheet is folded across the symmetry axis. The usefulness of these formulas lies in providing a very convenient and easy method of determining all the elastic constants of a medium from the rays propagating in the principal symmetry directions of the medium. Particular emphasis is given to the so-called oblique-mode QT rays with group velocity lying along a symmetry axis but with wave normal lying away from that axis in a symmetry plane. Through the use of these oblique modes the need to make off-axis measurements to obtain a complete set of elastic constants is circumvented. Moreover, we describe a method of clarifying the ambiguity that arises; with which symmetry plane is the wave normal of an oblique-mode QT ray propagating in the symmetry axis associated. Further, we show how the effect of a finite rise time source can be corrected for in the determination of a mixed index elastic constant.

Angular scattering of radio waves: Implications for mode coupling in the solar corona

view Abstract Citations (22) References (34) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Angular Scattering of Radio Waves: Implications for Mode Coupling in the Solar Corona Bastian, T. S. Abstract The solar corona is highly inhomogeneous. The magnetionic modes may therefore couple under certain circumstances, and the polarization properties of solar radio sources may, as a consequence, be modified. An application of the simple theory of mode coupling to the propagation of radio waves in the solar corona leads to the expectation that mode coupling in quasi-transverse (QT) magnetic field regions should always be weak (coupling ratio Q much less than 1) at meter wavelengths. Observations to date suggest that, on the contrary, mode coupling is moderate (Q approximately 1) to strong (Q much greater than 1) in QT regions at meter wavelengths. I suggest that observations and theory can be reconciled by including the effect of turbulence on mode coupling. Specifically, angular scattering on turbulent inhomogeneities greatly reduces the spatial scale relevant to the theory at low frequencies. As a result, the coupling ratio is increased by a corresponding factor and mode coupling may be moderate to strong in QT regions at meter wavelengths. Publication: The Astrophysical Journal Pub Date: January 1995 DOI: 10.1086/175190 Bibcode: 1995ApJ...439..494B Keywords: Coupled Modes; Polarization (Waves); Solar Corona; Solar Magnetic Field; Solar Radio Emission; Computation; Electron Density (Concentration); Plasma Turbulence; Propagation; Wave Scattering; Solar Physics; RADIATION MECHANISMS: NONTHERMAL; SUN: CORONA; SUN: RADIO RADIATION; TURBULENCE full text sources ADS |