Explicit asymptotic modelling of transient Love waves propagated along a thin coating

The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award

Cold Plasma Dispersion Relations in the Vicinity of a Schwarzschild Black Hole Horizon

We apply the ADM 3+1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.Comment: 27 pages, 11 figures accepted for publication in Gen. Relat. & Gravi

On Love-type waves in a finitely deformed magnetoelastic layered half-space

In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney–Rivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein–Gulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper

Cold Plasma Wave Analysis in Magneto-Rotational Fluids

This paper is devoted to investigate the cold plasma wave properties. The analysis has been restricted to the neighborhood of the pair production region of the Kerr magnetosphere. The Fourier analyzed general relativistic magnetohydrodynamical equations are dealt under special circumstances and dispersion relations are obtained. We find the $x$-component of the complex wave vector numerically. The corresponding components of the propagation vector, attenuation vector, phase and group velocities are shown in graphs. The direction and dispersion of waves are investigated.Comment: 22 pages, 18 figures, accepted for publication in Astrophys. Space Sc

Isothermal Plasma Wave Properties of the Schwarzschild de-Sitter Black Hole in a Veselago Medium

In this paper, we study wave properties of isothermal plasma for the Schwarzschild de-Sitter black hole in a Veselago medium. We use ADM 3+1 formalism to formulate general relativistic magnetohydrodynamical (GRMHD) equations for the Schwarzschild de-Sitter spacetime in Rindler coordinates. Further, Fourier analysis of the linearly perturbed GRMHD equations for the rotating (non-magnetized and magnetized) background is taken whose determinant leads to a dispersion relation. We investigate wave properties by using graphical representation of the wave vector, the refractive index, change in refractive index, phase and group velocities. Also, the modes of wave dispersion are explored. The results indicate the existence of the Veselago medium.Comment: 24 pages, 12 figures, accepted for publication in Astrophys. Space Sci. arXiv admin note: text overlap with arXiv:1101.0884 and arxiv:1007.285

The scattering of SH waves by a finite crack with a superposition based diffraction technique

The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited -- We construct an approximate solution by the addition of independent diffracted terms -- We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge -- This building block is then used to compute the diffraction of the main incident waves -- The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached -- We propose a recipe to determine the number of required interactions as a function of frequency -- The solution derived with the superposition technique can be applied at low and high frequencie

On the super-Rayleigh/subseismic elastodynamic indentation problem

The elastodynamic super-Rayleigh/subseismic indentation paradox is examined in this paper. Both the Craggs/Roberts steady-state problem and the Robinson/Thompson transient problem are reconsidered. Certain features of these solutions are discussed from a new point of view, by considering asymptotics at the end of the contact region, the influence of contact inequalities, energetics of the process and existence/uniqueness.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42681/1/10659_2004_Article_BF00044967.pd