Steady-state wave propagation in homogeneous anisotropic media

Thin inclusions of large or small conductivity in an anisotropic homogeneous medium

Elastic study on singularities interacting with interfaces using alternating technique

A hyper-lens with planar object/image surfaces and uniform magnification factor is designed based on directional projecting property of optic-null medium (ONM). The proposed planar hyper-lens only requires one homogeneous anisotropic medium, i.e. ONM. We use metallic plates inside ϵ-near-zero medium to realize the proposed hyper-lens. 0.191λ 0 resolution is observed (0.238λ 0 can be clearly resolved) in experimental measurement, which consists very well with 3D numerical simulations and verifies the performance of the proposed planar hyper-lens. The planar hyper-lens with uniform pre-designed magnification factor may have some applications in super-resolution imaging technology.

Deformable, rigid, and inviscid elliptical inclusions in a homogeneous incompressible anisotropic viscous fluid

Techniques for wireless acoustic communication and energy transfer along steel plates and piping to avoid physical penetrations and wire feed-throughs are presented. Longitudinal and shear acoustic waves (polarized in the direction of the plate/pipe wall thickness) transmitted into steel plates using steel wedges are analyzed using finite-element analysis. Propagation of steady-state waves at frequencies of 1 MHz in steel plates using triangular steel wedges with varying wave launch angles were used, where the steel plate was bounded by cement on one side and engine oil on the other. Successful simulation was achieved at large axial distance from the transmitting wedge with reception into a second reversed wedge, which is applicable for both power and data transmissions. At a distance of 0.41 m the energy transfer efficiency was seen to increase with increasing launch angle to 0.1 % for shear waves and 0.03 % for longitudinal waves when operating with an 80 degree wedge.

Diffraction of electromagnetic waves from an arbitrary source by an anisotropic cylindrical structure or by a cylindrical structure in an anisotropic medium is very difficult to handle in general. But if the source is a line source parallel to (or a plane wave normally incident to) the axis of an infinitely long cylindrical structure, where the transverse anisotropy of the structure is not coupled to that of the axial, the problems simplify in many cases. In all of these cases, Maxwell's equations lead to a single differential equation with parameters and boundary conditions which depend on the individual problems. Examples given are perfectly conducting wedges and a perfectly conducting cylinder in anisotropic media. There are a few cases where the electromagnetic waves depend only on the axial property of the medium, i.e. the waves do not see the anisotropic nature of the medium.

Layered composite, bonded with two half planes, one of which contains a crack, is compared with homogeneous anisotropic media, bonded similar half planes. This problem is analyzed for the case of antiplane strain. Stress singularities are investigated, and numerical results are presented and compared for these models. Conclusions drawn concern thresholds within which the model of homogeneous media can serve to simulate a layered composite.

The mechanism of reentrant ventricular tachycardia was studied in computer simulations and in thin (approximately 20 x 20 x 0.5-mm) slices of dog and sheep ventricular epicardial muscle. A two-dimensional matrix consisting of 96 x 96 electrically coupled cells modeled by the FitzHugh-Nagumo equations was used to analyze the dynamics of self-sustaining reentrant activity in the form of elliptical spiral waves induced by premature stimulation. In homogeneous anisotropic media, spirals are stationary and may last indefinitely. However, the presence of small parameter gradients may lead to drifting and eventual termination of the spiral at the boundary of the medium. On the other hand, spirals may anchor and rotate around small discontinuities within the matrix. Similar results were obtained experimentally in 10 preparations whose electrical activity was monitored by means of a potentiometric dye and high-resolution optical mapping techniques; premature stimulation triggered reproducible episodes of sustained or nonsustained reentrant tachycardia in the form of spiral waves. As a rule, the spirals were elongated, with the major hemiaxis parallel to the longitudinal axis of the cells. The period of rotation (183 +/- 68 msec [mean +/- SD]) was longer than the refractory period (131 +/- 38 msec) and appeared to be determined by the size of the spiral's core, which was measured using a newly devised "frame-stack" plot. Drifting of spiral waves was also observed experimentally. Drift velocity was 9.8% of the velocity of wave propagation. In some cases, the core became stationary by anchoring to small arteries or other heterogeneities, and the spiral rotated rhythmically for prolonged periods of time. Yet, when drift occurred, spatiotemporal variations in the excitation period were manifested as a result of a Doppler effect, with the excitation period ahead of the core being 20 +/- 6% shorter than the excitation period behind the core. As a result of these coexisting frequencies, a pseudoelectrocardiogram of the activity in the presence of a drifting spiral wave exhibited "QRS complexes" with an undulating axis, which resembled those observed in patients with torsade de pointes. The overall results show that spiral wave activity is a property of cardiac muscle and suggest that such activity may be the common mechanism of a number of monomorphic and polymorphic tachycardias.

Oscillatory numerical experiments in finely layered anisotropic viscoelastic media

A 2-D problem of the electromagnetic wave scattering in a homogeneous anisotropic medium from an infinitely long cylinder of arbitrary cross-section shape made of inhomogeneous anisotropic material is considered. The problem is formulated in the form of a system of integro-differential equations with respect to the field components over the cross-section of a scatterer. These equations are solved numerically via the moment method using pulse functions as the basis functions and the point-matching technique.

SUMMARY The influence of the free surface on shear wavetrains in a homogeneous anisotropic medium is analysed. We use a numerical technique which allows one to compute full waveforms from a buried dislocation source in a model with arbitrary symmetry. Azimuthally isotropic (hexagonal) and orthorhombic media are considered. In a transversely isotropic model and in symmetry planes of an orthorhombic medium the SH-wave preserves its polarization at the surface and orthogonal particle motions of the incident shear waves are clearly seen even beyond the critical angle. If sagittal symmetry is absent, particle motions in the horizontal and sagittal planes are seriously distorted beyond critical angles by head waves and inhomogeneous reflected SP phases. However, in spite of the transverse components acquired by head and reflected waves, shear wave polarizations in the transverse plane remain close to the polarizations of the incident waves up to incidence angles of 55-60. Some complications in the detection of shear wave splitting caused by source parameters and anisotropic structure are also investigated. Distinctive shear wave splitting in the transverse plane for angles of incidence 35-60 indicates the possibility of extending the limits of the shear wave window. Investigation of particle motions beyond critical angles may help to avoid ambiguities in the interpretation of the limited data set obtained inside the 'classical' shear wave window.

Time-Resolved Integrative Optical Imaging of Diffusion during Spreading Depression

An analytical solution of steady-state dynamic response of a multilayered viscoelastic medium to a moving distributed load is obtained using a novel approach that combines transfer matrix method with Sun’s convolution representation integrated over impulse response function of the layered medium. The layered media under consideration include elastic and viscoelastic media with four different viscoelastic constitutive models, while the moving load is allowed to have a circular spatial distribution, which is more realistic for mimicking tire footprint than a commonly used point load. Efficient numerical algorithms based on fast evaluation of various integral transformations and their inversions are developed and validated through numerical example.

The basic problem of the diffraction of an optical plane wave by an acoustic plane wave in an anisotropic homogeneous medium is considered. The acousto-optical interaction is considered indifferently of the isotropic or of the birefringent type. Coupled-wave equations are obtained rigorously and cast into an eigenvalue value problem. A general solution is obtained for the diffraction efficiency of diffracted orders, for any interaction length and diffraction regime. The theory includes the Bragg regime, the Raman-Nath regime, and all intermediate situations in the same formulation. The method of solution is both exact and computationally efficient. It is similar in character to the rigorous coupled-wave analysis of Moharam and Gaylord but differs by the choice of basis functions adapted to propagating rather than static gratings. Examples are given for acousto-optical interaction in paratellurite, TeO2.

Seepage flow problems in layered soils solved by the finite element method