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

Effective conductivity of anisotropic media with crack-like inclusions and cracks of arbitrary shapes

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

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.

view Abstract Citations (753) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Does the missing mass problem signal the breakdown of Newtonian gravity? Bekenstein, J. ; Milgrom, M. Abstract A nonrelativistic potential theory for gravity is considered which differs from the Newtonian theory. The theory is built on the basic assumptions of the modified dynamics, which were shown earlier to reproduce dynamical properties of galaxies and galaxy aggregates without having to assume the existence of hidden mass. The theory involves a modification of the Poisson equation and can be derived from a Lagrangian. The total momentum, angular momentum, and (properly defined) energy of an isolated system are conserved. The center-of-mass acceleration of an arbitrary bound system in a constant external gravitational field is independent of any property of the system. In other words, all isolated objects fall in exactly the same way in a constant external gravitational field (the weak equivalence principle is satisfied). However, the internal dynamics of a system in a constant external field is different from that of the same system in the absence of the external field, in violation of the strong principle of equivalence. These two results are consistent with the phenomenological requirements of the modified dynamics. A toy relativistic theory is sketched which has a nonrelativistic limit satisfying the requirements of the modified dynamics. Publication: The Astrophysical Journal Pub Date: November 1984 DOI: 10.1086/162570 Bibcode: 1984ApJ...286....7B Keywords: Galactic Rotation; Gravitation Theory; Mass Distribution; Missing Mass (Astrophysics); Newton Theory; Nonrelativistic Mechanics; Potential Theory; Computational Astrophysics; Cosmology; Equivalence; Poisson Equation; Astrophysics full text sources ADS |

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.

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 inclination of flow lines at the exit on the downstream side of a hydraulic structure has been found for a known degree of anisotropy and a given direction for the principal permeability. An analytical procedure is presented to find the exit gradient for steady confined flow in an anisotropic porous medium from known exit gradient of the corresponding fictitious isotropic flow domain. Results have been presented for distribution of exit gradient on the downstream side of a vertical sheet pile embedded in a homogeneous anisotropic porous medium of infinite depth. It is found that the zone vulnerable to piping on the downstream side of a vertical sheet pile is larger for the case of horizontal stratification than for vertical stratification.

The solution of a cracked dislocation under uniform stress in a homogeneous anisotropic elastic medium is given. The analysis is exact within the realm of classical linear elasticity. The solution is used to deduce criteria for cleavage fracture according to some dislocation models. The results are compared with the corresponding criteria for isotropic elastic materials.

The exact solution for the chiral field superpropagator in a constant external Abelian field is given.

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.

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