Planar hyper-lens with uniform pre-designed magnification factor by homogeneous medium

Elastic study on singularities interacting with interfaces using alternating technique

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

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

A general transformation for compact waveguide coupler by using homogeneous media

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.

In this paper, the Symmetric Galerkin Boundary Element Method for Linear Elastic Fracture Mechanics is extended to non-linear cohesive cracks propagating through homogeneous linear elastic isotropic media. The cohesive model adopted is based on the concept of free energy density per unit undeformed area. The corresponding constitutive cohesive equations present a softening branch which induces a potential instability. Thus, a suitable solution algorithm capable of following the growth of the cohesive zone is needed, and in the present work the numerical simulation is controlled by an arc-length method combined with a Newton-Raphson algorithm for the iterative solution of nonlinear equations. The Boundary ElementMethod is very attractive for modeling cohesive crack problems as all nonlinearities are located on the boundaries of linear elastic domains. Moreover a Galerkin approximation scheme, applied to a suitable symmetric boundary integral equation formulation, ensures an easy and efficient treatment of cracks in homogeneous media and an excellent convergence behavior of the numerical solution. The cohesive zone model is applied to simulate a pure mode I crack propagation in concrete. Numerical results for three-point bending test are used to check the numerical results for mode I and are compared with some numerical results obtained by FEM analysis found in the literature.

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.

Nanoscale synapse organization and dysfunction in neurodevelopmental disorders

Full-field numerical solutions for a crack which lies along the interface of an elastic-plastic medium and a rigid substrate are presented. The solutions are obtained using a small strain version of the J2-deformation theory with power-law strain hardening. In the present article, results for loading causing only small scale yielding at the crack tip are described; in subsequent articles the mathematical structure of the crack-tip fields under small scale yielding and results for contained yielding and fully plastic behavior will be presented. We find that although the near-tip fields do not appear to have a separable singular form, of the HRR-type fields as in homogeneous media, they do, however, bear interesting similarities to certain mixed-mode HRR fields. Under small scale yielding, where the remote elastic fields are specified by a complex stress-concentration vector Q = |Q|eiφ with φ being the phase angle between the two in-plane stress modes, we find that the plastic fields are members of a family parameterized by a new phase angle ξ, ≡ φ + εln(QQ/σ02L), and the fields nearly scale with the well-defined energy release rate as evaluated by the J-integral. Here σ0 is the reference yield stress and L is the total crack length (or a relevant length of the crack geometry). Numerical procedures appropriate for solving a general class of interface crack problems are also presented. A description of a numerical method for extracting the mixed mode stress intensities for cracks at interfaces and in homogeneous isotropic or anisotropic media, is included.

A so-called anti-optic-null medium (anti-ONM), which can be utilized to cancel the optic-null medium (ONM) and create many novel optical illusions, is introduced and designed by transformation optics (TO). Optical separation illusions can be achieved with an anti-ONM. With the help of the anti-ONM, we can achieve the same optical illusions where ONM is required via a shelled structure filled with low anisotropic medium, which is easier to realize for some novel optical devices designed by TO and optical surface transformation. The special function of the anti-ONM will lead to a new way to design optical devices or simplify the material requirements. Overlapping illusions, and wave-front reshapers are designed to demonstrate the function of the proposed method.

Oscillatory numerical experiments in finely layered anisotropic viscoelastic media

Spectroscopic single-molecule localization microscopy (sSMLM) is a novel super-resolution imaging technology, which simultaneously records the nanoscopic location and the corresponding full emission spectrum of every stochastic single-molecule emission event. This spectroscopic imaging capability of sSMLM necessitates the establishment of a theoretical foundation of the newly introduced spectral precision and to guide the system design and optimization. Based on numerical simulation and analytical solution, we introduced such a theoretical model to analyze spectral precision by considering the main system parameters, including signal and background shot noises, readout noise, and the spectral calibration procedure. Using this model, we demonstrated the delicate balance among these parameters in achieving the optimal spectral precision and discovered that the best spectral precision can only be achieved at a particular system spectral dispersion. For example, with a given signal of 3000 photons and a readout noise of 2 e-, a system spectral dispersion of 1.6 nm/pixel is required for sSMLM to achieve the highest spectral precision of 1.31 nm.

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.

Steady-state wave propagation in homogeneous anisotropic media