A double degenerated finite element for modeling the crack tip singularity

The objective of this paper is to propose a modified finite element called double quarter point finite element (DQPE) for modeling the singularity near the crack tip. Two techniques of evaluation (displacement correlation technique DCT and quarter point displacement technique QPDT) were used to estimate numerically the calibration factor for CN specimen. This study appears that the DQPE element is more effective than the QPE element. Not only that, but the length of the double quarter point finite element (DQPE) has little impact on the results. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed element.     

A construction of new exact periodic wave and solitary wave solutions for the 2D Ginzburg–Landau equation

Using a uniform algebraic method, new exact solitary wave solutions and periodic wave solutions for 2D Ginzburg–Landau equation are obtained. Moreover, three-dimensional and two-dimensional graphics of some solutions have been plotted.     

Optical transmission properties of an anisotropic defect cavity in one-dimensional photonic crystal

We investigate theoretically the possibility to control the optical transmission in the visible and infrared regions by a defective one dimensional photonic crystal formed by a combination of a finite isotropic superlattice and an anisotropic defect layer. The Green's function approach has been used to derive the reflection and the transmission coefficients, as well as the densities of states of the optical modes. We evaluate the delay times of the localized modes and we compare their behavior with the total densities of states. We show that the birefringence of an anisotropic defect layer has a significant impact on the behavior of the optical modes in the electromagnetic forbidden bands of the structure. The amplitudes of the defect modes in the transmission and the delay time spectrum, depend strongly on the position of the cavity layer within the photonic crystal. The anisotropic defect layer induces transmission zeros in one of the two components of the transmission as a consequence of a destructive interference of the two polarized waves within this layer, giving rise to negative delay times for some wavelengths in the visible and infrared light ranges. This property is a typical characteristic of the anisotropic photonic layer and is without analogue in their counterpart isotropic defect layers. This structure offers several possibilities for controlling the frequencies, transmitted intensities and the delay times of the optical modes in the visible and infrared regions. It can be a good candidate for realizing high-precision optical filters.     

Ultrasonic elastography using sector scan imaging and a radial compression

Elastography is an imaging technique based on strain estimation in soft tissues under quasi-static compression. The stress is usually created by a compression plate, and the target is imaged by an ultrasonic linear array. This configuration is used for breast elastography, and has been investigated both theoretically and experimentally. Phenomena such as strain decay with tissue depth and strain concentrations have been reported. However in some in vivo situations, like prostate or blood vessels imaging, this set-up cannot be used. We propose a device to acquire in vivo elastograms of the prostate. The compression is applied by inflating a balloon that covers a transrectal sector probe. The 1D algorithm used to calculate the radial strain fails if the center of the imaging probe does not correspond to the center of the compressor. Therefore, experimental elastograms are calculated with a 2D algorithm that accounts for tangential displacements of the tissue. In this article, in order to gain a better understanding of the image formation process, the use of ultrasonic sector scans to image the radial compression of a target is investigated. Elastograms of homogeneous phantoms are presented, and compared with simulated images. Both show a strain decay with tissue depth. Then experimental and simulated elastograms of a phantom that contains a hard inclusion are presented, showing that strain concentrations occur as well. A method to compensate for strain decay and therefore to increase the contrast of the strain elastograms is proposed. It is expected that such information will help to interpret and possibly improve the elastograms obtained via radial compression.     

Crystallographic distortion in CrAs0.50Sb0.50

X-ray diffraction has shown that CrAs_0.50Sb_0.50 undergoes at the Néel temperature a crystallographic distortion (NiAs → MnP) accompanied by a discontinuous volume change. Neutron diffraction revealed in this compound a helimagnetic structure very similar to the ‘double spiral’ in CrAs discovered recently. The pressure dependence of the Néel temperature is estimated in the framework of the Bean Rodbell theory and compared with the CrAs value.     

Molecular tectonics: from enantiomerically pure sugars to enantiomerically pure triple stranded helical coordination network

The self-assembly between a bis-monodentate tecton based on two pyridine units connected to an enantiomerically pure isomannide stereoisomer and HgCl2 leads to the formation of an enantiomerically pure triple stranded helical infinite coordination network which was structurally characterised by X-ray diffraction on single crystal.     

Multiple periodic solutions for nonautonomous Hamiltonian systems

In this paper, by the use of minimax method, we obtain some existence and multiplicity theorems for periodic solutions of nonautonomous Hamiltonian systems with bounded nonlinearity of the type:¶ J [(x)\dot] + ?H(t, x) + e(t) = 0. J \dot x + \nabla H(t, x) + e(t) = 0.     

Spectrum preserving linear mappings for scattered Jordan-Banach algebras

Given two semisimple complex Jordan-Banach algebras with identity and , we say that is a spectrum preserving linear mapping from to if is surjective and we have , for all . We prove that if is a scattered Jordan-Banach algebra, then is a Jordan isomorphism.