Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading

In this paper the problem of a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered. The shear modulus and the mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial cylinders. This mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) is also obtained by a numerical Laplace inversion technique. The DSIF is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation. The influences of the crack location, the FGM interlayer thickness and the relative magnitudes of the adjoining material properties are examined. It is found among others that, by increasing the FGM gradient, the DSIF can be greatly reduced.

Molecular Dynamics Study Of The Mechanical Behavior Of Nickel Nanowire: Strain Rate Effects

We present the analysis of uniaxial deformation of nickel nanowires using molecular dynamics simulations, and address the strain rate effects on mechanical responses and deformation behavior. The applied strain rate is ranging from 1 x 10(8) s(-1) to 1.4 x 10(11) s(-1). The results show that two critical strain rates, i.e., 5 x 10(9) s(-1) and 8 x 10(10) s(-1), are observed to play a pivotal role in switching between plastic deformation modes. At strain rate below 5 x 10(9) s(-1), Ni nanowire maintains its crystalline structure with neck occurring at the end of loading, and the plastic deformation is characterized by {111} slippages associated with Shockley partial dislocations and rearrangements of atoms close to necking region. At strain rate above 8x10(10) s(-1), Ni nanowire transforms from a fcc crystal into a completely amorphous state once beyond the yield point, and hereafter it deforms uniformly without obvious necking until the end of simulation. For strain rate between 5 x 10(9) s(-1) and 8 x 10(10) s(-1), only part of the nanowire exhibits amorphous state after yielding while the other part remains crystalline state. Both the {111} slippages in ordered region and homogenous deformation in amorphous region contribute to the plastic deformation. (C) 2007 Published by Elsevier B.V.

Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces art assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density,function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically, and using a numerical Laplace inversion technique, the dynamic stress intensity factors art obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

Elastodynamic stress-intensity factors for a semiinfinite crack under 3-d combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.

Elastodynamic stress intensity factor history for a semi-infinite crack under three-dimensional transient loading

The dynamic stress intensity factor history for a semi-infinite crack in an otherwise unbounded elastic body is analyzed. The crack is subjected to a pair of suddenly-applied point loadings on its faces at a distance L away from the crack tip. The exact expression for the mode I stress intensity factor as a function of time is obtained. The method of solution is based on the direct application of integral transforms, the Wiener-Hopf technique and the Cagniard-de Hoop method. Due to the existence of the characteristic length in loading this problem was long believed a knotty problem. Some features of the solutions are discussed and graphical result for numerical computation is presented.

3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

Hit-or-miss representation of a pattern spectrum and its optical implementation

We demonstrate that a pattern spectrum can be decomposed into the union of hit-or-miss transforms with respect to a series of structure-element pairs. Moreover we use a Boolean-logic function to express the pattern spectrum and show that the Boolean-logic representation of a pattern spectrum is composed of hit-or-miss min terms. The optical implementation of a pattern spectrum is based on an incoherent optical correlator with a feedback operation. (C) 1996 Optical Society of America

FUZZY SOLID SETS FOR MATHEMATICAL MORPHOLOGY AND OPTICAL IMPLEMENTATION

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated. (C) 1995 Optical Society of America

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures. (c) 2006 Published by Elsevier GmbH.

Structure and thermal stability of novel fluorophosphate glasses

A systematic investigation on glass formation in the PbF2-InF3-BaHPO4 ternary system has been carried out. These glasses have characterized by IR spectra, Raman spectra and differential thermal analysis. The results show that the structure of these glasses is mainly affected by BaHPO4 and InF3 contents. With decreasing BaHPO4 content, the glass structure gradually transforms from metaphosphate to polyphosphate. When InF3 content is low, it mainly acts as network modifier, when its content is high; it enters glass matrix and forms In(O,F)(6) groups connecting the polymerized phosphorus oxygen species. PbF2 mainly acts as network modifier in this system. Systematic variations of the glass transition temperature and the thermal stability index agree well with these results. The most stable glass with Delta T = 230 degrees C and S = 21.79 K is obtained. (c) 2004 Elsevier B.V. All rights reserved.

Y2O3 stabilized ZrO2 thin films deposited by electron-beam evaporation: Optical properties, structure and residual stresses

This paper describes the preparation and the characterization Of Y2O3 stabilized ZrO2 thin films produced by electric-beam evaporation method. The optical properties, microstructure, surface morphology and the residual stress of the deposited films were investigated by optical spectroscopy, X-ray diffraction (XRD), scanning probe microscope and optical interferometer. It is shown that the optical transmission spectra of all the YSZ thin films are similar with those of ZrO2 thin film, possessing high transparency in the visible and near-infrared regions. The refractive index of the samples decreases with increasing of Y2O3 content. The crystalline structure of pure ZrO2 films is a mixture of tetragonal phase and monoclinic phase, however, Y2O3 stabilized ZrO2 thin films only exhibit the cubic phase independently of how much the added Y2O3 content is. The surface morphology spectrum indicates that all thin films present a crystalline columnar texture with columnar grains perpendicular to the substrate and with a predominantly open microporosity. The residual stress of films transforms tensile from compressive with the increasing Of Y2O3 molar content, which corresponds to the evolutions of the structure and packing densities. (C) 2008 Elsevier Ltd. All rights reserved.

Investigation of responsivity decreasing with rising bias voltage in a GaN Schottky barrier photodetector

The unexpected decrease in measured responsivity observed in a specific GaN Schottky barrier photodetector (PD) at high reverse bias voltage was investigated and explained. Device equivalent transforms and small signal analysis were performed to analyse the test circuit. On this basis, a model was built which explained the responsivity decrease quantitatively. After being revised by this model, responsivity curves varying with bias voltage turned out to be reasonable. It is proved that the decrease is related to the dynamic parallel resistance of the photodiode. The results indicate that with a GaN Schottky PD, the choice of load resistance is restricted according to the dynamic parallel resistance of the device to avoid responsivity decay at high bias voltage.

High-temperature AlN interlayer for crack-free AlGaN growth on GaN

This paper presents a study of the transformation of high-temperature AlN (HT-AlN) interlayer (IL) and its effect on the strain relaxation of Al0.25Ga0.75N/HT-AlN/GaN. The HT-AlN IL capped with Al0.25Ga0.75N transforms into AlGaN IL in which the Al composition increases with the HT-AlN IL thickness while the total Ga content keeps nearly constant. During the HT-AlN IL growth on GaN, the tensile stress is relieved through the formation of V trenches. The filling up of the V trenches by the subsequent Al0.25Ga0.75N growth is identified as the Ga source for the IL transformation, whose effect is very different from a direct growth of HT-AlGaN IL. The a-type dislocations generated during the advancement of V trenches and their filling up propagate into the Al0.25Ga0.75N overlayer. The a-type dislocation density increases dramatically with the IL thickness, which greatly enhances the strain relaxation of Al0.25Ga0.75N. (c) 2008 American Institute of Physics.