A BIEM optimization method for fracture dynamics inverse problem

In the present paper, based on the theory of dynamic boundary integral equation, an optimization method for crack identification is set up in the Laplace frequency space, where the direct problem is solved by the author's new type boundary integral equations and a method for choosing the high sensitive frequency region is proposed. The results show that the method proposed is successful in using the information of boundary elastic wave and overcoming the ill-posed difficulties on solution, and helpful to improve the identification precision.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Application of enthalpy method for moving boundary problem in laser surface melting

A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization. The enthalpy method was applied to solve this two-phase axisymmetrical melting problem Computational results of temperature fields were obtained, which provide useful information to practical laser treatment processing. The validity of enthalpy method in solving such problems is presented.

Analysis of strip electric saturation model of crack problem in piezoelectric materials

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491-510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement field is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poring axis, the failure stress is not effected by the parallel applied electric field. In order to analyse the existed experimental results, the stress fields ahead of the tip of an elliptic notch in an infinite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under different remote electric displacement fields. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement field depending on the field direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475-1480).

On a Degenerate Parabolic Problem in Holder Spaces

In this paper, we study some degenerate parabolic equation with Cauchy-Dirichlet boundary conditions. This problem is considered in little Holder spaces. The optimal regularity of the solution v is obtained and is specified in terms of those of the second member when some conditions upon the Holder exponent with respect to the degeneracy are satisfied. The proofs mainly use the sum theory of linear operators with or without density of domains and the results of smoothness obtained in the study of some abstract linear differential equations of elliptic type.

A contact crack problem in an infinite plate

The problem of an infinite plate with crack of length 2a loaded by the remote tensile stress P and a pair of concentrated forces Q is discussed. The value of the force Q for the initial contact of crack face is investigated and the contact length elevated, while the Q force increases. The problem is solved assuming that the stress intensity factor vanishes at the end point of the contact portion. By the Fredholm integral equation for the multiple cracks, the reduction of stress intensity factor due to Q is found. (C) 1999 Elsevier Science Ltd. All rights reserved.

ON THE DANGLING-BOND RELAXATION PROBLEM IN HYDROGENATED AMORPHOUS-SILICON

The influence of pulsed bias light excitation on the absorption in the defect region of undoped a-Si:H film has been investigated. Ac constant photocurrent method has been used to measure the absorption spectrum. The absorption in the defect region increases with the light pulse duration.The analysis of obtained results does not support the existence of a long time relaxation process of dangling-bond states in a-Si:H.

Aberration measurement of projection optics in lithographic tools based on two-beam interference theory

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy. (c) 2006 Optical Society of America.

Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools

As the feature size decreases, degradation of image quality caused by wavefront aberrations of projection optics in lithographic tools has become a serious problem in the low-k1 process. We propose a novel measurement technique for in situ characterizing aberrations of projection optics in lithographic tools. Considering the impact of the partial coherence illumination, we introduce a novel algorithm that accurately describes the pattern displacement and focus shift induced by aberrations. Employing the algorithm, the measurement condition is extended from three-beam interference to two-, three-, and hybrid-beam interferences. The experiments are performed to measure the aberrations of projection optics in an ArF scanner. (C) 2006 Optical Society of America.

Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

Application of fast Pade approximation in simulating photonic crystal nanocavities by FDTD technology

The exact calculation of mode quality factor Q is a key problem in the design of high-Q photonic crystal nanocavity. On the basis of further investigation on conventional Pade approximation, FDM and DFT, Pade approximation with Baker's algorithm is enhanced through introducing multiple frequency search and parabola interpolation. Though Pade approximation is a nonlinear signal processing method and only short time sequence is needed, we find the different length of sequence requirements for 2D and 3D FDTD, which is very important to obtain convergent and accurate results. By using the modified Pade approximation method and 3D FDTD, the 2D slab photonic crystal nanocavity is analyzed and high-Q multimode can be solved quickly instead of large range high-resolution scanning. Monitor position has also been investigated. These results are very helpful to the design of photonic crystal nanocavity devices. (C) 2008 Elsevier B.V. All rights reserved.

Statistical Interpolation Method of Turbulent Phase Screen

A relative displacement between the grid points of optical fields and those of phase screens may occur in the simulation of light propagation through the turbulent atmosphere. A statistical interpolator is proposed to solve this problem in this paper. It is evaluated by the phase structure function and numerical experiments of light propagation through atmospheric turbulence with/without adaptive optics (AO) and it is also compared with the well-known linear interpolator under the same condition. Results of the phase structure function show that the statistical interpolator is more accurate in comparison with the linear one, especially in the high frequency region. More importantly, the long-exposure results of light propagation through the turbulent atmosphere with/without AO also show that the statistical interpolator is more accurate and reliable than the linear one. (C) 2009 Optical Society of America.