Fracture mechanics of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in an infinite piezoelectric or on the interface of piezoelectric bimaterials. For homogeneous materials it is found that the normal electric displacement D-2, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the crack slit, the perturbed electric fields induced by the crack are also constant and not affected by the applied electric displacement fields. For bimaterials, generally speaking, an interface crack exhibits oscillatory behavior and the normal electric displacement D-2 is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D-2 is also constant along the crack faces and the electric field E-2 has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homogeneous materials and bimaterials having certain symmetry. Both the crack front parallel to the poling axis and perpendicular to the poling axis are discussed. It is revealed that the energy release rates are always positive for stable materials and the applied electric displacements have no contribution to the energy release rates.

Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a staggered-mesh grid system. The convection terms are discretized with a fifth-order-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth-order difference approximation on a cell-centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented.

Simulations of oil spread on a water surface

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called sigma transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

Crack problems of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in piezoelectrics or on the interfaces of piezoelectric bimaterials. A class of boundary problems involving many cracks is also solved. For homogeneous materials it is found that the normal electric displacement D-2 induced by the crack is constant along the crack faces which depends only on the applied remote stress field. Within the crack slit, the electric fields induced by the crack are also constant and not affected by the applied electric field. For the bimaterials with real H, the normal electric displacement D-2 is constant along the crack faces and electric field E-2 has the singularity ahead of the crack tip and a jump across the interface.

A Constrained Particle Dynamics for Continuum-Particle Hybrid Method in Micro- and Nano-Fluidics

A hybrid method of continuum and particle dynamics is developed for micro- and nano-fluidics, where fluids are described by a molecular dynamics (MD) in one domain and by the Navier-Stokes (NS) equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip boundary conditions.

Semi-weight function method on computation of stress intensity factors in dissimilar materials

Semi-weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi-weight functions were obtained as virtual displacement and stress fields with eigenvalue-lambda. Integral expression of fracture parameters, K-I and K-II, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi-weight function method is a simple, convenient and high precision calculation method.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

An Atomistic-Continuum Hybrid Simulation Of Fluid Flows Over Superhydrophobic Surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper, an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces, in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths, which cannot be obtained by molecular dynamics simulation alone.

An atomistic-continuum hybrid simulation of fluid flows over superhydrophobic surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths which cannot be obtained by molecular dynamics simulation alone.

Analysis of electromagnetic propagation in birefringent thin film

In general, the propagating behavior of extraordinary wave in anisotropic materials is different from that in isotropic materials. With the tangential continuity of Maxwell's equations, the electromagnetic propagating behaviors have been investigated at the incident and exit interfaces of the uniaxial anisotropic thin film. The emphasis was placed on two interesting optical phenomena such as homolateral refraction behavior and wide-angle Brewster's phenomenon, which occurred at the interfaces of uniaxial anisotropic thin film.

Co和Cu薄膜电学特性和连续性特征的判据

采用离子束溅射沉积了不同厚度的Co膜和Cu膜，利用四电极法测量了薄膜的电阻率，从而得到了Co膜和Cu膜的电导率随薄膜厚度的变化关系。实验结果表明，Co膜和Cu膜的电学特性都具有明显的尺寸效应。比较了同时考虑表面散射和晶界散射的电导理论得到的电导率公式与实验结果，不同薄膜厚度电导率的理论结果与实验结果符合较好。提出了厚度作为金属薄膜生长从不连续膜进入连续膜的一个特征判据，并利用原子力显微镜（AFM）观测了膜厚在特征厚度附近的Co膜和Cu膜的表面形貌。

Y-chromosome evidence for no independent origin of modern human in China

East Asia is one of the few regions in the world where a large number of human fossils have been unearthed. The continuity of hominid fossils in East Asia, particularly in China has been presented as strong evidence supporting an independent origin of mod

Electron microscopic examination of the viromatrix of Rana grylio virus in a fish cell line

Rana grylio virus (RGV), a Ranavirus belonging to the family Iridoviridae, assembles in the viromatrix which is a factory for viral genome replication and particle assembly. Ultrastructural studies of the viromatrix will clarify the pathway of assembly. The viromatrix and quantitative changes in RGV infected epithelipma papulosum cyprini (EPC) cells, one of fish cell lines, were studied by electron microscopy. It was shown that viromatrices were adjacent to the nucleus, and the electron density was lower than that of the surrounding cytoplasm. The viromatrix contained virus particles with different forms, electron-dense materials and amorphous structures which included tubules and membranous materials. Tubules were often observed in direct continuity with empty capsids. Several bundles of intermediate filaments were seen alongside the viromatrix and crystalline aggregates. Large clusters of mitochondria occurred in proximity to viromatrix. A total of 990 cells profiles were examined. The results showed that 394 cells contained viromatrix: 89.3% contained one, and 10.7% contained two to four viromatrices. The number of viromatrices increased gradually and reached a peak at 16 h p.i. The viromatrix area at 24 h p.i. increased up to 7.4 +/- 0.69 mu m(2) which was three-times lower than that at 6 h p.i. The number of empty capsids within viromatrix was generally more than that of "full" particles at different time points, and there was a strong positive correlation between them. (c) 2005 Elsevier B.V. All rights reserved.