Real-Time Measurement on Deformation Fields of Hole-Excavated Samples under Impact Tension

In this paper, the real-time deformation fields are observed in two different kinds of hole-excavated dog-bone samples loaded by an SHTB, including single hole sample and dual holes sample with the aperture size of 0.8mm. The testing system consists of a high-speed camera, a He-Ne laser, a frame grabber and a synchronization device with the controlling accuracy of I microsecond. Both the single hole expanding process and the interaction of the two holes are recorded with the time interval of 10 mu s. The observed images on the sample surface are analyzed by newly developed software based on digital correlation theory and a modified image processing method. The 2-D displacement fields in plane are obtained with a resolution of 50 mu m and an accuracy of 0.5 mu m. Experimental results obtained in this paper are proofed, by compared with FEM numerical simulations.

Real-Time Measurement on Deformation Fields of Notched Samples Under Impact Tension

In this paper, a real-time and in situ optical measuring system is reported to observe high-velocity deformations of samples subjected to impact loading. The system consists of a high-speed camera, a He-Ne laser, a frame grabber, a synchronization device and analysis software based on digital correlation theory. The optical system has been adapted to investigate the dynamic deformation field and its evolution in notched samples loaded by an split Hopkinson tension bar, with a resolution of 50 pin and an accuracy of 0.5 mum. Results obtained in experiments are discussed and compared with numerical simulations. It is shown that the measuring system is effective and valid.

Real-Time Measurement on Deformation Fields of Hole-Excavated Samples under Impact Tension

In this paper, the real-time deformation fields are observed in two different kinds of hole-excavated dog-bone samples loaded by an SHTB, including single hole sample and dual holes sample with the aperture size of 0.8mm. The testing system consists of a high-speed camera, a He-Ne laser, a frame grabber and a synchronization device with the controlling accuracy of I microsecond. Both the single hole expanding process and the interaction of the two holes are recorded with the time interval of 10 mu s. The observed images on the sample surface are analyzed by newly developed software based on digital correlation theory and a modified image processing method. The 2-D displacement fields in plane are obtained with a resolution of 50 mu m and an accuracy of 0.5 mu m. Experimental results obtained in this paper are proofed, by compared with FEM numerical simulations.

Analysis of super compact finite difference method and application to simulation of vortex-shock interaction

Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures. In this paper a super compact finite difference method (SCFDM) is presented, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison shows that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge-Kutta method for approximation of the compressible Navier-Stokes equations, is used to solve the complex flow structures induced by vortex-shock interactions. The basic nature of the near-field sound generated by interaction is studied.

A multi-frame image super-resolution method

Multi-frame image super-resolution (SR) aims to utilize information from a set of low-resolution (LR) images to compose a high-resolution (HR) one. As it is desirable or essential in many real applications, recent years have witnessed the growing interest in the problem of multi-frame SR reconstruction. This set of algorithms commonly utilizes a linear observation model to construct the relationship between the recorded LR images to the unknown reconstructed HR image estimates. Recently, regularization-based schemes have been demonstrated to be effective because SR reconstruction is actually an ill-posed problem. Working within this promising framework, this paper first proposes two new regularization items, termed as locally adaptive bilateral total variation and consistency of gradients, to keep edges and flat regions, which are implicitly described in LR images, sharp and smooth, respectively. Thereafter, the combination of the proposed regularization items is superior to existing regularization items because it considers both edges and flat regions while existing ones consider only edges. Thorough experimental results show the effectiveness of the new algorithm for SR reconstruction. (C) 2009 Elsevier B.V. All rights reserved.

Real-time counting of single electron tunneling through a T-shaped double quantum dot system

Real-time detection of single electron tunneling through a T-shaped double quantum dot is simulated, based on a Monte Carlo scheme. The double dot is embedded in a dissipative environment and the presence of electrons on the double dot is detected with a nearby quantum point contact. We demonstrate directly the bunching behavior in electron transport, which leads eventually to a super-Poissonian noise. Particularly, in the context of full counting statistics, we investigate the essential difference between the dephasing mechanisms induced by the quantum point contact detection and the coupling to the external phonon bath. A number of intriguing noise features associated with various transport mechanisms are revealed.

小麦抗禾谷孢囊线虫（ Heterodera avenae）相关基因的研究

禾谷孢囊线虫严重影响禾谷类作物的产量，在小麦中由禾谷孢囊线虫引起的产量损失可达30-100%。尤其在澳大利亚、欧洲、印度和中东危害严重，目前禾谷孢囊线虫已成为危害我国作物的主要病源。控制禾谷孢囊线虫的方法主要有：作物轮作、杀线虫剂、寄主抗性等等，其中基因工程方法培育抗线虫小麦品种被认为是最经济有效的方法。分离抗禾谷类孢囊线虫基因对揭示抗性基因结构与功能及其表达调控具有重要意义。 尽管小麦是重要的粮食作物，在小麦中已发现的抗禾谷孢囊线虫的基因很少，而比其近缘属如节节麦、易变山羊草、偏凸山羊草中含有丰富的抗源。目前已鉴定出禾谷孢囊线虫抗性位点Cre，并发现了9个禾谷孢囊线虫抗性基因(Cre1,2, 3, 4, 5, 6, 7, 8, and R) ，其中只有Cre1和Cre8直接从普通小麦中获得。从节节麦中获得的Cre3基因能最有效的控制线虫数量，其次是Cre1和Cre8。这些基因的克隆对于了解禾谷孢囊线虫抗性机制及进一步的育种应用都是非常关键的。然而，目前为止仅有Cre3基因通过图位克隆的方法从节节麦中被分离得到。该基因已被克隆得到的多数线虫抗性基因一样均属于核苷酸结合位点区（NBS）－亮氨酸重复序列区（LRR）基因家族。目前，已有很多抗性基因被分离，这些已知的NBS-LRR类抗性基因的保守序列为应用PCR的方法克隆新的抗性基因提供了可能。 因此本课题的目的是采用保守区同源克隆、3′RACE 和5′RACE 等方法从抗禾谷孢囊线虫小麦-易变山羊草小片段易位系E10 中克隆小麦抗禾谷孢囊线虫基因全序列，进而通过半定量PCR 和荧光定量PCR 研究该基因的表达模式。同时通过mRNA 差别显示技术和任意引物PCR（RAP-PCR）技术分离克隆植物禾谷孢囊线虫抗性基因及其相关基因，为阐明植物抗病性分子机制以及改良作物抗病性和作物育种提供基础，为通过分子标记辅助育种和基因工程方法实现高效、定向转移抗病基因到优良小麦品种奠定了重要的理论和物质基础。主要研究结果： 1． 本实验根据此前从抗禾谷孢囊线虫材料E-10 扩增得到的与来自节节麦的抗禾谷孢囊线虫Cre3 基因及其他的NBS-LRR 类抗性基因的NBS 和LRR 保守区序列设计了两对特异性引物，从E10 中扩增到532bp 和1175bp 的两个目标条带，它们有一个32bp 的共同序列，连接构成总长为1675bp 的NBS-LRR 编码区（命名为RCCN）。根据RCCN设计引物，利用NBS-LRR区序列设计引物，通过5′RACE 和3′RACE 技术采用3′-Full RACE Core Set(TaKaRa)和5'-Full RACE Kit (TaKaRa)试剂盒，反转录后通过嵌套引物GSP1 和GSP2 分别进行两轮基因特异性扩增，分别将NBS_LRR 区向5′端和3′端延伸了1173bp 和449bp，并包含了起始密码子和终止密码子。根据拼接的得到的序列重新设计引物扩增进行全基因扩增的结果与上面获得的一致。拼接后得到全长2775 bp 的基因序列（记作CreZ, GenBank 号：EU327996）。CreZ 基因包括完整的开放阅读框，全长2775 bp，编码924个氨基酸。序列分析表明它与已知的禾谷孢囊线虫抗性基因Cre3的一致性很高，并且它与已经报到的NBS-LRR 类疾病抗性基因有着相同的保守结构域。推测CreZ基因可能是一个新的NBS-LRR 类禾谷孢囊线虫抗性基因，该基因的获得为通过基因工程途径培育抗禾谷孢囊线虫小麦新品种奠定了基础，并为抗禾谷孢囊线虫基因的调控表达研究提供了参考。 2． 通过半定量PCR和SYBR Green荧光定量PCR技术对CreZ基因的相对表达模式进行了研究。以α-tubulin 2作为参照，采用半定量PCR 分析CreZ 基因在不同接种时期1d, 5d, 10, 15d 的E-10的根和叶的的表达情况。在内参扩增一致的条件下，CreZ 在E-10的根部随着侵染时间的增加表达量有明显的增加，在没有侵染的E-10的根部其表达量没有明显变化，而在叶中没有检测表达，说明该基因只在抗性材料的根部表达。SYBR Green定量PCR分析接种前后E10根部基因CreZ基因的表达水平为检测CreZ基因的表达建立了一套灵敏、可靠的SYBRGreen I 荧光定量PCR 检测方法。接种禾谷孢囊线虫后E10根内CreZ基因的相对表达水平显著高于接种前。随接种时间的延长持续增加，最终CreZ基因的相对表达量达到未接种的对照植株的10.95倍。小麦禾谷孢囊线虫抗性基因CreZ的表达量与胁迫呈正相关，表明其与小麦的的禾谷孢囊线虫抗性密切相关，推测CreZ基因可能是一个新的禾谷孢囊线虫候选抗性基因。 3． 针对小麦基因组庞大、重复序列较多，禾谷孢囊线虫抗性基因及其相关基因的片断难以有效克隆的问题，通过mRNA 差别显示技术及RAP-PCR 技术分离克隆植物禾谷孢囊线虫抗性及其相关基因。试验最终得到154 条差异表达条带，将回收得到的差异条带的二次PCR 扩增产物经纯化后点到带正电的尼龙膜上，进行反向Northern 杂交筛选，最终筛选得到102 个阳性差异点。将其中81 个进行测序，并将序列提交到Genbank 中的dbEST 数据库，分别获得登录号(FE192210 -FE192265，FE193048- FE193074 )。序列比对分析发现，其中26 个序列与已知功能的基因序列同源；有28 条EST 序列在已有核酸数据库中未找到同源已知基因和EST，属新的ESTs 序列；另外27 个EST 序列与已知核酸数据库中的ESTs 具有一定相似性，但功能未知。其所得ESTs 序列补充了Genbank ESTs 数据库，为今后进一步开展抗禾谷类孢囊线虫基因研究工作打下了基础。结合本试验功能基因的相关信息，对小麦接种禾谷孢囊线虫后产生的抗性机制进行了探讨。接种禾谷孢囊线虫后植物在mRNA 水平上的应答是相当复杂的，同时植物的抗病机制是一个复杂的过程，涉及到多个代谢途径的相互作用。 The cereal cyst nematode (CCN), Heterodera avenae Woll, causes severe yieldreductions in cereal crops. The losses caused by CCN can be up to 30-100% in somewheat fields. At present, cereal cyst nematode has become the major disease sourcein China and it also damaged heavily in Australia, Europe, India and Middle East.The damage caused by CCN can be mitigated through several methods, includingcrop rotation, nematicide application, cultural practice, host resistance, and others.Of these methods, incorporating resistance genes into wheat cultivars and breedingresistant lines is considered to be the most cost-effective control measure forreducing nematode populations. Although wheat is an economically important crop around the world, far fewergenes resistant to CCN were found in wheat than were detected in its relatives, suchas Aegilops taucchi, Aegilops variabilis and Aegilops ventricosa. Cloning these genesis essential for understanding the mechanism of this resistance and for furtherapplication in breeding. Because of the huge genome and high repeat sequencescontent, the efficient methods to clone genes from cereal crops, are still lacking. A resistance locus, Cre, has been identified and 9 genes resistant to CCN (designatedCre1, 2, 3, 4, 5, 6, 7, 8, and R) have been described, in which Cre1 and Cre8 werederived directly from common wheat. The Cre3 locus, which was derived from Ae.tauschii, has the greatest impact on reducing the number of female cysts, followed byCre1 and Cre8. Cloning these genes is essential for understanding the mechanism ofthis resistance and for further application in breeding. However, to this point, only Cre3, a NBS-LRR disease resistance gene, has been obtained through mappingcloning in Ae. tauschii. The majority of nematode resistance genes cloned so far belong to a super familywhich contains highly conserved nucleotide-binding sites (NBS) and leucine-richrepeat (LRR) domains. To date, many NBS-LRR resistance genes have been isolated.The conserved sequences of these recognized NBS-LRR resistance genes provide thepossibility to isolate novel resistance genes using a PCR-based strategy. The aim of the present study was to clone the resistance gene of CCN fromWheat/Aegilops variabilis small fragment chromosome translocation line E10 whichis resistant to CCN and investigate the espression profiles of this gene withsemi-quantitative PCR and real-time PCR. Another purpose of this study is cloningthe relational resistance gene for CCN by mRNA differential display PCR andRAP-PCR. These works will offer a foundation for disease defence of crop andbreeding and directional transferring resistance gene into wheat with geneengineering. Primary results as following: 1．According to the conversed motif of NBS and LRR region of cereal cystnematode resistance gene Cre3 from wild wheat (Triticum tauschlii) and the knownNBS-LRR group resistance genes, we designed two pairs of specific primers for NBSand LRR region respectively. One band of approximately 530bp was amplified usingthe specific primers for conversed NBS region and one band of approximately 1175bpwas amplified with the specific primers for conversed LRR region. After sequencing,we found that these two sequences included 32bp common nucleotide having 1675bpin total, which was registered as RCCN in the Genbank. Based on the conservedregions of known resistance genes, a NBS-LRR type CCN resistance gene analog wasisolated from the CCN resistant line E-10 of the wheat near isogenic lines (NILs), by5′RACE and 3′ RACE.designated as CreZ (GenBank accession number: EU327996) .It contained a comlete ORF of 2775 bp and encoded 924 amino acids. Sequencecomparison indicated that it shared 92% nucleotide and 87% amino acid identitieswith those of the known CCN-resistance gene Cre3 and it had the same characteristic of the conserved motifs as other established NBS-LRR disease resistance genes. 2． Usingα-tubulin 2 as exoteric reference, semi-quantitative PCR and real-timePCR analysis were conducted. The expression profiling of CreZ indicated that it wasspecifically expressed in the roots of resistant plants and its relative expression levelincreased sharply when the plants were inoculated with cereal cyst nematodes. therelative expression level of the 15days-infected E10 is the 10.95 times as that ofuninfected E10,ultimately. It was inferred that the CreZ gene be a novel potentialresistance gene to CCN. 3．We cloned the relational resistance gene for CCN by mRNA differentialdisplay PCR and arbitrarily primed PCR fingerprinting of RNA from wheat whichpossess huge and high repeat sequence content genomes. Total 154 differentialexpression bands were separated and second amplified by PCR. The products werenylon membrane. The 102 positive clones were filtrated by reverse northern dot blotand 81 of those were sent to sequence. The EST sequences were submitted toGenbank (Genbank accession: FE192210 - FE192265, FE193048 - FE193074). Thesequences alignment analysis indicated 26 of them were identical with known genes;28 were not found identical sequence in nucleic acid database; another 27 ests wereidentical with some known ests, but their functions were not clear. These ESTsenriched Genbank ESTs database and offered foundation for further research ofresistance gene of CCN.

基于精细结构描述及数值试验的断续节理岩体力学参数智能选取

Evaluating the mechanical properties of rock masses is the base of rock engineering design and construction. It has great influence on the safety and cost of rock project. The recognition is inevitable consequence of new engineering activities in rock, including high-rise building, super bridge, complex underground installations, hydraulic project and etc. During the constructions, lots of engineering accidents happened, which bring great damage to people. According to the investigation, many failures are due to choosing improper mechanical properties. ‘Can’t give the proper properties’ becomes one of big problems for theoretic analysis and numerical simulation. Selecting the properties reasonably and effectively is very significant for the planning, design and construction of rock engineering works. A multiple method based on site investigation, theoretic analysis, model test, numerical test and back analysis by artificial neural network is conducted to determine and optimize the mechanical properties for engineering design. The following outcomes are obtained: (1) Mapping of the rock mass structure Detailed geological investigation is the soul of the fine structure description. Based on statistical window，geological sketch and digital photography，a new method for rock mass fine structure in-situ mapping is developed. It has already been taken into practice and received good comments in Baihetan Hydropower Station. (2) Theoretic analysis of rock mass containing intermittent joints The shear strength mechanisms of joint and rock bridge are analyzed respectively. And the multiple modes of failure on different stress condition are summarized and supplied. Then, through introducing deformation compatibility equation in normal direction, the direct shear strength formulation and compression shear strength formulation for coplanar intermittent joints, as well as compression shear strength formulation for ladderlike intermittent joints are deducted respectively. In order to apply the deducted formulation conveniently in the real projects, a relationship between these formulations and Mohr-Coulomb hypothesis is built up. (3) Model test of rock mass containing intermittent joints Model tests are adopted to study the mechanical mechanism of joints to rock masses. The failure modes of rock mass containing intermittent joints are summarized from the model test. Six typical failure modes are found in the test, and brittle failures are the main failure mode. The evolvement processes of shear stress, shear displacement, normal stress and normal displacement are monitored by using rigid servo test machine. And the deformation and failure character during the loading process is analyzed. According to the model test, the failure modes quite depend on the joint distribution, connectivity and stress states. According to the contrastive analysis of complete stress strain curve, different failure developing stages are found in the intact rock, across jointed rock mass and intermittent jointed rock mass. There are four typical stages in the stress strain curve of intact rock, namely shear contraction stage, linear elastic stage, failure stage and residual strength stage. There are three typical stages in the across jointed rock mass, namely linear elastic stage, transition zone and sliding failure stage. Correspondingly, five typical stages are found in the intermittent jointed rock mass, namely linear elastic stage, sliding of joint, steady growth of post-crack, joint coalescence failure, and residual strength. According to strength analysis, the failure envelopes of intact rock and across jointed rock mass are the upper bound and lower bound separately. The strength of intermittent jointed rock mass can be evaluated by reducing the bandwidth of the failure envelope with geo-mechanics analysis. (4) Numerical test of rock mass Two sets of methods, i.e. the distinct element method (DEC) based on in-situ geology mapping and the realistic failure process analysis (RFPA) based on high-definition digital imaging, are developed and introduced. The operation process and analysis results are demonstrated detailedly from the research on parameters of rock mass based on numerical test in the Jinping First Stage Hydropower Station and Baihetan Hydropower Station. By comparison，the advantages and disadvantages are discussed. Then the applicable fields are figured out respectively. (5) Intelligent evaluation based on artificial neural network (ANN) The characters of both ANN and parameter evaluation of rock mass are discussed and summarized. According to the investigations, ANN has a bright application future in the field of parameter evaluation of rock mass. Intelligent evaluation of mechanical parameters in the Jinping First Stage Hydropower Station is taken as an example to demonstrate the analysis process. The problems in five aspects, i. e. sample selection, network design, initial value selection, learning rate and expected error, are discussed detailedly.

Stress-strain fields and the effectiveness shear properties for three-phase composites with imperfect interface

Based on the 'average stress in the matrix' concept of Mori and Tanaka (:Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusion. Acta Metall. 21, 571-580) a micromechanical model is presented for the prediction of the elastic fields in coated inclusion composites with imperfect interfaces. The solutions of the effective elastic moduli for this kind of composite are also obtained. In two kinds of composites with coated particulates and fibers, respectively, the interface imperfections are takes to the assumption that the interface displacement discontinues are linearly related to interface tractions like a spring layer of vanishing thickness. The resulting effective shear modulus for each material and the stress fields in the composite are presented under a transverse shear loading situation.

Influence of Local Magnetic Fields on P-Doped Si Floating Zone Melting Crystal Growth in Microgravity

A two-dimensional axisymmetric numerical model is presented to study the influence of local magnetic fields on P-doped Si floating zone melting crystal growth in microgravity. The model is developed based on the finite difference method in a boundary-fitted curvilinear coordinate system. Extensive numerical simulations are carried out, and parameters studied include the curved growth interface shape and the magnetic field configurations. Computed results show that the local magnetic field is more effective in reducing the impurity concentration nonuniformity at the growth interface in comparison with the longitudinal magnetic field. Moreover, the curved growth interface causes more serious impurity concentration nonuniformity at the growth interface than the case with a planar growth interface.

DPIV and Interferometry Technique for Velocity Field and Concentration Fields Measurement in Crystal Growth

The property of crystal depends seriously on the solution concentration distribution near the growth surface of a crystal. However, the concentration distributions are affected by the diffusion and convection of the solution. In the present experiment, the two methods of optical measurement are used to obtained velocity field and concentration field of NaClO₃ solution. The convection patterns in sodium chlorate (NaClO₃) crystal growth are measured by Digital Particle image Velocimetry (DPIV) technology. The 2-dimentional velocity distributions in the solution of NaClO3 are obtained from experiments. And concentration field are obtained by a Mach-Zehnder interferometer with a phase shift servo system. Interference patterns were recorded directly by a computer via a CCD camera. The evolution of velocity field and concentration field from dissolution to crystallization are visualized clearly. The structures of velocity fields were compared with that of concentration field.

Elastic fields of interacting elliptic inhomogeneities

This paper presents a method for the calculation of two-dimensional elastic fields in a solid containing any number of inhomogeneities under arbitrary far field loadings. The method called 'pseudo-dislocations method', is illustrated for the solution of interacting elliptic inhomogeneities. It reduces the interacting inhomogeneities problem to a set of linear algebraic equations. Numerical results are presented for a variety of elliptic inhomogeneity arrangements, including the special cases of elliptic holes, cracks and circular inhomogeneities. All these complicated problems can be solved with high accuracy and efficiency.

Nano-Tribological Study on a Super-Hydrophobic Film Formed on Rough Aluminum

A novel super-hydrophobic stearic acid (STA) film with a water contact angle of 166° was prepared by chemical adsorption on aluminum wafer coated with polyethyleneimine (PEI) film. The micro-tribological behavior of the super-hydrophobic STA monolayer was compared with that of the polished and PEI-coated Al surfaces. The effect of relative humidity on the adhesion and friction was investigated as well. It was found that the STA monolayer showed decreased friction, while the adhesive force was greatly decreased by increasing the surface roughness of the Al wafer to reduce the contact area between the atomic force microscope (AFM) tip and the sample surface to be tested. Thus the friction and adhesion of the Al wafer was effectively decreased by generating the STA monolayer, which indicated that it could be feasible and rational to prepare a surface with good adhesion resistance and lubricity by properly controlling the surface morphology and the chemical composition. Both the adhesion and friction decreased as the relative humidity was lowered from 65% to 10%, though the decrease extent became insignificant for the STA monolayer.

Mode I and Mode II Crack Tip Asymptotic Fields with Strain Gradient Effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

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.