Inhomogeneous behavior of antiplane shear crack in softening material with local unloading

Examined in this work is the anti-plane stress and strain near a crack in a material that softens beyond the elastic peak and unloads on a linear path through the initial state. The discontinuity in the constitutive relation is carried into the analysis such that one portion of the local solution is elliptic in character and the other hyperbolic. Material elements in one region may cross over to another as the loading is increased. Local unloading can thus prevail. Presented are the inhomogeneous character of the asymptotic stress and strain in the elliptic and hyperbolic region, in addition to the region in which the material elements had experienced unloading. No one single stress or strain coefficient would be adequate for describing crack instability.

Magnetostatic relations including fluctuation fields - the local expansion

Using the approach of local expansion, we analyze the magnetostatic relations in the case of conventional turbulence. The turbulent relations are obtained consisten tly for themomentum equation and induction equation of both the average and fluctuation relations.In comparison with the magnetostatic relations as discussed usually, turbulent fluctuationfields produce forces, one of which 1/(4π)(α1×B0)×B0 may have parallel and perpendicular components in the direction of magnetic field, the other of which 1/(4π)K×B0 is introduced by the boundary value of turbulence and is perpendicular to the magnetic field. In the case of 2-dimensional configuration of magnetic field, the basic equation will be reduced into a second-order elliptic equation, which includes some linear and nonlinear terms introduced by turbulent fluctuation fields. Turbulent fields may change the configuration of magnetic field and even shear it non-uniformly. The study on the influence of turbulent fields is significant since they are observed in many astrophysical environments.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

Magnetic field configurations of radio jets in the double source of radio galaxy

As an improvement of resolution of observations, more and more radio galaxies with radiojets have been identified and many fine structures in the radio jets yielded. In the presentpaper, the two-dimensional magnetohydrodynamical theory is applied to the analysis of themagnetic field configurations in the radio jefs. Two-dimensional results not only are con-sistent theoretically, but also explain the fine structures of observations. One of the theo-retical models is discussed in detail, and is in good agreement as compared with the observedradio jets of NGC6251. The results of the present paper also show that the magneticfields in the radio jets are mainly longitudinal ones and associate with the double sources ofQSOs if the magnetic field of the central object is stronger; the fields in the radio jets aremainly transverse ones and associate with the double sources of radio galaxies if the fieldof the central object is weaker. The magnetic field has great influence on the morphol-ogy and dynamic process.

The permanence of density waves of galaxy and the numerical investigation of waser mechanism

This paper deals with in detail the permanence of the spiral structure of galaxies andthe characters of waser mechanism. A simplified model of galaxy is adopted. Variousdynamical characters of density waves are studied using numerical calculation method. Theresults verify very well the switch character f waser and the tunnel effect of density wavesat the potential barrier of corotation circle as is shown in a previous work of the author.

Information Preservation (IP) Method in Simulation

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Information preservation (IP) method in simulation of internal rarefied gas flows in MEMS

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands m ? long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( 1000 L m ? = ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( 5 L m ? = ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Analytical calculations of Eulerian and Lagrangian time correlations in turbulent shear flows

The Taylor series expansion method is used to analytically calculate the Eulerian and Lagrangian time correlations in turbulent shear flows. The short-time behaviors of those correlation functions can be obtained from the series expansions. Especially, the propagation velocity and sweeping velocity in the elliptic model of space-time correlation are analytically calculated and further simplified using the sweeping hypothesis and straining hypothesis. These two characteristic velocities mainly determine the space-time correlations.

Computation of flow over a rotating body on unstructured Chimera mesh

Flow around moving boundary is ubiquitous in engineering applications. To increse the efficienly of the algorithm to handle moving boundaries is still a major challenge in Computational Fluid Dynamics (CFD). The Chimera grid method is one type of method to handle moving boundaries. A concept of domain de-composition has been proposed in this paper. In this method, sub-domains are meshed independently and governing equations are also solved separately on them. The Chimera grid method was originally used only on structured (curvilinear) meshes. However, in a problem which involves both moving boundary and complex geometry, the number of sub-domains required in a traditional (structured) Chimera method becomes fairly large. Thus the time required in the interior boundary locating, link-building and data exchanging also increases. The use of unstructured Chimera grid can reduce the time consumption significantly by the reduction of domain(block) number. Generally speaking, unstructured Chimera grid method has not been developed. In this paper, a well-known pressure correction scheme - SIMPLEC is modified and implemented on unstructured Chimera mesh. A new interpolation scheme regarding the pressure correction is proposed to prevent the possible decoupling of pressure. A moving-mesh finite volume approach is implemented in an inertial reference frame. This approach is then used to compute incompressible flow around a rotating circular and elliptic cylinder. These numerical examples demonstrate the capability of the proposed scheme in handling moving boundaries. The numerical results are in good agreement with other experimental and computational data in literature. The method proposed in this paper can be efficiently applied to more challenge cases such as free-falling objects or heavy particles in fluid.

Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil

The hydrodynamics of a free flapping foil is studied numerically. The foil undergoes a forced vertical oscillation and is free to move horizontally. The effect of chord-thickness ratio is investigated by varying this parameter while fixing other ones such as the Reynolds number, the density ratio, and the flapping amplitude. Three different flow regimes have been identified when we increase the chord-thickness ratio, i.e., left-right symmetry, back-and-forth chaotic motion, and unidirectional motion with staggered vortex street. It is observed that the chord-thickness ratio can affect the symmetry-breaking bifurcation, the arrangement of vortices in the wake, and the terminal velocity of the foil. The similarity in the symmetry-breaking bifurcation of the present problem to that of a flapping body under constraint is discussed. A comparison between the dynamic behaviors of an elliptic foil and a rectangular foil at various chord-thickness ratios is also presented.

Space-time correlations of fluctuating velocities in turbulent shear flows

Space-time correlations or Eulerian two-point two-time correlations of fluctuating velocities are analytically and numerically investigated in turbulent shear flows. An elliptic model for the space-time correlations in the inertial range is developed from the similarity assumptions on the isocorrelation contours: they share a uniform preference direction and a constant aspect ratio. The similarity assumptions are justified using the Kolmogorov similarity hypotheses and verified using the direct numerical simulation DNS of turbulent channel flows. The model relates the space-time correlations to the space correlations via the convection and sweeping characteristic velocities. The analytical expressions for the convection and sweeping velocities are derived from the Navier-Stokes equations for homogeneous turbulent shear flows, where the convection velocity is represented by the mean velocity and the sweeping velocity is the sum of the random sweeping velocity and the shearinduced velocity. This suggests that unlike Taylor’s model where the convection velocity is dominating and Kraichnan and Tennekes’ model where the random sweeping velocity is dominating, the decorrelation time scales of the space-time correlations in turbulent shear flows are determined by the convection velocity, the random sweeping velocity, and the shear-induced velocity. This model predicts a universal form of the spacetime correlations with the two characteristic velocities. The DNS of turbulent channel flows supports the prediction: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

外差干涉仪混频误差分析

共光路外差干涉仪具有很高的分辨率．但因为安装、调试误差会产生非线性误差．影响系统的测量精度。着重分析了在共光路外差干涉仪中由激光光源的椭圆偏振化和沃拉斯顿棱镜的安装方位角误差同时存在的情况下，引起的频率混叠综合误差的大小及变化规律。结果发现其造成的非线性误差可达2．2nm，同时还发现两者造成的误差在某些情况下存在一定程度的相互抵消作用。讨论了提高测量系统精度的有效措施，对正确设计和调试激光外差测试系统、提高测量系统精度具有重要意义。

小麦春化相关基因元件克隆分析与小麦矮化突变体的研究

一、 春化相关基因全长cDNA序列及其启动子的克隆与分析研究 通过建立小麦（Triticum aestivum. L. cv Jingdong No.1）胚芽春化cDNA文库，以春化相关基因VER2的3’端序列为探针，筛选获得全长1195 bp cDNA序列，它编码300个氨基酸。在VER2中存在植物疾病抗性反应蛋白和茉莉酸诱导凝集素两种蛋白的结构域。另外在VER2蛋白中存在核定位信号和多种磷酸酶的作用位点，VER2可能参与了多种调控途径。 以VER2基因的cDNA为探针，利用改进的池式PCR以及高密度膜杂交筛选的方法，从小麦TAC基因组文库中获得41,788 bp的基因组克隆，该序列含有11个基因，其中VER2基因位于第三个基因。VER2基因组序列含有3个内含子，4个外显子与cDNA序列100%同源。通过对转录起始点和转录终止点的分析，进一步证明从cDNA文库筛选得到的VER2基因为全长序列。 对VER2基因的上游启动子区域进行分析，发现基因上游启动子区存在三个小的重复序列，每个片段有482 bp，另有两个较大的重复序列，每个片段有2,161 bp。对上游2.8 kb启动子区（不含重复序列）的响应元件分析，其包括ABA响应元件（ABRE）、茉莉酸甲酯响应元件（Me-JARE）、胚乳特异性表达元件、参与淀粉酶合成的元件以及存在类似GA响应元件（ATAACAAAC）如ATAACATAC等等。根据VER2基因上游6 kb序列结构特点，将VER2启动子区域进行缺失突变形成10个片段，分别以GUS和GFP为报告基因构建成瞬间表达载体和植物表达载体等四类质粒。通过基因枪方法将最大片段（6 kb）驱动GFP报告基因的瞬间表达载体转入经春化处理或未春化处理的小麦幼叶中，结果发现GFP在春化处理的幼叶中表达，而在未春化处理的幼叶中不表达，说明VER2基因的启动子驱动基因转录受春化处理调控。 二、 小麦矮化突变体的研究 通过对小麦矮化突变体gaid遗传生理分析发现该突变体为半显性阻断GA信号途径，由此发现在赤霉素信号途径中，α-淀粉酶的诱导一定程度上通过某些与株高相关的基因控制。突变体gaid呈现对高浓度的脱落酸更敏感，当ABA浓度达到10-6M时，突变体的生长几乎完全受到了抑制，而野生型的生长需要ABA浓度达到10-5M时才能完全受到抑制。通过突变体gaid对乙烯等抑制型生长调节剂的响应实验研究，首次提出GA调控植物伸长生长存在两条信号途径，即GA基础水平信号途径（GA basal level signaling pathway）和GA正常水平信号途径（GA normal level signaling pathway），而乙烯以及高浓的GA合成抑制剂（如PAC）是通过第一条途径（GA基础水平信号途径）起作用。光形态建成中对植株生长的抑制作用存在独立于GA的信号途径。 突变体gaid的根系在强光照（63.5 Es-1m-2）和培养基内（低氧）的生长条件下，表现出弯曲、变短、加粗等异常性状，而随光照强度的减弱，这种根系异常生长的表型也减弱，在暗培养中则完全消失，但无论在哪种环境条件下，相对野生型对照而言，突变体的种子根短、侧根少。低浓度的ABA（10-8M）可以恢复突变体gaid根系在强光低氧条件下的正常生长发育。然而利用IAA及其极性运输的抑制剂（TIBA）、乙烯生物合成前提物（ACC）及合成抑制剂（AOA）处理突变体gaid，并没有发现突变体根系的生长发育得到恢复。 突变体gaid可能是一个新的属于小麦GA信号途径中的负调控基因（GAID）发生了突变或超表达，导致其负调控作用增强，呈现半显性的矮化突变。在与另一已知小麦GA信号途径中的负调控基因RHT的关系研究上发现，GAID可能对RHT蛋白磷酸化后的降解途径起抑制作用。通过双向电泳发现突变体gaid与野生型对照（京冬1号）在生长过程中存在差异蛋白，这将有助于对GA信号途径分子机理的深入研究。

一类Koblitz椭圆曲线的快速点乘

考虑一类特征3的Koblitz椭圆曲线的快速点乘算法.在这类曲线上适合建立低带宽的、可证明安全的密码体制.结果显示,利用这类曲线的复乘性质,使用模约减和Frobenius展开技巧,这类曲线上存在一种不带预计算的快速点乘算法,其运算速度是通常的重复加倍-点加算法的6倍.该算法的快速优化原理与有限域算术优化和椭圆曲线点的坐标表示的选取无关.