不分裂卷积完全匹配层与旋转交错网格有限差分在孔隙弹性介质模拟中的应用

完全匹配层吸收边界在地震波模拟中已广泛使用,但常用的场分裂格式完全匹配层吸收边界(SPML)和传统的不分裂完全匹配层吸收边界(NPML)对极低频入射波或大角度入射波的边界吸收效果不好.一种无需分裂和显式卷积计算的完全匹配层吸收边界(CPML)不仅能够解决常规PML吸收边界的不足,而且具有存储量小、计算效率高、易于编程实现的特点.本文将这种完全匹配层(CPML)吸收边界引入到孔隙弹性介质速度应力格式的旋转交错网格有限差分算法中,对完全匹配层吸收边界参数进行数值分析,得到一组优化的参数.孔隙弹性介质数值模拟结果表明这种不分裂卷积完全匹配层的吸收效果优于常规完全匹配层.

探地雷达FDTD数值模拟中不分裂卷积完全匹配层对倏逝波的吸收效果研究

介绍了CPML边界条件的原理,推导了CPML的GPR正演FDTD差分公式,对比分析了Berenger PML、UPML、CPML三种PML对倏逝波的吸收性能.开展了PML边界中关键参数κ和α的选取实验,确定了参数的取值范围与选取原则.然后,以二维TM波为例,研究了倏逝波产生的机理,分析了决定逝波性吸收性能的影响因素.均匀介质的波场快照、检测点的反射误差及全局反射误差对比,说明了3种边界条件对传输波都具有较好的吸收能力,而对低频倏逝波的吸收表现迥异,其中CPML因为引入了参数α,对倏逝波的吸收效果最佳,但离散化造成的全域误差也最大.最后,应用加载UPML和CPML边界条件的FDTD程序,开展了GPR二维剖面法、宽角法矩状地电模型及三维复杂模型的正演,展示了倏逝波反射对雷达正演剖面及波场快照的影响.进一步对比了UPML与CPML对倏逝波的吸收表现优劣,结果显示,CPML可有效减少边界反射误差,并能取得满意的精度,综合考虑对倏逝波的吸收、全域误差、编程难易程度等因素,在GPR正演中推荐使用CPML.

Euler方法中的不分裂输运算法

为解决用Euler方法求解多种介质的流体力学问题时,物质的输运中维数分裂算法容易出现重复或遗漏的问题,以Youngs界面重构技术为基础,输运步中采用维数不分裂算法,除了考虑相邻4个网格的输运外,同时还考虑斜对角网格的输运计算,有效地解决了消除重复或遗漏输运的问题.论证了不分裂算法的合理性,给出了向相邻8个网格输运的所有可能分配量的表达式.数值模拟结果表明,不分裂输运算法的精度有所提高.

基于不分裂算法的Euler网格细分方法

对考虑多物质相互作用的爆炸冲击数值模拟,Euler型流体动力学方法是最有效的方法之一。采用维数不分裂算法处理Euler坐标下的纯物质网格,混合网格在Youngs界面重构技术的基础上进行细分,消除混合网格复杂的输运计算。对纯物质网格和细分后网格,都具体给出了往相邻8个网格输运的所有可能分配量的表达式。最后将该方法加入到自行开发的MMIC-2D通用多物质二维爆炸与冲击问题数值仿真程序中,数值算例显示该方法不仅能有效地提高计算精度,同时能降低问题的计算工作量,节省计算时间。

计算体积分数函数的Youngs不分裂算法

为提高有交界面流动问题的计算精度 ,通过引入不分裂的界面推进 ,对现有的 Youngs算法 (流体体积法的一种 )进行改进 ,推导其算法公式。在此基础上 ,分别用 Donor-Acceptor算法、分裂和不分裂的 Youngs算法计算典型算例。几种计算结果比较后表明 :不分裂 Youngs算法在空间和时间上都具有较高精度 。

多轴完全匹配层的非分裂实现

完全匹配层吸收边界(PML)已经被证明是非常有效的边界吸收技术,对体波和面波的吸收都具有非常好的效果,已经被广泛应用于弹性波的数值模拟中.但是在某些情况下传统的PML和C-PML(卷积完全匹配层)还是存在一定的问题,比如在一些介质中有固有的不稳定性等等.基于分裂的多轴完全匹配层(M-PML)通过引入多个衰减剖面可以有效地消除不稳定的现象.本文采用C-PML中不分裂的递推卷积方法,对M-PML进行了实现,这样在实现过程中不用分裂变量,与原来的分裂方法相比,直观易懂,方便简单,易于编程,而且可以减少计算量和存储量,节约计算成本.基于一阶速度-应力方程,采用交错网格高阶有限差分法对不同的介质模型进行了数值模拟,结果证明了本文的不分裂M-PML可以消除不稳定性,得到比较好的计算结果.

同轴两个气泡融合特性的数值研究

为了进一步研究气泡融合特性以及开发高效的界面追踪程序,以PLIC界面重构技术为基础,采用不分裂算法计算了目标网格向周围26个网格的输运流量;采用统一的表达式计算输运流量,大大降低了程序编写的难度。将PLIC算法与气液两相流动控制方程相结合,数值计算了直径为0.8～14mm的单个气泡的最终运动速度,模拟结果与文献中的实验结果吻合良好。研究了同轴两个气泡的融合过程,发现表面张力很大时,两个气泡近似独立运动,不发生融合;表面张力很小时,气泡容易发生破碎;气泡发生严重破碎时,尾部气泡会从顶部气泡的轴心穿过;液体黏度与表面张力对气泡融合时间的影响不是单调的。

基于旋转交错网格的双相各向异性介质二维三分量波场模拟

基于Biot双相介质模型,推导了双相TTI介质二维三分量一阶速度-应力弹性波方程,采用旋转交错网格(RSG)技术建立了各向异性孔隙介质波动方程的二维三分量高精度有限差分格式(FDTD),并引入不分裂卷积完全匹配层(CPML)作为吸收边界条件。为了验证算法可行性,对均匀双相TTI介质中的弹性波场进行了模拟。结果表明:使用旋转交错网格有限差分技术能够模拟出双相TTI介质中存在的快横波、慢横波、快纵波和慢纵波;双相各向异性介质中存在明显的横波分裂、波前面尖角和三分叉现象;不分裂卷积完全匹配层对边界反射的吸收效果较好。通过对比传统交错网格(SSG)和旋转交错网格有限差分技术,证明了旋转交错网格有限差分算法稳定性较强,精度较高,是一种实用的地震波场数值模拟方法。

三维空间PLIC VOF算法研究

在对二维VOF算法的研究基础上,开发了三维空间下基于Youngs液面假设的界面重构算法,开发了基于算子不分裂的流体运动算法,从而形成了整套的三维空间分段线性界面前沿确定算法,称之为PLIC VOF算法。编写程序对多种界面重构情况进行验证,并通过方腔模拟结果对比与压射水实验模拟结果对比,对整套算法进行了验证,证明了该算法具备良好的界面前沿捕捉能力。

CPML条件下黏弹介质地震波传播的有限差分模拟与特征分析

在波动方程有限差分波场数值模拟中,为了使计算得到的边界波场值更接近于真实的边界波场值,需要使用边界条件以减少来自计算区域边界的人为反射能量。传统的分裂式完全匹配层(SPML)吸收边界条件不能有效吸收掠射波,后来发展的不分裂卷积完全匹配层(CPML)能够较好地处理这个问题,并且CPML在处理边界问题时无需对波场进行非物理分裂。本文针对Kelvin-Voigt模型的黏弹性介质,采用高阶交错网格有限差分方法进行数值模拟,同时利用CPML吸收边界条件进行边界处理。数值模拟结果表明:与弹性波相比,大角度入射产生的低频掠射波对黏弹性波的影响更大;CPML吸收边界条件对低频掠射波的吸收效果比传统的SPML吸收边界条件更好。

In vitro Plant Regeneration of Pepper Cytoplasmic Male Sterility (CMS) Lines via Cotyledon Culture

An in vitro shoot regeneration procedure was developed in pepper （ Capsicum annuum L. ） cytoplasmic male sterility （CMS） lines 9704A and 8214A using cotyledon as explant. The callus and bud cluster derived from cotyledon tissue explants were proliferated on Murashige and Skoog （MS） medium supplemented with different combinations of 6-benzladenine （6-BA）, indole-3-acetic acid （IAA）, gibberellic acid （GA3） and silver nitrate （AgNO3）. From the formula of MS appended with 5.0 mg/L 6-BA, 1.0 mg/L IAA and 5.0 mg/L AgNO3, for the explants callus and bud cluster, the maximum differentiation rates （ respectively 100.0% and 58.3% ） and average number of adventitious bud from each explant （respectively 18.8 and 13.2） were obtained. The optimum medium combination for the elongation of adventitious bud was determined to be： MS ＋ 3.0 mg/L 6-BA ＋ 1.0 mg/L IAA ＋ 5.0 mg/L AgNO3 ＋ 2.0 mg/L GA3, from which the elongation rates of buds from callus and bud cluster were both 100%, and the average number of per explant adventitious bud number reached 6.3 and 5.8, respectively. And all the elongated shoots were successfully rooted on half-strength MS medium supplemented with 0.3-0.5 mg/L IAA.

Effects of MEK inhibitor U0126 on meiotic progression in mouse oocytes: microtuble organization, asymmetric division and metaphase Ⅱ arrest

In this study we used U0126, a potent and specific inhibitor of MEK, to study the roles of MEK/ERK/p90rsk signaling pathway in the meiotic cell cycle of mouse oocytes. The phosphorylation of MAP kinase and p90rsk in the oocytes treated with 1.5 μMU0126 was the same as that in oocytes cultured in drug-free medium. With 1.5 μM U0126 treatment, the spindles appeared normal as they formed in oocytes, but failed to maintain its structure.Instead, the spindle lost one pole or elongated extraordinarily. After further culture, some oocytes extruded gigantic polar bodies (＞30 μm) that later divided into two small ones. Some oocytes underwent symmetric division and produced two equal-size daughter cells in which normal spindles formed. In oocytes with different division patterns,MAP kinase was normally phosphorylated. When the concentration of U0126 was increased to 15 mM, the phosphorylation of both MAPK and p90rsk were inhibited, while symmetric division was decreased. When incubating in medium containing 15 μM U0126 for 14 h, oocytes were activated, but part of them failed to emit polar bodies. MII oocytes were also activated by 15 μM U0126, at the same time the dephosphorylation of MAP kinase and p90rsk was observed. Our results indicate that 1) MEK plays important but not indispensable roles in microtubule organization;2) MEK keeps normal meiotic spindle morphology, targets peripheral spindle positioning and regulates asymmetric division by activating some unknown substrates other than MAP kinase/p90rsk; and 3) activation of MEK/ERK/p90rsk cascade maintains MII arrest in mouse oocytes.

Tripartite Splitting Arbitrary 2-Qubit Quantum Information by Using Two Asymmetric W States

In this paper we propose a tripartite scheme for splitting an arbitrary 2-qubit quantum information by using two asymmetric W states as the quantum channel. In the schemem if the two recipients collaborate together, they can deterministically recover the quantum information by performing first a 4-qubit collective unitary operation and then two single-qubit unitary operations. In addition, since the asymmetric W states are employed as the quantum channel, the scheme is robust against decoherence.

Asymmetric breakup of a droplet in an axisymmetric extensional flow

The asymmetric breakups of a droplet in an axisymmetric cross-like microfluidic device are investigated by using a three-dimensional volume of fluid(VOF) multiphase numerical model. Two kinds of asymmetries(droplet location deviation from the symmetric geometry center and different flow rates at two symmetric outlets) generate asymmetric flow fields near the droplet, which results in the asymmetric breakup of the latter. Four typical breakup regimes(no breakup, one-side breakup, retraction breakup and direct breakup) have been observed.Two regime maps are plotted to describe the transition from one regime to another for the two types of different asymmetries, respectively. A power law model, which is based on the three critical factors(the capillary number,the asymmetry of flow fields and the initial volume ratio), is employed to predict the volume ratio of the two unequal daughter droplets generated in the direct breakup. The influences of capillary numbers and the asymmetries have been studied systematically in this paper. The larger the asymmetry is, the bigger the oneside breakup zone is. The larger the capillary number is, the more possible the breakup is in the direct breakup zone. When the radius of the initial droplet is 20 μm, the critical capillary numbers are 0.122, 0.128, 0.145,0.165, 0.192 and 0.226 for flow asymmetry factor AS= 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5, respectively, in the flow system whose asymmetry is generated by location deviations. In the flow system whose asymmetry is generated by two different flow rates at two outlets, the critical capillary numbers are 0.121, 0.133, 0.145, 0.156 and 0.167 for AS= 1/21, 3/23, 1/5, 7/27 and 9/29, respectively.

The variational inequality formulation for unconfined seepage through three-dimensional dense fracture networks

The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes,i.e.,seepage paths.After triangulation on these polygons,a finite element mesh for 3D fracture network seepage is obtained.Through introduction of the generalized Darcy's law,conservative equations for both fracture surface and fracture interactions are established.Combined with the boundary condition of Signorini's type,a partial differential equation(PDE) formulation is presented for the whole domain concerned.To solve this problem efficiently,an equivalent variational inequality(VI) formulation is given.With the penalized Heaviside function,a finite element procedure for unconfined seepage problem in 3D fracture network is developed.Through an example in a homogeneous rectangular dam,validity of the algorithm is verified.The analysis of an unconfined seepage problem in a complex fracture network shows that the proposed algorithm is very applicable to complex three-dimensional problems,and is effective in describing some interesting phenomenon usually encountered in practice,such as "preferential flow".

A Note on Heegaard Splittings of Amalgamated 3-Manifolds

Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi∪Hi Wi with d（H1） ＋ d（H2） ≥ 2（g（M0 ＋ g（M2） - g（F）） ＋ 1, then g（M） = g（M1） ＋ g（M2） - g（F）.

The -Stabilization of a Heegaard Splitting with Distance at Least 6 is Unstabilized

Let M be a compact orientable 3-manifold with 0M connected. If V Us W is a Heegaard splitting of M with distance at least 6, then the 0-stabilization of V Us W along OM is unstabilized. Hence M has at least two unstabilized Heegaard splittings with different genera. The basic tool is a result on disk complex given by Masur and Schleimer.

A new variational inequality formulation for unconfined seepage flow through fracture networks

Darcy's law only applying to the flow domain is extended to the entire fracture network domain including the dry domain.The partial differential equation(PDE) formulation for unconfined seepage flow problems for discrete fracture network is established,in which a boundary condition of Signorini's type is prescribed over the potential seepage surfaces.In order to reduce the difficulty in selecting trial functions,a new variational inequality formulation is presented and mathematically proved to be equivalent to the PDE formulation.The numerical procedure based on the VI formulation is proposed and the corresponding algorithm has been developed.Since a continuous penalized Heaviside function is introduced to replace a jump function in finite element analysis,oscillation of numerical integration for facture elements cut by the free surface is eliminated and stability of numerical solution is assured.The numerical results from two typical examples demonstrate,on the one hand the effectiveness and robustness of the proposed method,and on the other hand the capability of predicting main seepage pathways in fractured rocks and flow rates out of the drainage system,which is very important for performance assessments and design optimization of complex drainage system.

On the hyperbolicity of flows

Let X be a C1 vector field on a compact boundaryless Riemannian manifold M（dim M≥2）,and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = Es Eu with Es uniformly contracting and Eu uniformly expanding.We prove that if,in addition,A is chain transitive,then the hyperbolic splitting is continuous,i.e.,A is a hyperbolic set.In general,when A is not necessarily chain transitive,the chain recurrent part is a hyperbolic set.Furthermore,we show that if the whole manifold M admits a hyperbolic splitting,then X has no singularity,and the flow is Anosov.

Review of controlled clinical trials on acupuncture versus sham acupuncture in Germany

OBJECTIVE: To examine German controlled clinical trials on the therapeutic effects of acupuncture vs sham acupuncture, and to find whether there are problems with the conclusion that sham acupuncture has no significant deviation from acupuncture. METHODS: We focused on literature from the last ten years (2002-2011) included in PubMed about controlled clinical trials on acupuncture vs sham acupuncture carried out in Germany. The methods applied in sham acupuncture are summarized, and the difference between the acupuncture and sham groups were analyzed. We measured effects based on the following criteria: acupuncture is effective and superior to sham, acupuncture is effective but similar to sham, both of them have uncertainty regarding treatment effect, or no significant effect. Finally, we reviewed the hypotheses of different scholars on sham acupuncture and analyzed their results.RESULTS: Four types of controlled clinical trials including sham acupuncture on non-Traditional Chinese Medicine acupoints, minimal acupuncture on non-acupoints, placebo needle and sham laser acupuncture had varying results in the 57 articles analyzed. Some showed that acupuncture had a better effect than sham, while some suggest acupuncture and sham had similar effects. In all studies using sham acupuncture on non-therapeutic points, sham electrodes, and sham electro-acupuncture, the therapeutic effect was better than sham. Of the trials, 37 demonstrated that acupuncture had a better effect than sham acupuncture. Only nine trials found no significant difference between acupuncture and sham. Two controlled trials for the same condition (neck pain) conducted by two different German research institutes used the same control method, but reached contradictory conclusions. CONCLUSION: We found problems in conclusions based on results of controlled clinical trials of sham acupuncture in Germany. Therefore, there is still not enough evidence to support the statements that "acupuncture and sham acupuncture have no difference in treatment effect" and "acupuncture is just a placebo effect." The control methods of sham acupuncture used in Germany may not be standardized and may not be suitable for acupuncture clinical trial research. We suggest that research on the methodology of sham acupuncture should be given priority in the design of acupuncture trials in the future.