Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

Feasibility study on buoyancy–weight ratios of a submerged floating tunnel prototype subjected to hydrodynamic loads

The research progress of a novel traffic solution,a submerged floating tunnel(SFT),is reviewed in terms of a study approach and loading scenario.Among existing publications,the buoyancy-weight ratio(BWR) is usually predefined.However,BWR is a critical structural parameter that tremendously affects the dynamic behaviour of not only the tunnel tube itself but also the cable system.In the context of a SFT prototype(SFTP) project in Qiandao Lake(Zhejiang Province,China),the importance of BWR is illustrated by finite element analysis and subsequently,an optimized BWR is proposed within a reasonable range in the present study.In the numerical model,structural damping is identified to be of importance.Rayleigh damping and the corresponding Rayleigh coefficients are attained through a sensitivity study,which shows that the adopted damping ratios are fairly suitable for SFTP.Lastly,the human sense of security is considered by quantifying the comfort index,which helps further optimize BWR in the SFTP structural parameter design.     

The Effect of the Spacer of Bis(biurea) Ligands on the Structure of A2L3‐type (A=anion) Phosphate Complexes

By tuning the length and rigidity of the spacer of bis(biurea) ligands L, three structural motifs of the A₂L₃ complexes (A represents anion, here orthophosphate PO₄^3?), namely helicate, mesocate, and mono‐bridged motif, have been assembled by coordination of the ligand to phosphate anion. Crystal structure analysis indicated that in the three complexes, each of the phosphate ions is coordinated by twelve hydrogen bonds from six surrounding urea groups. The anion coordination properties in solution have also been studied. The results further demonstrate the coordination behavior of phosphate ion, which shows strong tendency for coordination saturation and geometrical preference, thus allowing for the assembly of novel anion coordination‐based structures as in transition‐metal complexes.     

“二三结合”开发模式渗流特征研究

L油田B区块开展"二三结合"实验区,"二三结合"开发模式渗流特征对区块的合理高效开发具有重要意义。为了明确其渗流特征,利用油藏数值模拟软件Eclipse建立代表意义的油藏数值模型,研究区块"二三结合"开发模式下原射孔层和补孔层的渗流特征,分析了"二三结合"开发模式下,不同开发阶段综合含水率、采出程度、井底压力、地层压力及含水饱和度的变化特征。研究表明,"二三结合"开发模式先通过水驱开发挖潜原射孔层剩余油,提高厚油层顶部剩余油的采出程度,再通过聚合物驱进一步提高开发效果,通过水驱与聚驱的综合作用,最终得到较好的开发效果。     

模型论中的拓扑学方法

本文利用拓扑学方法研究了ω-范畴理论的性质,并对模型个数问题进行了讨论.     

Commuting and stable feedback design for switched linear systems

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for commuting and stable feedback controllers. For second-order systems, a necessary and sufficient condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.     

“神龙一号”注入器研制

“神龙一号”注入器是直线感应加速器的束流源，它采用了感应叠加的高压加载方式，包括脉冲功率系统、感应腔、阴阳极杆、绝缘支撑、二极管和束流传输系统等子系统. 在研制中采用了径向绝缘支撑、对中支撑调节系统、类Pierce阴极等先进技术，以及二极管线圈内置和外径为800mm的铁氧体大环等创新. 参数测试显示，3.5MeV注入器达到了世界先进水平.     

Jensen's inequality for g-expectation: part 1

Briand et al. (Electron. Comm. Probab. 5 (2000) 101–117) gave a counterexample and proposition to show that given g,g-expectations usually do not satisfy Jensen's inequality for most of convex functions. This yields a natural question, under which conditions on g, do g-expectations satisfy Jensen's inequality for convex functions? In this paper, we shall deal with this question in the case that g is convex and give a necessary and sufficient condition on g under which Jensen's inequality holds for convex functions. To cite this article: Z. Chen et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).