Unique Orbital Normal Form for Vector Fields of Hopf-Zero Singularity

Normal forms for vector fields of Hopf-zero singularity in R³ are studied. Multiple Lie bracket method is used to give unique normal forms under both conjugacy and orbital equivalence for such vector fields with a generic quadratic part.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

具有局部非线性动力系统周期解及稳定性方法

对于具有局部非线性的多自由度动力系统，提出一种分析周期解的稳定性及其分岔的方法该方法基于模态综合技术，将线性自由度转换到模态空间中，并对其进行缩减，而非线性自由度仍保留在物理空间中在分析缩减后系统的动力特性时，基于Ｎｅｗｍａｒｋ法的预估－校正－局部迭代的求解方法，与Ｐｏｉｎｃａｒé映射法相结合，推导出一种确定周期解，并使用Ｆｌｏｑｕｅｔ乘子判定其稳定性及分岔的方法     

Targeted energy transfer between 2-D wing and nonlinear energy sinks and their dynamic behaviors

Nonlinear Dynamics - The flow-induced vibration of two-dimensional wing coupled with two nonlinear energy sinks (NESs) under freestream is studied by numerical methods, and the relationship between...     

Numerical bifurcation analysis of static stall of airfoil and dynamic stall under unsteady perturbation

By the finite element method combined with Arbitrary-Lagrangian-Eulerian (ALE) frame and explicit Characteristic Based Split Scheme (CBS), the complex flows around stationary and sinusoidal pitching airfoil are studied numerically. In particular, the static and dynamic stalls are analyzed in detail, and the natures of the static stall of NACA0012 airfoil are given from viewpoint of bifurcations. Following the bifurcation in Map, the static stall is proved to be the result from saddle-node bifurcation which involves both the hysteresis and jumping phenomena, by introducing a Map and its Floquet multiplier, which is constructed in the numerical simulation of flow field and related to the lift of the airfoil. Further, because the saddle-node bifurcation is sensitive to imperfection or perturbation, the airfoil is then subjected to a perturbation which is a kind of sinusoidal pitching oscillation, and the flow structure and aerodynamic performance are studied numerically. The results show that the large-scale flow separation at the static stall on the airfoil surface can be removed or delayed feasibly, and the ensuing lift could be enhanced significantly and also the stalling incidence could be delayed effectively. As a conclusion, it can be drawn that the proper external excitation can be considered as a powerful control strategy for the stall. As an unsteady aerodynamic behavior of high angle of attack, the dynamic stall can be investigated from viewpoint of nonlinear dynamics, and there exists a rich variety of nonlinear phenomena, which are related to the lift enhancement and drag reduction.     

Vibration analysis of fluid-conveying nanotubes embedded in an elastic medium considering surface effects

An analytical model is developed to study the surface effects on the vibration behavior including the natural frequency and the critical flow velocity of fluid-conveying nanotubes embedded in an elastic medium. The effects of surface elasticity and residual surface stress are accounted through the surface elasticity model and the Young-Laplace equation. A Winkler-type foundation is employed to model the interaction of nanotubes and the surrounding medium. The results show that the surface effects have more prominent influences on the nature frequency with smaller nanotube thickness, larger aspect ratio and larger elastic medium constants. Both surface layers and the elastic medium enhance the stability of nanotubes. This study might be helpful for designing the fluid-conveying nanotube devices in NEMS and MEMS systems.     

通气超空泡稳定性分析的一种数值算法

根据Logvinovich独立膨胀原理发展了一种用于计算非定常通气超空泡形态的计算方法,并运用该方法对通气超空泡形态稳定性进行了数值仿真研究. 研究表明:Semenenko提出的稳定性判据可以有效判定通气超空泡形态稳定性,当超空泡处于判据的稳定区域时,超空泡表面形成的扰动波在扰动停止一段时间后消失,超空泡恢复到初始形态;当超空泡处于判据的不稳定区域时,超空泡发生自激振荡,超空泡表面形成的扰动波振幅逐渐增大,导致超空泡形态与内部压力发生周期性或准周期性振荡.      

Growth and downconversion luminescence of Ho3+/Yb3+ codoped α‐NaYF4 single crystals by the Bridgman method using a KF flux

Downconversion (DC) luminescence with emission at about 1000 nm under excitation of 448‐nm light in Ho³⁺/Yb³⁺ codoped α‐NaYF₄ single crystal is realized. The crystal was grown by the Bridgman method using KF as an assisting flux in a NaF‐YF₃ system. The energy‐transfer process and quantum cutting (QC) mechanisms are presented through the analysis of the spectra. The energy‐transfer processes of first‐ and second‐order cooperative DC are responsible for the increase of the emission intensity at 1000 nm, and it is the first‐order cooperative DC that is dominant for the DC process. When the Ho³⁺ concentration is fixed at about 0.8 mol%, the optimal concentration for ∼1000 nm emission is 3.02 mol% Yb³⁺ in the current research. The energy‐transfer efficiency and the total quantum efficiency are analyzed through the luminescence decay curves. The maximum quantum cutting efficiency approaches to 184.4% in α‐NaYF₄ single crystals of 0.799 mol% Ho³⁺ and 15.15 mol% Yb³⁺. However, the emission intensity at 1000 nm decreases while the energy‐transfer efficiency from Ho³⁺ to Yb³⁺ increases, which may result from the fluorescence quenching between Ho³⁺ and Yb³⁺ ions, Yb³⁺ and Yb³⁺ ions.     

Sol-Gel Distribution of Polycondensation Reaction

A theoretical approach to polycondensation reaction of Aa-Bb type Involving intramolecular cycllzatlon has been proposed by Tang Au-chin et al.. In this paper, the theoretical sol-gel distribution is tested by polycondensation of adipic acid with trimethylol propane in a sto-ichiometric ratio of 0. 8, and the effect of intramolecular cyclization is discussed in detail.     

Unique normal forms for Hopf-zero vector fields

We consider normal forms of Hopf-zero vector fields in $\text{R}{}^3$. Unique normal forms under conjugacy and orbital equivalence for the generic case are given. To cite this article: G. Chen et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).