具有 Cauchy-Ventcel边界条件的有界域中亚临界半线性波方程的稳定与控制

We analyze the exponential decay property of solutions of the semilinear wave equation in bounded domain Ω of R^N with a damping term which is effective on the exterior of a ball and boundary conditions of the Cauchy-Ventcel type. Under suitable and natural assumptions on the nonlinearity, we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p 〈 5. The results obtained in R^3 and RN by B. Dehman, G. Lebeau and E. Zuazua on the inequalities of the classical energy （which estimate the total energy of solutions in terms of the energy localized in the exterior of a ball） and on Strichartz＇s estimates, allow us to give an application to the stabilization controllability of the semilinear wave equation in a bounded domain of R^N with a subcritical nonlinearity on the domain and its boundary, and conditions on the boundary of Cauchy-Ventcel type.     

次临界分数阶Laplace方程具有两个bubbles的变号解存在性

考虑次临界分数阶Laplace问题{(-△)~su=︳u︳~(p-1-ε)u,x∈Ω,u=0,x∈?Ω}具有两个bubbles的变号解的存在性,其中Ω是R~N中的有界光滑区域,N2s,0s1,p=(N+2s)/(N-2s),ε0充分小.这个工作可以看作Bartsch,Micheletti,Pistoia在文[On the existence and the profile of nodal solutions of elliptic equations involving critical growth,Calc.Var.Partial Differential Equations,2006,3:265-282]结果的一种非局部形式的推广.     

Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems

The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated, with the flow speed as the bifurcation parameter. The center manifold theory and complex normal form method are Used to obtain the bifurcation equation. Interestingly, for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical. It is found, mathematically, this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter. The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.     

Subcritical and supercritical shear flows above an uneven bottom

The concepts of subcritical and supercritical flows are introduced for the long-wave approximation model describing stationary free-boundary rotational flows of an ideal incompressible fluid. Shear flows of a fluid layer above an uneven bottom are analyzed. Exact solutions describing different flow regimes are constructed, and the flow properties are studied as a function of the flow regime. Flows with backward streamlines are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 26–38, July–August, 2006. An erratum to this article is available at .     

Intermittency,Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.     

以亚临界水为流动相的高效液相色谱方法的进展

由于纯水在高温高压下形成亚临界液体水时氢键网络发生改变,导致其极性、粘度等物理性质产生较大的变化。以亚临界水为流动相的高效液相色谱方法(SubWC)是近年来发展起来的一种新型分离技术。SubWC的仪器系统可以采用通过改装的一般的气相色谱(GC)或液相色谱(LC)装置;分离色谱柱既可以采用液相色谱填充柱,也可以采用类似于GC的毛细管柱;选择性既可以通过调节柱系统的温度和压力,也可以通过在流动相中添加有机调节剂或盐类进行调节;检测既可用氢火焰离子化检测器检测,也可用紫外检测器检测,极大地拓宽了色谱分离和最佳条件选择的范围。SubWC无论在仪器系统、流动相的洗脱还是固定相的选择等方面均有一定的特征。这种新的分离模式目前尚处于研究与开发阶段,且多用于极性、中等极性样品的快速分离。     

Effects of spanwise system rotation on turbulent stripes in a plane Poiseuille flow

In the transitional channel flow, the large-scale intermittent structure of localised turbulence, which is called the turbulent stripe pattern, can be found in the form of stripe arrangement. The structure of the turbulent stripe pattern is an oblique laminar–turbulent banded pattern and is inclined with respect to the streamwise direction. We performed direct numerical simulation at a transitional Reynolds number and very low-rotation numbers, and focused on the turbulent stripe pattern in the plane Poiseuille flow subjected to spanwise system rotation. We captured the turbulent stripe pattern in a rotating channel flow and found the augmentation and diminution of the turbulent stripe pattern were affected by the spanwise rotation. The contents of the discussion are the spatial size of the turbulent stripe pattern on the basis of the instantaneous flow fields, the energy spectra, and various statistics relating to the spanwise velocity component that characterise the turbulent stripe pattern. The turbulent stripe pattern was found to contain kinetic energy that was larger in very weakly rotating flows than in the static system. It was also found that the magnitude of the spanwise secondary flow increases, while the quasi-laminar region is wider at a very lowrotation number.     

非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究

研究了二元机翼非线性颤振系统的Hopf分岔．应用中心流形定理将系统降维,并利用复数正规形方法得到了以气流速度为分岔参数的分岔方程．研究发现,分岔方程中一个系数不含分岔参数的一次幂,故使得分岔具有超临界和亚临界双重性质．用等效线性化法和增量谐波平衡法验证了所得结果．     

Global well‐posedness and blow‐up criterion for the periodic quasi‐geostrophic equations in Lei‐Lin‐Gevrey spaces

In this paper we consider a periodic 2‐dimensional quasi‐geostrophic equations with subcritical dissipation. We show the global existence and uniqueness of the solution for small initial data in the Lei‐Lin‐Gevrey spaces . Moreover, we establish an exponential type explosion in finite time of this solution.     

基于FPGA技术的加速器切束控制系统设计

针对加速器驱动次临界系统(ADS)中强流质子直线加速器,即ADS注入器Ⅱ,设计了采用现场可编程门阵列(FPGA)切束技术的加速器快保护控制系统。当系统检测到束流异常故障信号时能快速切断束流,并上传故障信息,方便故障排查和后期数据分析。该控制器基于FPGA设计,可实现光纤通信、串口通信、逻辑电平信号输出等功能。其中,光纤通信功能用于控制斩波器电源快速切断束流;串口通信用于实时传输设备状态信息;逻辑电平信号输出用于控制继电器产生开关量信号去远程控制保护设备,以防止运行设备的损害。通过现场运行测试,切束响应时间在10 s之内,达到安全设计要求。