On <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">1</Emphasis></Superscript>-summability and asymptotic profiles for smooth solutions to Navier–Stokes equations in a 3D exterior domain

The exterior nonstationary problem is studied for the 3D Navier-Stokes equations. The L ¹ -summability is proved for smooth solutions which correspond to initial data satisfying certain symmetry and moment conditions. The result is then applied to show that such solutions decay in time more rapidly than observed in general. Furthermore, an asymptotic expansion is deduced and a lower bound estimate is given for the rates of decay in time. Mathematics Subject Classifications (1991): 35Q30, 76D05.On leave of absence from Institute of Applied Mathematics, Academy of Mathematics and System Sciences. Academia Sinica, Beijing 100080, Peoples Republic of China. Supported by JSPS     

完全可压缩渗流驱动问题的特征线有限元方法及其误差分析

多孔介质中渗流驱动问题数值方法的研究，对合理经济地开发油田，了解地下油水运动规律有一定意义。特征线法结合差分或有限元法解渗流问题，在理论和应用上获得了成功３－５，但还有很多问题需进一步研究２．前人研究多是假定流体不可压或微可压，本文研究一类完全可压缩两相驱动问题。采用特征线法与有限元法相结合，构造并分析了全离散数值格式，基于周期性假设，证明了最优Ｌ２模误差估计。     

Effects on the evolution of microstructure and properties of low-silicon cast aluminum alloys in service

ABSTRACT

The microstructure evolution and property change of four kinds of low silicon cast aluminum alloy exposed to heat for 0–50?h at 200°C were studied by means of Brinell hardness test, tensile property test, friction and wear property test and XRD analysis. The results show that with increasing thermal exposure time, the tensile strength of each group of samples decreased and the amount of wear increased. The tensile strength of samples with more Si content decreased slowly. When the time increased to 50?h, the increase of wear loss was the largest. The hardness of samples after thermal exposure increases compared with that before thermal exposure. The residual stress of (311) diffraction crystal surface of AlSi3.5Mg0.66 under different thermal exposure time was measured. The type of residual stress changed from residual tensile stress to residual compressive stress after thermal exposure. There is an abnormal phenomenon that the hardness of the sample increased and the amount of wear increased, and it is evident that the distribution of residual stress was inhomogeneous after thermal exposure. It is found that with increasing thermal exposure time to 50?h, the average lattice distortion ε of the low-index crystal plane and the high-index crystal plane in the aluminum alloys gradually increased.     

Generation of entanglement via atomic coherence in a two-mode three-level cascade atomic system

The generation of continuous variable entanglement via atomic coherence in a two-mode three-level cascade atomic system is discussed according to the entanglement criterion proposed by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)]. Atomic coherence between the top and bottom levels is induced with two photons of a strong external pump field. It shows that entanglement for the two-mode field in the cavity can be generated under certain conditions. Moreover, by means of the input-output theory, we show that the two-mode entanglement could also be approached at the output.     

A Rhodamine Derivative Based Chemosensor with High Selectivity and Quick Respond to Cr<Superscript>3+</Superscript> in Aqueous Solution

In this paper, a new kind of colorimetric chemsensor aiming at detecting Cr³⁺ has been synthesized, and it is based on the “Off-On” effect of a rhodamine derivative. Comparing with other metal irons (Na⁺, K⁺, Ni²⁺, Hg²⁺, Fe³⁺, Mn²⁺, Co²⁺, Cd²⁺, Cu²⁺, Pb²⁺, Zn²⁺, Mg²⁺, Ba²⁺, Ag⁺, Fe²⁺, Ce³⁺), the chemsensor has a quick and accurate response to Cr³⁺ in H₂O-EtOH solution (4/1, v/v). There is an obvious change in color, from colorless to bright pink when Cr³⁺ is detected. According to the fitting curve based on Benesi-Hildebrand equation and working curve of absorption strength in UV-vis spectrum, the binding pattern of Cr³⁺ and the rhodamine derivative follows a 1:1 stoichiometry. The chemsensor shows great potential in monitoring Cr³⁺ in the aqueous medium with high efficiency, which is supposed to complete the recognition in the minimum as 5.2?×?10^?7 mol/L within 5 min.     

Laser speckle reduction using motionless image conduits

We have demonstrated a speckle reduction method using motionless image conduits (MICs). Different experimental conditions by introducing the high-coherence HeNe laser and the low-coherence laser diode (LD) as the illumination light sources, by employing the straight MIC and the curved MIC as the speckle reduction components, and by recording speckle images without (objective speckle) and with (subjective speckle) the imaging lens mounted on the CCD camera are conducted, respectively. The most efficient speckle reduction condition is found by the combination of using the LD and the curved MIC, where the objective speckle contrast ratio is reduced from 0.7378 to 0.1725. Experimental results are discussed, and the causes for these speckle reduction efficiency changes are given.