Zero dissipation limit to rarefaction waves for the one-dimensional navier-stokes equations of compressible isentropic gases

We study the zero dissipation limit problem for the one-dimensional Navier-Stokes equations of compressible, isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions. We prove that the solutions of the Navier-Stokes equations with centered rarefaction wave data exist for all time, and converge to the centered rarefaction waves as the viscosity vanishes, uniformly away from the initial discontinuities. In the case that either the effects of initial layers are ignored or the rarefaction waves are smooth, we then obtain a rate of convergence which is valid uniformly for all time. Our method of proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure. © 1993 John Wiley & Sons, Inc.     

Chemiluminescence of CdTe nanocrystals induced by direct chemical oxidation and its size-dependent and surfactant-sensitized effect

CdTe nanocrystals (NCs) capped with thioglycolic acid (TGA) were synthesized via a microwave-assisted method. The chemiluminescence (CL) of CdTe NCs induced by directly chemical oxidation and its size-depended and surfactant-sensitized effect in aqueous solution were then investigated. It was found that oxidants, especially hydrogen peroxide and potassium permanganate, could directly oxidize CdTe NCs to produce strong CL emission in basic conditions. The oxidized CL of CdTe NCs displayed size-dependent effect and its intensity increased along with increasing the sizes of the NCs. Moreover, the CL intensity could, if surfactants CTAB or beta-cyclodextrin were added to the above CL system, be sensitized to some degree. The sensitized CL induced by CTAB and beta-cyclodextrin is mainly contributing to the formation of aggregate nanostructure and the micellar micronanoenvironment, respectively. The possible oxidized CL mechanisms were further examined by means of photoluminescence spectra, CL spectra, and transmission electron microscopy studies. The CL properties of CdTe NCs not only will be helpful to study physical chemistry properties of semiconductor nanocrystals but also are expected to find use in many fields such as luminescence devices, bioanalysis, and multicolor labeling probes.     

多体动力学的几何积分方法研究进展

动力系统的几何积分研究是近20年来工程计算领域非常活跃的方向.多体动力学方程(微分方程, 微分代数方程)是一类典型的动力系统,将其从Lagrange体系向Hamilton系统过渡,目的在于从欧氏几何过渡到辛几何形态, 将对偶变量引入到力学研究中,然后利用辛几何的数学框架对多体系统动力学方程进行数值计算,可以预知多体动力学系统的一些定性信息,并在数值离散时能保持这些定性性质特征,尤其在表示关键的物理意义时需要强调保持这些几何性质.简要介绍多体系统(无约束多刚体系统、完整约束多刚体系统和柔性多体系统)的Hamilton正则方程的建立和几何积分方法的构造,着重介绍了在多体动力学计算中非常有应用前景的高阶辛算法(合成辛算法、分裂合成辛算法和辛精细积分法)、多辛算法,以及广义Hamilton 系统与Lie 群积分方法等计算几何力学方法, 并对Lie群积分的投影方法、流形局部坐标法等方法进行了阐述.      

氧化石墨烯量子点修饰氧掺杂多孔g-C3N4在光催化降解和抗菌中的应用（英文）

偶氮类合成色素具有遗传毒性、致癌性和致泻性,而食源性致病菌易引发细菌性感染和食物中毒事件,食品加工过程中产生的色素废水和致病菌废水若未经妥善处理就排入水体,会对水体及环境造成污染,废水中的偶氮类色素和致病菌还会通过食物链对人体健康产生威胁.因此,寻求更为高效、绿色、安全的处理技术和净化材料有效去除食品废水中高污染性和毒害性的偶氮类色素和致病菌显得尤为迫切.g-C3N4是一种具有可见光响应的有机半导体光催化材料,广泛应用于降解污染物、杀灭致病菌、催化有机反应等领域.然而,g-C3N4本身存在着比表面积小、光吸收性能差、光氧化能力低以及光生载流子迁移效率低等缺点,限制了其光催化性能.针对上述问题,我们对g-C3N4的空间和电子结构进行了设计,将形貌调控、元素掺杂和助催化剂修饰三种改性方法相结合,以获得兼具大比表面积、优异光吸收性能、强氧化能力以及快速光生载流子迁移能力的高活性g-C3N4基光催化体系.本文通过水热法制备了氧掺杂多孔氮化碳(PCNO),通过酸剥离法制备了氧化石墨烯量子点(ox-GQDs),最后通过自组装法将助催化剂ox-GQDs修饰到PCNO上,制备了ox-GQDs/PCNO复合光催化剂.零维的ox-GQDs可以通过氢键、π-π作用和化学键作用,与二维的PCNO实现紧密接触,均匀地分散在PCNO的表面和内部孔道上.由于ox-GQDs独特的上转换特性、电子捕获能力和过氧化物酶活性,ox-GQDs/PCNO复合光催化剂具有比PCNO更佳的光吸收性能、更高的电荷转移效率以及更强的光氧化能力.因此,ox-GQDs/PCNO复合材料在降解偶氮类色素和杀灭致病菌方面均表现出更为优异的可见光催化性能,活性最佳的复合材料ox-GQDs-0.2%/PCNO降解偶氮类色素苋菜红的速率常数约是PCNO的3.1倍,并且该材料能在可见光照射4 h内杀灭99.6%的大肠杆菌,远超过PCNO 31.9%的抗菌活性.另外,光生空穴、超氧自由基和羟基自由基被证实是ox-GQDs/PCNO体系在光催化反应中产生的活性物种,可以彻底矿化偶氮类色素并有效杀灭致病菌.本研究可以拓展g-C3N4基光催化剂在环境净化领域的应用前景,并为阐明ox-GQDs在复合光催化体系中的作用提供新的见解.     

MT-1型真空摩擦磨损试验机的研制

MT-1型真空摩擦磨损试验机可以提供从大气到6.7×10~(-3)Pa的压力环境,其可测载荷和速度的可调范围以及温度和振动特性等的变化范围都比较大,并且采用微机系统进行数据采集和处理,测量参数多,重复性和精确度都比较好,因而是航天工业、真空工业和摩擦学基础研究中一种有用的工具。     

Stability of Contact Discontinuities for the 1-D Compressible Navier-Stokes Equations

In this paper, we study the large-time asymptotic behavior of solutions of the one-dimensional compressible Navier-Stokes system toward a contact discontinuity, which is one of the basic wave patterns for the compressible Euler equations. It is proved that such a weak contact discontinuity is a metastable wave pattern, in the sense introduced in [24], for the 1-D compressible Navier-Stokes system for polytropic fluid by showing that a viscous contact wave, which approximates the contact discontinuity on any finite-time interval for small heat conduction and then runs away from it for large time, is nonlinearly stable with a uniform convergence rate provided that the initial excess mass is zero. This result is proved by an elaborate combination of elementary energy estimates with a weighted characteristic energy estimate, which makes full use of the underlying structure of the viscous contact wave.     

Impedimetric aptasensor for Staphylococcus aureus based on nanocomposite prepared from reduced graphene oxide and gold nanoparticles

We describe here an aptasensor for the ultrasensitive detection of Staphylococcus aureus by electrochemical impedance spectroscopy (EIS). Single-stranded DNA was linked to a nanocomposite prepared from reduced graphene oxide (rGO) and gold nanoparticles (AuNP). Thiolated ssDNA was covalently linked to the AuNPs linked to rGO, and probe DNA was immobilized on the surface of an AuNP-modified glassy carbon electrode to capture and concentrate Staph. aureus. The probe DNA of the aptasensor selectively captures the target bacteria in its three-dimensional space, and these results in a dramatic increase in impedance. Scanning electron microscopy, cyclic voltammetry and EIS were used to monitor the single steps of the electrode assembly process. The effect was utilized to quantify the bacteria in the concentration range from 10 to 10⁶ cfu mL^?1 and with a detection limit of 10 cfu mL^?1 (S/N?=?3). The relative standard deviation of Staphylococcus aureus detection was equal to 4.3 % (10⁵ cfu mL^?1, n?=?7). In addition to its sensitivity, the biosensor exhibits high selectivity over other pathogens.

A dual-color flow cytometry protocol for the simultaneous detection of Vibrio parahaemolyticus and Salmonella typhimurium using aptamer conjugated quantum dots as labels

A sensitive, specific method for the collection and detection of pathogenic bacteria was demonstrated using quantum dots (QDs) as a fluorescence marker coupled with aptamers as the molecular recognition element by flow cytometry. The aptamer sequences were selected using a bacterium-based SELEX strategy in our laboratory for Vibrio parahaemolyticus and Salmonella typhimurium that, when applied in this method, allows for the specific recognition of the bacteria from complex mixtures including shrimp samples. Aptamer-modified QDs (QD-apt) were employed to selectively capture and simultaneously detect the target bacteria with high sensitivity using the fluorescence of the labeled QDs. The signal intensity is amplified due to the high photostability of QDs nanoparticles, resulting in improved sensitivity over methods using individual dye-labeled probes. This proposed method is promising for the sensitive detection of other pathogenic bacteria in food stuff if suitable aptamers are chosen. The method may also provide another potential platform for the application of aptamer-conjugated QDs in flow cytometry.     

Global Shock Waves¶for the Supersonic Flow Past a Perturbed Cone

We prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone. The flow is governed by the potential equation, as well as the boundary conditions on the shock and the surface of the body. It is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self-similar solution under some suitable conditions. Our analysis is based on a global uniform weighted energy estimate for the linearized problem. Combining this with the local existence result of Chen–Li [1] we establish the global existence and decay rate of the solution to the nonlinear problem. Received: 1 August 2001 / Accepted: 14 January 2002