On scaling invariance and type-I singularities for the compressible Navier-Stokes equations

Science China Mathematics - We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-I singularities of solutions with $$\mathop {\lim...     

On strong convergence to 3D steady vortex sheets

In this paper, we first establish a strong convergence criterion of approximate solutions for the 3D steady incompressible Euler equations. For axisymmetric flows, under the assumption that the vorticity is of one sign and uniformly bounded in L¹ space, we obtain a sufficient and necessary condition for the strong convergence in of approximate solutions. Furthermore, for one-sign and L¹-bounded vorticity, it is shown that if a sequence of approximate solutions concentrates at an isolated point in (r,z)-plane, then the concentration point can appear neither in the region near the axis (including the symmetry axis itself) nor in the region far away from the axis. Finally, we present an example of approximates solutions which converge strongly in by using Hill's spherical vortex.     

Viscous limits for piecewise smooth solutions to systems of conservation laws

In this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity. It is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order as the viscosity coefficient goes to zero. The proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles.     

真空中GCr15钢球／CVD Cr7C3镀层钢盘摩擦副摩擦振动的研究

作者在对GCr15钢球/CVDCr_7C_3镀层钢盘摩擦副于大气中滑动干摩擦引起的摩擦振动进行考察分析的基础上,本文又对这种摩擦副在真空(6.67×10~(-3)Pa)中的摩擦振动特性进行了试验研究。试件系统为低刚度和小阻尼的弹性系统。试验信号由微机采集、处理并进行频谱分析。结果表明,真空中摩擦力振动的类型呈准谐波周期性自持振动,其与正压力及拖动速度无关,振动频率接近于系统在水平方向上的固有频率;摩擦副运动的平稳性与平均滑动摩擦系数接近反比例关系;真空中摩擦力的粘着分量是使摩擦振动加剧的主要原因;钢球的磨损体积与摩擦振动特性无关。     

金川Ⅲ矿区岩体分类及其力学特性参数预测

本文针对金川Ⅲ矿区岩体质量及参数,并在11个钻孔数据资料的基础上,采用数学统计和数值模型来分别分析矿区岩体质量和力学参数的特征。对11个钻孔的资料进行详细的统计分析,进行每一个钻孔不同深度的岩体节理裂隙统计和岩体分类评价,并由此获得了建立矿块力学参数模型的数据。再建立表征整个岩体特性的三维力学模型,并揭示了矿块力学特性的分布特性和变化规律。此研究为崩落法采矿设计和数值模拟提供可靠的依据。     

Visual detection and microplate assay for Staphylococcus aureus based on aptamer recognition coupled to tyramine signal amplification

We have developed a specific method for the visual detection of Staphylococcus aureus based on aptamer recognition coupled to tyramine signal amplification technology. A biotinylated aptamer specific for S. aureus was immobilized on the surface of the wells of a microplate via biotin-avidin binding. Then, the target bacteria (S. aureus), the biotinylated-aptamer-streptavidin-HRP conjugates, biotinylated tyramine, hydrogen peroxide and streptavidin-HRP were successively placed in the wells of the microplate. After adding TMB reagent and stop solution, the intensity of the yellow reaction product can be visually inspected or measured with a plate reader. Under optimized conditions, there is a linear relationship between absorbance at 450 nm and the concentration of S. aureus in the 10 to 10⁷ cfu mL^?1 concentration range (with an R² of 0.9976). The limit of detection is 8 cfu mL^?1.

Sensitive flow-injection chemiluminescence determination of terbutaline sulfate based on enhancement of the luminol–permanganate reaction

A novel and highly sensitive chemiluminescence (CL) method for the determination of terbutaline sulfate, coupled with flow-injection analysis (FIA), is described in this paper. The method is based on enhancement by terbutaline sulfate of the chemiluminescence emission of the luminol–permanganate system under alkaline conditions. Under the conditions selected the concentration of terbutaline sulfate is proportional to CL intensity in the range 5×10^–10–5×10^–7 g mL^–1, with a detection limit of 1.7×10^–10 g mL^–1 (3). The relative standard deviation is 2.8% for 1×10^–8 g mL^–1 terbutaline sulfate (n=11). Ninety samples can be determined per hour. The proposed method has been used to determine terbutaline sulfate in pharmaceutical preparations and in plasma and urine samples with satisfactory results. The possible mechanism of the chemiluminescence reaction is discussed briefly.     

Uniqueness via the adjoint problems for systems of conservation laws

We prove a result of uniqueness of the entropy weak solution to the Cauchy problem for a class of nonlinear hyperbolic systems of conservation laws that includes in particular the p-system of isentropic gas dynamics. Our result concerns weak solutions satisfying the, as we call it, Wave Entropy Condition, or WEC for short, introduced in this paper. The main feature of this condition is that it concerns both shock waves and rarefaction waves present in a solution. For the proof of uniqueness, we derive an existence result (respectively a uniqueness result) for the backward (respectively forward) adjoint problem associated with the nonlinear system. Our method also applies to obtain results of existence or uniqueness for some linear hyperbolic systems with discontinuous coefficients. © 1993 John Wiley & Sons, Inc.     

Existence of Vortex Sheets with¶Reflection Symmetry in Two Space Dimensions

The main purpose of this work is to establish the existence of a weak solution to the incompressible 2D Euler equations with initial vorticity consisting of a Radon measure with distinguished sign in H ^{? 1}, compactly supported in the closed right half-plane, superimposed on its odd reflection in the left half-plane. We make use of a new a priori estimate to control the interaction between positive and negative vorticity at the symmetry axis. We prove that a weak limit of a sequence of approximations obtained by either regularizing the initial data or by using the vanishing viscosity method is a weak solution of the incompressible 2D Euler equations. We also establish the equivalence at the level of weak solutions between mirror symmetric flows in the full plane and flows in the half-plane. Finally, we extend our existence result to odd L ¹ perturbations, without distinguished sign, of our original initial vorticity.