Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.     

The Determination of Protonation Constants of Some Amino Acids and Their Esters by Potentiometry in Different Media

In this study, stoichiometric protonation constants of L-tyrosine, L-cysteine, L-tryptophane, L-lysine, and L-histidine, and their methyl and ethyl esters in water and ethanol–water mixtures of 30, 50, and 70% ethanol (v/v), were determined potentiometrically using a combined pH electrode system calibrated as the concentration of hydrogen ion. Titrations were performed at 25^∘C and the ionic strength of the medium was maintained at 0.10 mol⋅L⁻¹ using sodium chloride. Protonation constants were calculated by using the BEST computer program. The effect of solvent composition on the protonation constants is discussed. The log₁₀ K₂ values of esters generally decreased with increasing ethanol content. However, the log₁₀ K₁ values of the esters of L-tyrosine, L-cysteine, and L-tryptophane were found to increase with increasing ethanol content in contrast those of L-lysine and L-histidine esters.     

含气率对PTS时压力容器内流动与传热的影响

本文对反应堆压力容器紧急安注时的流动与传热特性在1/10的模型上进行了流动可视化、局部传热系数以及混合函数的试验研究。针对三个热冲击敏感区域的部分测点,比较了环腔流速为0.5m/s、安注流速为1～30 m/s时不同含气率对下降环腔内流动与传热特性的影响,得出并分析了不同测点传热系数、混合函数的变化规律。研究结果表明:随着含气率增大,安注流体与环腔流体的混合增强;下降环腔内的含气率对小安注流速时的流动与传热影响显著,而对大安注流速时影响较小。     

Investigation of hypersonic nozzle flow uniformity using NO fluorescence

Planar laser-induced fluorescence visualisation is used to investigate nonuniformities in the flow of a hypersonic conical nozzle. Possible causes for the nonuniformity are outlined and investigated, and the problem is shown to be due to a small step at the nozzle throat. Entrainment of cold boundary layer gas is postulated as the cause of the signal nonuniformity. PACS 47.80.Jk, 47.40.Ki, 47.60.+i     

非线性互补问题的一种全局收敛的显式光滑Newton方法

本针对Po函数非线性互补问题，给出了一种显式光滑Newton方法，该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程，并在适当的假设条件下，证明了算法的全局收敛性。     

电路过渡过程的计算机辅助分析

电路过渡过程所列方程是微分方程，本文中采用的是方框图模型分析法，即将微分方程的复杂示解分解成最基本的加（减）、乘（除）、积分（微分）、增益等运算，采用VB设计用户界面产进行计算，并给出了一算例。     

The number of powers of 2 in a representation of large even integers II

It is proved that for any integerk≥ 54 000, there isN _k >0 depending onk only such that every even integer ≥N _k is a sum of two odd prime numbers andk powers of 2. Project partially supported by RGC Research Grant (No.HKU 7122/97P) and Post-Doctoral Fellowship of the University of Hong Kong.     

Surfaces of Constant Mean Curvature Bounded by Two Planar Curves

In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary.     

Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.