二维三温热传导方程组的分数步隐式差分格式

本文给出一个解二维三温热传导方程组的分数步隐式有限差分格式，利用离散变分形式及能量方法，给出差分格式的最优阶离散H^1范数先验误差及稳定性估计。     

NA序列重对数律的几个极限定理

设{X_n;n≥1}均值为零、方差有限的NA平稳序列。记S_n=∑_(k=1)~n X_k,M_n=maxk≤n|S_k|,n≥1.假设σ~2=EX_1~2+2∑_(k=2)~∞EX_1X_k>0。本文讨论了:当ε 0时,P{M_n≥εσ(2nloglogn)~(1/2)的一类加权级数的精确渐近性质,以及当ε∞时,P{M_n≤εσ(π~2n/(8loglogn))~(1/2)}的一类加权级数的精确渐近性质。这些性质与重对数律和Chung重对数律的速度有关。     

On the use of negative penalty parameters in aeroelastic divergence analysis of lifting surfaces

This paper shows that a numerical modelling method in which constraints are replaced with positive and negative penalty functions, which may be regarded as artificial elastic restraints of positive and negative stiffness, may be safely used to determine the critical speed associated with aeroelastic divergence. The critical speeds of a beam with restraints of positive and negative stiffness are found to converge to that of the constrained system, from below if the stiffness is positive and from above otherwise. A uniform Euler–Bernoulli beam clamped at the rear end is analysed using an artificial restraint to enforce the constraint of zero rotation at the clamp, and the results are compared with the exact critical speed of the constrained system obtained analytically. The paper shows that, contrary to common belief that the penalty parameter must be positive, the inclusion of a negative penalty parameter enables the determination of errors due to violation of the constraints.     

A slit viscometer for the measurement of the viscosity of aqueous systems at high temperatures

A slit viscometer has been constructed to measure the viscosity of aqueous systems at temperatures up to 140 °C. Liquid is forced backwards and forwards through the slit by the use of varying air pressure. The flow rate is obtained from the time for the liquid to pass conductivity probes located in liquid reservoirs either side of the slit. The pressure difference between two points on the slit wall is determined using a differential pressure transducer. By varying the slit height measurements can be made on liquids with viscosities in the range 10 to 10^–3 Pa s. Shear rates from 10 to 10⁴ s^–1 can be achieved. A simple microcomputer control system enables the shear stress to be automatically increased and decreased stepwise. Representative data on polysaccharide solutions and strach suspensions are presented. The viscometer is particularly well-suited for following temperature-dependent biopolymer transitions and the thermal depolymerisation of water soluble polymers.     

Thermal expansion in 3d-metal Prussian Blue Analogs—A survey study

We present a comprehensive study of the structural properties and the thermal expansion behavior of 17 different Prussian Blue Analogs (PBAs) with compositions M^II₃[(M′)^III(CN)₆]₂·nH₂O and M^II₂[Fe^II(CN)₆]·nH₂O, where M^II=Mn, Fe, Co, Ni, Cu and Zn, (M′)^III=Co, Fe and n is the number of water molecules, which range from 5 to 18 for these compounds. The PBAs were synthesized via standard chemical precipitation methods, and temperature-dependent X-ray diffraction studies were performed in the temperature range between −150 °C (123 K) and room-temperature. The vast majority of the studied PBAs were found to crystallize in cubic structures of space groups Fm3?m, F4?3m and Pm3?m. The temperature dependence of the lattice parameters was taken to compute an average coefficient of linear thermal expansion in the studied temperature range. Of the 17 compounds, 9 display negative values for the average coefficient of linear thermal expansion, which can be as large as 39.7×¹0⁻⁶ K⁻¹ for Co₃[Co(CN)₆]₂·12H₂O. All of the M^II₃[Co^III(CN)₆]₂·nH₂O compounds show negative thermal expansion behavior, which correlates with the Irving–Williams series for metal complex stability. The thermal expansion behavior for the PBAs of the M^II₃[Fe^III(CN)₆]₂·nH₂O family are found to switch between positive (for M=Mn, Co, Ni) and negative (M=Cu, Zn) behavior, depending on the choice of the metal cation (M). On the other hand, all of the M^II₂[Fe^II(CN)₆]·nH₂O compounds show positive thermal expansion behavior.     

Specific O₂⁻ generation in corona discharge for ion mobility spectrometry

This study deals with O₂⁻ generation in corona discharge (CD) in point to plane geometry for single flow ion mobility spectrometry (IMS) with gas outlet located behind the ionization source. We have designed CD of special geometry in order to achieve the high O₂⁻ yield. Using this ion source we have achieved in zero air conditions that up to 74% all negative ions were O₂⁻ or O₂⁻(H₂O). It has been demonstrated that the non-electronegative nitrogen positively influences the efficiency of O₂⁻ generation in O₂/N₂ mixtures. The reduced ion mobility of 2.27 cm² V⁻¹ s⁻¹ has been measured for O₂⁻/O₂⁻(H₂O) ions in zero air. Additional ions detected in zero air (less than 200 ppb CO₂) using the mass spectrometric and IMS technique were, NO₂⁻, N₂O₂⁻ (2.37 cm² V⁻¹ s⁻¹), NO₃⁻, N₂O₃⁻ and N₂O₃⁻(H₂O). The CO₃⁻ and CO₄⁻ ions have been detected after the introduction of 5 ppm CO₂ into zero air.     

A two-phase approach for setting targets in DEA with negative data

Conventional DEA models have been introduced to deal with non-negative data. In the real world, in some occasions, we have outputs and/or inputs, which can take negative data. In DEA literature some approaches have been presented for evaluating performance of units, which operate with negative data. In this paper, firstly, we give a brief review of these works, then we present a new additive based approach in this framework. The proposed model is designed to provide a target with non-negative value associated with negative components for each observed unit, failed by other methods. An empirical application in banking is then used to show the applicability of the proposed method and make a comparison with the other approaches in the literature.     

Experimental study of air–water flow in downward sloping pipes

This paper presents results from seven experimental facilities on the co-current flow of air and water in downward sloping pipes. As a function of the air flow rate, pipe diameter and pipe slope, the required water discharge to prevent air accumulation was determined. In case the water discharge was less than the required water discharge, the air accumulation and additional gas pocket head loss were measured. Results show that volumetric air discharge as small as 0.1% of the water discharge accumulate in a downward sloping section. The experimental data cover all four flow regimes of water-driven air transport: stratified, blow-back, plug and dispersed bubble flow. The analysis of the experimental results shows that different dimensionless numbers characterise certain flow regimes. The pipe Froude number determines the transition from blow-back to plug flow. The gas pocket head loss in the blow-back flow regime follows a pipe Weber number scaling. A numerical model for the prediction of the air discharge as a function of the relevant system parameters is proposed. The novelty of this paper is the presentation of experimental data and a numerical model that cover all flow regimes on air transport by flowing water in downward inclined pipes.     

An experimental study of fuel injection strategies in CAI gasoline engine

Combustion of gasoline in a direct injection controlled auto-ignition (CAI) single-cylinder research engine was studied. CAI operation was achieved with the use of the negative valve overlap (NVO) technique and internal exhaust gas re-circulation (EGR). Experiments were performed at single injection and split injection, where some amount of fuel was injected close to top dead centre (TDC) during NVO interval, and the second injection was applied with variable timing. Additionally, combustion at variable fuel-rail pressure was examined.Investigation showed that at fuel injection into recompressed exhaust fuel reforming took place. This process was identified via an analysis of the exhaust-fuel mixture composition after NVO interval. It was found that at single fuel injection in NVO phase, its advance determined the heat release rate and auto-ignition timing, and had a strong influence on NO_X emission. However, a delay of single injection to intake stroke resulted in deterioration of cycle-to-cycle variability. Application of split injection showed benefits of this strategy versus single injection. Examinations of different fuel mass split ratios and variable second injection timing resulted in further optimisation of mixture formation. At equal share of the fuel mass injected in the first injection during NVO and in the second injection at the beginning of compression, the lowest emission level and cyclic variability improvement were observed.