THE LIMITING CASE OF THIELE'S INTERPOLATING CONTINUED FRACTION EXPANSION

1. IntroductionWhen we talk abode the interpolation by polynomials, it is natural for us to have at heatthe Lagrange interpolation, the Heedte interpolation aam the Newton interPOlation. Of theSeinterpolats, the Newton interpolating polyno~ is probably most favourite because of itsadVantages in carrying out compilations and performing ~s. As we know, a Newton interpolating polynondal is established on the basis of the divided ~, whose recursivecalculation maal it possible that the Newton i…     

用逼近方法建立代数无关性(Ⅱ)

设ｆ（ｘ）是以ａｎｘ为元素的连分式,其中系数ａｎ是正代数数．应用［１］中的判别法则,在某些仅与ａｎ有关的条件下证明了对任何绝对值互异的非零实代数数ａ１,…,ａｓ值ｆ（ａ１）代数无关．还对某些实超越数建立了的代数无关性．     

CRYSTAF Analysis of Polyethylene Synthesized with Phillips Catalyst

Crystallization analysis fractionation (CRYSTAF) was used for the first time to investigate the solution crystallization behavior of ethylene homopolymers and copolymers made with Phillips CrO_x/SiO₂ catalyst. Interestingly, the crystallization peak temperatures (T_p) of copolymers of ethylene and cyclopentene increased with increasing cyclopentene molar fraction in the copolymer. Comparing two factors (short chain branches (SCBs) and cyclopentene incorporation), decreasing SCB frequency is proposed as the dominant factor to explain the increase of crystallization peak temperatures with increasing cyclopentene incorporation. In addition, SCB frequency and molecular weight might be the two significant factors determining the crystallization temperature of polyethylene made with Phillips CrO_x/SiO₂ catalyst with different cocatalysts (triethylaluminum and diethylaluminum ethoxide).     

Finite temperature aspect ratio in ultra-cold Bose gas for large N

We present a detailed study of the temperature dependence of the condensate fraction, collective excitation and aspect ratio profiles of a Bose-condensed gas in a harmonic trap for large numbers of condensate atoms up to 85000. These quantities are calculated self-consistently using the generalized Hartree–Fock–Bogoliubov (GHFB) equations. We determine the evolution of the aspect ratio at zero and finite temperature via the condensed fraction. We compare our results with experimental data and we find a good agreement.     

用拓扑优化设计多体分比蜂窝状结构

提出用拓扑优化及增材制造法设计同一材料制作的蜂窝状结构,并把设计可归结为在不同的设计域内使用不同的体分比的拓扑优化问题。首先推导了多体分比约束条件下的蜂窝状结构拓扑优化问题;然后提出了基于多阈值的等值面法及与商用有限元分析软件对接的算法。给出了有三个体积约束的最小柔顺性问题的数值算例。计算结果表明,对于具有三个体积约束的拓扑优化设计问题,存在一个最佳的体积约束组合;使用等量的材料,与两个体积约束的最佳拓扑设计相比,用最佳体积约束组合所得到的优化结构的柔顺性还要小10%。     

RESPONSE OF MICROPOLAR THERMOELASTIC SOLID WITH VOIDS DUE TO VARIOUS SOURCES UNDER GREEN NAGHDI THEORY

Green-Naghdi (G-N) theory of thermoelasticity is employed to study the deformation of micropolar thermoelastic solid with voids considering the influence of varions sources acting on the plane surface....     

Gas–liquid flows in a microscale fractal-like branching flow network

Two-phase air–water flows in a microscale fractal-like flow network were experimentally studied and results were compared to predictions from existing macroscale void fraction correlations and flow regime maps. Void fraction was assessed using (1) two-dimensional analysis of high-speed images (direct method) and (2) experimentally determined using gas velocities (indirect method). Fixed downstream-to-upstream length and width ratios of 1.4 and 0.71, respectively, characterize the five-level flow network. Channels were fabricated in a 38 mm diameter silicon disk, 250 μm deep disk with a terminal channel width of 100 μm. A Pyrex top allowed for flow visualization. Superficial air and water velocities through the various branch levels were varied from 0.007 m/s to 1.8 m/s and from 0.05 m/s to 0.42 m/s, respectively. Two-phase flow regime maps were generated for each level of the flow network and are well predicted by the Taitel and Dukler model. Void fraction assessed using the indirect method shows very good agreement with the homogeneous void fraction model for all branch levels for the given range of flow conditions. Void fraction determined directly varies considerably from that assessed indirectly, showing better agreement with the void fraction correlation of Zivi.     

Application of the ultrasonic technique and high-speed filming for the study of the structure of air–water bubbly flows

Multiphase flows are very common in industry, oftentimes involving very harsh environments and fluids. Accordingly, there is a need to determine the dispersed phase holdup using noninvasive fast responding techniques; besides, knowledge of the flow structure is essential for the assessment of the transport processes involved. The ultrasonic technique fulfills these requirements and could have the capability to provide the information required. In this paper, the potential of the ultrasonic technique for application to two-phase flows was investigated by checking acoustic attenuation data against experimental data on the void fraction and flow topology of vertical, upward, air–water bubbly flows in the zero to 15% void fraction range. The ultrasonic apparatus consisted of one emitter/receiver transducer and three other receivers at different positions along the pipe circumference; simultaneous high-speed motion pictures of the flow patterns were made at 250 and 1000 fps. The attenuation data for all sensors exhibited a systematic interrelated behavior with void fraction, thereby testifying to the capability of the ultrasonic technique to measure the dispersed phase holdup. From the motion pictures, basic gas phase structures and different flows patterns were identified that corroborated several features of the acoustic attenuation data. Finally, the acoustic wave transit time was also investigated as a function of void fraction.     

An application of the wavelet analysis technique for the objective discrimination of two-phase flow patterns

This paper presents an application of the wavelet analysis technique for two-phase flow pattern identification by using the void fraction signals obtained from a multi-channel Impedance Void Meter (IVM) in a vertical-upward air–water flow. A new method for the objective discrimination of the two-phase flow pattern has been developed to provide information regarding the local energy of void fraction signals at a given scale on the joint time–frequency diagram. The void signals are processed with Continuous Wavelet Transform (CWT) to get the local wavelet energy coefficients map on the time–frequency diagram. The effective local wavelet energy and the effective scale are then calculated. Then the criteria for flow pattern identification are, finally, obtained. A series of void fraction measurements were conducted over a wide range of air–water vertical-upward flow condition to provide an extensive database to cover several types of flow patterns. The results show that the proposed method has a high precision for characterizing different flow regimes in two-phase flow, and is considerably more promising for the online recognition of two-phase flow patterns due to the short time of data processing.     

Modelling of The Rheological Properties of Bimodal Emulsions

The model of Ouchiyama and Tanaka 1 - 3 was successfully adapted to calculate the maximum packing fraction (ϕ_m) of polymer latexes with varying bimodal particle size distributions based upon rheological measurements performed on its constituent parts. The values of ϕ_m calculated from the model can be used to predict the rheological properties of the latices. The model was experimentally validated and used for the prediction the viscosity of studied bimodal latices of known concentration using the master curve of viscosity-reduced volume fraction (η vs. ϕ/ϕ_m).