Averaged topological equations for dispersed two-phase flows

A general relationship between the volume fraction and the specific interfacial area for averaged dispersed two-phase flows is proposed. This relationship, expressed as a basic set of two scalar evolution equations and two vectorial non-uniformity state equations, is an analytical result obtained by a systematic approach using the derivatives of some generalized functions and a local volume-averaging technique. The proposed set of equations was expressed for measurable macroscopic parameters of the system and has the same generality as the averaged transport equations of two-phase flows. By combination of the basic set of equations, called the averaged topological equations (ATEs), second-order ATEs for the volume fraction were found. The second-order ATEs were expressed both by a Lagrangian formulation and by a Eulerian formulation. The importance and physical meaning of the ATEs developed in this study were clarified within the framework of the theory of kinematic waves.     

On the Statistics of Partial Quotients of Finite Continued Fractions

We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss-Kuzmin statistics.     

Three Types of Expression in Dark-Soliton Perturbation Theory Based on Squared Jost Solutions

Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of perturbagion on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.     

Measurement of acoustic particle velocities in enclosed sound field: Assessment of two Laser Doppler Velocimetry measuring systems

The performances of two Laser Doppler Velocimetry (LDV) systems adapted for measuring the acoustic particle velocities are assessed in enclosed sound field. This assessment is performed by comparing the acoustic velocities measured by means of LDV to reference acoustic velocities estimated from sound pressure measurements. The two LDV systems are based on a single optical bench which delivers an optical signal called Doppler signal. The Doppler signal, which is frequency modulated, is analyzed by means of two signal processing systems, the BSA (Burst Spectrum Analyser from Dantec) on the one hand, and a system specifically developed for the estimation of the acoustic velocity on the other hand. Once the experimental setup has been optimized for minimizing the errors made on the reference velocities, the assessment is performed and shows that both systems can measure the acoustic velocity in enclosed field in two the frequency ranges [0-4 kHz] and [0-2 kHz] respectively for acoustic velocity amplitudes of 10 mm/s and 1 mm/s.     

Monotone Mappings and Flows of Viscous Media

We establish solvability of the boundary-value problems describing stationary and periodic flows of viscoplastic media. In the case of stationary flows we study the question of convergence of the Galerkin method. For the problem of periodic flows we prove a version of the second Bogolyubov theorem.     

Galactic Metrics

The paths of stars in galaxies have circular velocity independent of their distance from the centre of the galaxy. Newtonian mechanics with a logarithmic potential has such paths. In relativity these paths can be taken to be geodesics and this requirement places a restricting equation on the spacetime metric. This equation has a non-unique spherically symmetric solution that in the Newtonian limit has a logarithmic potential. It also can be solved in terms of a conformal factor. In particular it has solutions which are conformal to the vacuum-Einstein solutions and such spacetimes are solutions to the vacuum-Bach equations. Therefore it is suggested that the Bach equations describe dynamics on galactic length scales.     

垂直低温两相流管底液氮汽泡上升速度的实验研究

本文对垂直低温两相流管底部液氮汽泡的上升速度运用高速摄像机进行了可视化实验研究,对所采集的实时图像进行处理.在Cole和Mendelson汽泡上升速度经验公式的基础上,通过对液氮汽泡的上升速度的分析,提出了圆管管路底部液氮汽泡的上升速度的拟合公式,分析研究其变化规律,为进一步探求圆管内液氮弹状汽泡的生成机理提供依据.     

GC-MS与GC-FTIR联合测定C9烃馏分组成

混合碳九组成复杂,估计为环状烯烃、芳烃、多环烃、烷烃等,目前该产品主要用于生产石油树脂。随着我国乙烯生产能力的不断扩大,其产量也在不断增加,为充分利用碳九资源,研究开拓其新的应用领域非常必要。而此研究的首要条件在于对其组成进行较为全面、准确地分析。传统的分析方法不能对其组成提供详尽的数据资料,直接影响了对碳九进行综合利用研究。GC-MS兼有GC的高效分离能力与MS很好的定性功能,且灵敏度较高,是分析有机混合物十分有效的手段。本文将GC-MS应用于碳九组成的定性分析中。但由于碳九组分中含有较多的同分异构体如三甲苯与二甲苯等,同分异构体的质谱图几乎相同,GC-MS对其不易鉴别,而红外(FTIR)对有机物同分异构体尤其苯系物的异构体具有非常好的鉴别能力。因此本文将GC-MS与GC-FTIR联合使用,对碳九组成进行定性分析,样品定量采用色谱氢火焰检测器峰面积归一化法得到的各组分峰面积相对百分含量,较好地解决了碳九组分的定性定量问题,为开发碳九新的应用领域提供依据。     

Comparison of the Dynamics of Water Molecules in Crystals of Proton-Ordered Ice IX and Its Proton-Disordered Analog III

A computer simulation of proton-ordered ice IX and its proton-disordered analog III (768 molecules, 90 K) was carried out by the molecular dynamics method using Poltev–Malenkov's potential. For ice IX, the differences in the dynamic characteristics of molecules with O(1) and O(2) are much wider than those in the case of ice III. The libration spectrum of ice IX has a number of distinct acute peaks, and the spectrum of ice III is strongly smoothed. These peculiarities are explained by the proton ordering of ice IX and disordering of ice III. The latter is responsible for the great differences in the short- and especially long-range environment of water molecules in ice crystals and hence for the presence of many molecules with different dynamic characteristics. Thus averaging over a large number of different vibrational spectra of molecules leads to a smoothed total spectrum in the case of the proton-disordered crystal modification of ice.     

Tree-gel and loop-gel conversions in nonlinear polymerization

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