有效集法在数学规划加权残值法中的应用

本文研究有效集法在数学规划加权残值法求解微分方程问题中的应用。从理论上和实际应用方面 阐明，对于数学规划加权残值法和线性规划问题，有效集法比常用的单纯形法更简便、易程序化、计算速度更快，因此更适用于数学规划加权残值法求解微分方程问题。     

Investigation of the flow and heat transfer of viscous reacting fluids in long tubes

Heat transfer and resistance in the case of laminar flow of inert gases and liquids in a circular tube were considered in [1–4], the justification of the use of boundary-layer type equations for investigating two-dimensional flows in tubes being provided in [4]. The flow of strongly viscous, chemically reacting fluids in an infinite tube has been investigated analytically and numerically in the case of a constant pressure gradient or constant flow rate of the fluid [5–8]. An analytic analysis of the flow of viscous reacting fluids in tubes of finite length was made in [9, 10]. However, by virtue of the averaging of the unknown functions over the volume of the tube in these investigations, the allowance for the finite length of the tube reduced to an analysis of the influence of the time the fluid remains in the tube on the thermal regime of the flow, and the details of the flow and the heat transfer in the initial section of the tube were not taken into account. In [11], the development of chemical reactions in displacement reactors were studied under the condition that a Poiseuille velocity profile is realized and the viscosity does not depend on the temperature or the concentration of the reactant; in [12], a study was made of the regimes of an adiabatic reactor of finite length, and in [13] of the flow regimes of reacting fluids in long tubes in the case of a constant flow rate. The aim of the present paper is to analyze analytically and numerically in the two-dimensional formulation the approach to the regimes of thermal and hydrodynamic stabilization in the case of the flow of viscous inert fluids and details of the flow of strongly viscous reacting fluids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–25, January–February, 1930.     

Remarks on the Behavior of Simple Directionally Reinforced Incompressible Nonlinearly Elastic Solids

The effect of directional reinforcing in generating qualitative changes in the mechanical response of a base neo-Hookean material is examined in the context of homogenous deformation. Single axis reinforcing giving transverse isotropy is the major focus, in which case a standard reinforcing model is characterized by a single constitutive reinforcing parameter. Various qualitative changes in the mechanical response ensue as the reinforcing parameter increases from the zero-value associated with neo-Hookean response. These include (in order): the existence of a limiting contractive stretch for transverse-axis tensile load; loss of monotonicity in off-axis simple shear; loss of monotonicity in on-axis compression; loss of positivity in the stress-shear product in off-axis simple shear; and loss of monotonicity for plane strain in on-axis compression. The qualitative changes in the simple shear response are associated with stretch relaxation in the reinforcing direction due to finite rotation. This revised version was published online in August 2006 with corrections to the Cover Date.     

化学跑合对齿轮胶合的影响

选用了３ 种跑合剂在ＣＬ－１００ 型齿轮试验机上进行满载跑合能力对比试验和齿轮抗胶合载荷级对比试验．结果表明：材质为４５＃ 钢的试验齿轮副和材质为２０ＣｒＭｎＴｉ钢的试验齿轮副用含磨料跑合剂进行１ 次满载跑合试验时,发生严重胶合;而采用化学跑合剂可以实现１ 次满载跑合,且用化学跑合剂跑合后的齿面比用普通油跑合后的齿面抗胶合能力提高１ 个载荷级,显示化学跑合剂在齿轮中的应用很有潜力．     

Some electrodynamic effects in a MHD generator duct

Theoretical and experimental studies made in recent years show that the plasma flow in the duct of a real MHD generator differs significantly from the quasi-uniform model of the flow in an idealized MHD duct. This difference appears primarily in the analysis of the electrodynamics of the MHD generator. Usually the actual electrical characteristics of the generator are poorer than expected, which may be caused, in particular, by flow nonuniformities and electrical leaks in the duct. The influence of these factors shows up particularly strongly in the presence of the Hall effect.Some qualitative and quantitative estimates of these phenomena have already been made in the literature. The necessity for taking into account the influence of the cold boundary layer on the effective conductance of the plasma in the duct was shown in [1]; in [2] it was shown that this influence increases markedly in the presence of the Hall effect. The influence of shunting of the plasma by the electrically conductive walls of the duct was considered in [3–5].The present paper describes an analysis of the combined influence of the effects associated with flow nonuniformities and electrical leaks for the case of anisotropy of the plasma conductivity, and an example is presented of the calculation of flow in a MHD generator with finite variation of the parameters.     

双柱单锥型液-液旋流管内流场的激光诊断

应用激光测速仪，对一种双柱单锥型液 液旋流管内的流动结构，进行了全场范围内的多工况流动诊断研究．揭示出其切向速度由内旋流区和外旋流区构成，其中内旋流区中的速度分布符合准强制涡关系，外旋流区中的速度分布符合准自由涡关系；轴向速度由上行流动区和下行流动区构成，两者之间在直管段以零速点作分界，在锥体段则以零速区作过渡并伴随有一定的回流出现，且该过渡区或回流区的大小随锥体截面的收缩而减小，直到进入直管段后消失；各湍流量的分布以管芯处最大向外逐渐减小，沿轴向是直管段中的湍流度大于锥体段中的湍流度，而且湍流度在旋流管内具有各向异性的特性．     

Comparison theorems for some problems of filtration in inhomogeneous ground

The influence of variation in the inhomogeneity of the ground on the solution of filtration problems in the case of earth dams and canals is investigated. A class of problems is identified for which one can specify variations of the filtration coefficient that lead to a change in the position of the depression curve in a definite direction. Similar comparison theorems for the case of a change in the shape of particular sections of the boundary of the region were obtained in [1], in which, in particular, the change in the position of the depression curve was investigated. As examples of the application of the results, the solution for a dam with a vertical inhomogeneity of the ground is estimated in terms of the solution for a homogeneous dam with the same profile, and an axisymmetric problem is also estimated in terms of the solution of the corresponding two-dimensional problem. The obtained results can be used both in a theoretical investigation of such problems as well as with a view to obtaining estimates of a required solution in terms of known solutions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 165–169, March–April, 1981.We thank N. B. Il'inskii for constant interest in the work.     

Separation zone in fluctuating flow past an obstacle in a channel

The results of an experimental investigation of hydrodynamic processes in separated turbulent flows in the presence of superimposed flow-rate fluctuations are presented. A sharp shortening of the separation zone in the fluctuating flow is found to exist in the vicinity of Sh = 1. The dependence of the separation zone length on the superimposed fluctuation frequency is the same in the cases in which the obstacle is located in the regions of antinodes of both the flow velocity and the pressure.     

Ultrasonic measurement of the bending of a bolt in a shear joint

An ultrasonic pulse/echo technique is used to measure preload in bolts used in structural joints. In this paper, the same instrument is used in a different way to measure change in the ultrasonic measurements due to bending in the bolts. A theory that explains the ultrasonic measurements is developed. The bending loads result in a rotation and a translation of the ultrasonic pulse reflecting face. It also creates a stress gradient in the bolt. This results in a phase variation (or gradient) in the received ultrasonic beam across the face of the transducer. It also results in a physical shift in the received beam relative to the ultrasonic transducer. The phase gradient and the shift in the beam results in change in the pulse travel time. A number of experiments were performed on the bolt to study the effect of the bending on the ultrasonic measurements. The experiments and the theory validate a sensitive new method for measuring the bending loads in the bolts.     

Drag reduction and heat transfer in surfactant solutions with excess counterion

We present the results of a study of turbulent drag reduction in a small circulating loop using surfactant solutions with excess counterion. In addition, these solutions were used in measurements of heat transfer, both in pipe flow and in an impinging jet. Both frictional drag and heat transfer were reduced in the pipe flow experiments. Measurements of heat transfer in the impinging jet revealed a dependence on the molar concentration ratio of the counterion. When the counterion was added at a molar concentration 30 times higher than that of the surfactant, the resulting surfactant solution did not reduce the rate of heat transfer in the impinging jet. By using this surfactant system in an impinging jet, we show both a reduction in pipe friction and normal heat transfer potential in a circulating heat exchange system. In order to investigate this difference in heat transfer between pipe flows and impinging jet flows, a comparison was made of the wall shear stress between these two flow regimes. The estimated wall shear stress was of the same order in both flows, and thus was not considered to be the primary cause of the difference in heat transfer. It is instead suggested that the micellar structure of the surfactant is influenced by a compressive deformation of the impinging flow in a manner that is different from the shear deformation observed in pipe flow.     

Increase of initial velocity and pressure upon impact on an inhomogeneous target

It is proved on the basis of an analysis conducted by means of the method of (p, u)-diagrams in an acoustic approximation that the mass velocity of the material of a target increases when a shock wave propagates along a target in which the acoustic resistance of the layers decreases in the direction of propagation, and it can even exceed the initial velocity of the striker. An increase in pressure behind the wave front similar to the example of unbounded accumulation in a plane shock wave considered in [2] is observed when a striker impacts on a target in which the acoustic impedance of the layers increases in the direction of propagation of the shock wave. The increase in velocity is experimentially verified.     

Plate cascade in subsonic unsteady gas flow

Accounting for fluid compressibility creates serious difficulties in solving the problem of oscillations of a grid of thin, slightly curved profiles in a subsonic stream. The problem has been solved in [1–3] for a widely-spaced cascade without stagger whose profiles oscillate in phase opposition. The phenomenon of aerodynamic (acoustic) resonance, which may arise in a grid in the direction transverse to the stream for definite values of the stream velocity and profile oscillation frequency, was discovered in [2]. An approximate solution of the problem in which account is not taken of the effect of the vortex trails on the gas flow has been obtained in [4]. In [5, 6] Meister studied in the exact linear formulation the problem of unsteady gas motion through an unstaggered cascade of semi-infinite plates. In [7] Meister considered a grid of profiles with finite chords, but the problem solution was not completed. The problem of subsonic gas flow through a staggered lattice whose profiles oscillate following a single law with constant phase shift was solved most completely in the studies of Kurzin [8, 9] using the method of integral equations. A method of solving the problem for the case of arbitrary harmonic oscillation laws for the lattice profiles was indicated in [10]. The results of the calculation of the unsteady aerodynamic forces for the particular case of a plate cascade without stagger are presented in [9,11], and the possibility of the occurrence of aerodynamic resonance in the cascade in the directions transverse to and along the stream is indicated.Another method of solving the problem is given in [12], in which the more general problem of unsteady subsonic gas flow through a three-dimensional cascade of plates is solved. In the present study this method is applied to the solution of the problem of oscillations of staggered plate cascades in a two-dimensional subsonic gas flow. The results are presented of an electronic computer calculation of the unsteady aerodynamic characteristics of the cascade profiles, which show the essential influence of fluid compressibility on these characteristics. In particular, a sharp decrease of the aerodynamic damping in the acoustic resonance regimes is obtained.     

Relaxed representations and improving stability in time-stepping analysis of three-dimensional structural nonlinear dynamics

In the present paper, we propose a representation of the discrete motion equations in structural nonlinear dynamics to obtain an improvement in the stability of time numerical integrations. A geometrically nonlinear total Lagrangian formulation for three-dimensional beam elements in the hypotheses of large rotations and small strains is presented. In this formulation, slopes are used instead of rotation parameters to compute the nonlinear representations of the strain measures in the inertial frame of reference. Such representations of the internal strains??rotations compatibility are then imposed in their time derivatives version. The results, related to Newmark approximations for the variations in the displacement and velocity vectors, show a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations required in the time integration steps. The numerical tests, furthermore, show that the variation in the total energy in the time steps has bounded oscillations about the zero value.     

Prefacein：in dedication to Professors Yong Jin and Zhiqing Yu

This special issue of China PARTICUOLOGY is dedicated to Professors Yong Jin and Zhiqing Yu of Tsinghua University, China, to celebrate over five decades of their careers in chemical engineering research and education. Prof. Jin graduated in 1959 from Ural Polytechnic College in Svivdelovsk in the former USSR and then completed his post-graduate studies in Tianjin University in China in 1960. Thereafter, he taught at the Chinese University of Science and Technology for 13 years before joining Tsinghua University in 1973. Prof. Yu graduated in 1956 from Tianjin University in China and joined Tsinghua University thereafter. Between 1957 and 1959, Prof. Yu undertook more studies in Moscow Mendeleev Institute of Chemical Technology in the former USSR. During the 1970s, Professors Jin and Yu jointly created the Reaction Engineering Program in the Department of Chemical Engineering at Tsinghua University, which later became one of the largest fluidization research groups in the world, known as FLOTU - Fluidization Laboratory of Tsinghua University.     

Forced capillary-gravity wave motion of two-layer fluid in three-dimensions

A class of problems associated with forced capillary-gravity wave motion in a channel are analyzed in the presence of surface and interfacial tensions in a two-layer fluid in both the cases of finite and infinite water depths. The two and three-dimensional Green functions associated with the capillary-gravity wave problems in the presence of surface and interfacial tensions are derived using the fundamental source potentials. Using the two-dimensional Green function along with Green’s second identity, the expansion formulae for the velocity potentials associated with the capillary-gravity wavemaker problems in two-dimensions are obtained. The two-dimensional results are generalized to derive the expansion formulae for the velocity potentials associated with the forced capillary-gravity wave motion in the presence of surface and interfacial tensions in three-dimensions. Certain characteristics of the eigen-system associated with the expansion formulae are derived. The velocity potentials associated with the free oscillation of capillary-gravity waves in a closed basin and semi-infinite open channel in the presence of surface and interfacial tensions are obtained. The utility of the forced motion in a channel is demonstrated by analyzing the capillary-gravity wave reflection by a wall in a channel in the presence of surface and interfacial tensions. Long wave equations associated with capillary-gravity wave motion in the presence of surface and interfacial tensions are derived under shallow water approximation and the associated dispersion relation are obtained. Various expansion formulae and Green functions derived in the present study will be useful for analyzing a large class of physical problems in ocean engineering and mathematical physics.     

半晶态聚合物拉伸变形的微观机理

应用大规模分子动力学方法,采用粗粒化聚乙烯醇模型,模拟了晶区与非晶区随机交杂的半晶态聚合物模型系统,研究了半晶态聚合物在单轴拉伸变形过程中的应力-应变行为和微观结构演变.应力-应变曲线表现出4个典型变形阶段:弹性变形、屈服、应变软化和应变强化.在拉伸变形过程中,主要存在晶区折叠链之间的滑移、晶区破坏、非晶区的解缠结,以及分子链沿拉伸方向重新取向等4种主要的微结构演变形式.在屈服点附近,晶区分子链之间排列紧密程度减小而发生滑移,之后晶区变化需要的应力变小,从而形成应变软化现象.随着应变的增大,经各分子链段协同作用使非晶区分子链的解缠结和重新取向行为扩展到相对宏观尺度,导致拉伸应力增大而形成应变强化现象.      

Dissipative-convergent intermittency in dynamics of tidal waves in estuaries

The effect of dissipative-convergent intermittency in dynamics of tidal waves in estuaries is described. The effect manifests itself in spatial modulation of the tide amplitude. The effects of convergent channel and turbulent friction are competitive in dynamics of tidal waves in bays, gulfs, and estuaries. This manifests itself in the alternating excess of the action of one effect over another as the tidal wave penetrates deep the estuary. The effect of dissipative-convergent intermittency is manifested most completely in “strange” bays in which the mean water depth is commensurable with the Stokes layer thickness. It is shown that the spatial distribution of the tidal wave amplitude has a minimum in the convergent channel. If the minimum point lies beyond the estuary, then the effect of convergent channel predominates and the wave height increases to the vertex. If the minimum point lies in the neighborhood of the estuary vertex then the effect of turbulent friction predominates along the entire bay length and the wave height decreases to the bay vertex. Finally, if the minimum point finds itself in the middle part of the estuary, then the case of the “strange” bays arises, namely, in such bays the wave height decreases to crossing the minimum point and begins increases again after its passage. The local increase in the tidal wave amplitude can be manifested further in the mouth of the inflowing river.     

Heat exchange between a gas bubble and a liquid

The nonlinear problem of thermal and dynamic interaction between a single gas bubble and surrounding liquid is considered. This problem is met in studies of gas-liquid mixture flows, in particular, in Shockwave propagation in such media. A numerical solution is presented for various modes of bubble surface radial motion. The modes correspond to bubble behavior directly beyond a shock-wave front, where the latter enters the bubble screen, and to the behavior of a bubble located in the depths of the bubble curtain, where the wave becomes diffuse. Analytic solutions of the linearized problem of thermal conductivity for free and constrained small harmonic oscillations of a gas bubble in a liquid were obtained in [1, 2]. Cooling of a hot gas bubble was considered in [3], that study, however, contains inaccuracies. In particular, it was assumed in the solution that the gas density in the bubble was homogeneous. The equation for heat flux in dimensionless variables was written inaccurately. However, in the examples considered in [3] these inaccuracies do not lead to significant errors in the numerical results.     

动脉狭窄对血液流速的影响

为了定量计算动脉局部狭窄对动脉管中血液流动速度的影响，本文分别对狭窄区域内定常流和非定常流动进行了求解，得出了狭窄区域内定常流和脉动流的速度表达式。本文将均匀段的流速形经Ｆｏｕｒｉｅｒ分解成定常和脉动两部分，然后分别计算出狭窄区域内对应的定常和脉动流速，经Ｆｏｕｒｉｅｒ合成还原成流速时域波形，同时针对各种情况将不同狭窄对不同的流速波形的作了分析比较。     

Structure of the detonation wave front in a mixture of nitromethane with acetone

It is shown that the leading front of an inhomogeneous detonation wave is a shock wave in which wave structures of the type of triple shock configurations are moving. It was experimentally found that the reaction in these inhomogeneities occurs in oblique shock waves. The reaction sites at the wave front are ring-shaped. In a 75: 25 mixture of nitromethane with acetone, up to 70% of the front surface is occupied by the reaction at the sites in the wave front. Measurements of the mass velocity profile indicate that afterburning takes place in the unloading area behind the Jouguet plane. Calculations of the heat release in the reaction mixture with a decrease in the mass velocity indicate that the material that have not reacted in the inhomogeneities can be ignited in the induction zone. It is suggested that the adiabatic flashes are a mechanism that generates inhomogeneities in the detonation wave front.