GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS

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Generalized H-KKM Type Theorems in H-Metric Spaces with Applications

The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalized recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of know results in recent literature. Paper from DING Xie-ping, Member of Editoral Committee, AMM Foundation item: the National Natural Science Foundation of China (19871059) Biography: DING Xie-ping (1938-), Professor     

The attenuation of monochromatic surface waves due to the presence of an inextensible cover

The attenuation of surface gravity waves is an important process associated with air–sea and wave–current interactions. Here we investigate experimentally the attenuation of monochromatic surface gravity waves due to the presence of various surface covers. The surface covers are fixed in space such that they do not advect with the wave motion and are selected such that the bending modulus is negligible for the wave frequencies used in the experiment in order to minimize any flexural effects. Wave attenuation rates are found to be independent of wave steepness and the type of cover used over the tested parameter range. Results are consistent with the theoretical attenuation rate for an inextensible surface cover.     

Effect of flow and physical parameters on the wax deposition of Middle East crude oil under subsea condition: heat transfer viewpoint

Change in pressure, temperature, flow rate and concentration of oil causes precipitation and deposition of wax particles in the pipelines which has become a major problem for oil industries. By decreasing the capacity and economic efficiency of land oil reserves, demand for offshore reserves increases. Change in temperature in subsea pipelines is more possible and so the wax deposition happens under this condition more. Low water temperature and subsea condition change overall heat transfer coefficient and heat transfer rate in pipe cross-section which affects the wax transportation from bulk fluid to the wall. In this study, the effects of temperature, flow rate and oil characteristic in different pipeline diameters on Middle East oil which covers the most oil reserves of the world have been investigated under Persian Gulf water condition. Higher inlet temperature postpone the wax deposition to far locations and higher flow rate causes lower wax thickness in first stages of pipe and higher wax thickness after passing the first stage.     

Interaction between an incompressible flow and elastic cantilevers of circular cross-section

The purpose of this work is to study the deformation of elastic cantilevers due to hydrodynamic forces by coupled fluid–structure interaction simulations. The cantilever is placed in a rectangular duct and the Reynolds number based on bulk velocity and cantilever diameter is 400. Reduced velocities in the range π/4 to 2π are studied, which covers both un-synchronised motion and the initial branch of synchronisation. The cantilever surface is represented by a virtual boundary method which replaces a solid object in flow by additional force distribution to satisfy local boundary condition. The flow field is solved using a Cartesian finite difference code and the deformation of the cylinder a finite element approach using one-dimensional beam elements is used.     

A Simple Hysteretic Constitutive Model for Unsaturated Flow

The present study covers the problem of rotation of a porous disk under a viscous incompressible fluid that fills the half-space above the disk, which is the generalization of the von Karman’s problem. It is found that, instead of solving the exact problem, which is rather complicated by coupling the motions of the free fluid and that contained inside the permeable disk, it is sufficient to solve a much simpler problem of the motion of the free fluid placed onto a permeable plane. Assuming the flow in the permeable disk is described by the Brinkman equations, we obtain a self-similar formulation of the problem. Employing this formulation, we also show that the boundary condition associated with continuity of the tangential strains and tangential velocity components is satisfied at the fluid–porous body interface. The coefficient for the vertical velocity component is furthermore obtained. Various extreme cases are identified.     

The slow rotation of a sphere submerged in a fluid with a surfactant surface layer

The effect of a layer of an adsorbed surfactant monomolecular film of fluid which covers the surface of a large volume of a different substrate fluid is considered with respect to the fluid motion caused by the slow rotation of a submerged sphere. For a semi-infinite substrate, the boundary value problem posed with the surfactant boundary condition of Scriven and Goodrich is solved exactly for any depth of the submerged sphere. Comprehensive numerical calculations are given for the torque and surface velocity for various values of the parameters defining the depth of the sphere and the surface shear viscosity. Asymptotic expressions for the solution are given for the cases of a deeply submerged sphere or when the substrate has a finite depth. The relevance of the work to providing an experimental technique for measuring surface shear viscosity is also considered.     

An experimental study on the interactions between surface waves and floating viscoelastic covers

A possible mathematical ice model for the wave interactions in polar seas was developed based on the assumption that an ice cover behaved as a Voigt viscoelastic material. The dispersion relation was found to depend on the rheological properties of the cover. In the present study, an experimental approach was developed that can enable the verification of the theoretical predictions in the laboratory. The approach utilized the blended mixture of white oil and Polydimethylsiloxane (PDMS) material with various mass percentages of a curing agent, to create a floating layer with a range of targeted viscoelastic properties. Due to the large coverage required for wave flume experiments, special curing procedures were also established for the preparation of PDMS material. The rheological results showed that the mechanical behavior of the floating cover was close to a Voigt material. Experiments were conducted to analyze the wave interactions with the floating viscoelastic cover. The measured data showed an obvious change of wavelength when waves propagated along the cover region. It is observed that the change in wavelength can be linked quantitatively to the viscoelastic properties based on the numerical predictions by Wang and Shen (2010). Some differences were however noted for less viscous covers under longer wave periods. A direct comparison of the PDMS covers with a polypropylene (PP) cover was also performed for verification. Only wave lengthening was observed under the PP cover. With a shear modulus more than three orders of magnitude greater than that of PDMS, the theoretical wavelength for the PP cover from Wang and Shen (2010) is very close to that of the thin elastic plate theory from Fox and Squire (1990). Comparison between these two theoretical results and the measured data again deviated with longer wave periods. In both PDMS and PP cases, edge effects and pitching motion of the covers were present at various degrees. In addition, the materials were not strictly a Voigt type. The small deviation from the idealized rheological behavior could also contribute to differences between theoretical and experimental results.     

金属材料疲劳行为的应力场强法描述

基于近年来发展的应力场地对金属材料的多种疲劳行为作了系统的描述，给出了缺口疲劳系Ｋｆ，疲劳尺寸系数ε，疲劳加载方式因子ＣＬ，多轴疲劳极限方程，缺口件Ｓ－Ｎ曲线的预测等多方面的定量描述，并引用了大量的实验数据加以验证，由此表明应场强法是一种很好的抗疲劳设计方法。     

Critical heat flux in forced convective subcooled boiling with a plane wall jet (effect of subcooling on CHF)

Critical heat flux (CHF) during forced convective subcooled boiling with a plane jet has been yet made insufficient except for saturation condition when comparing CHF with impinging jet system including multiple jets. The present experiment has measured the CHF with plane jet on a rectangular heated surface of 40, 60, and 80 mm in length and 10 and 20 mm in width. Subcooled liquid being supplied through the plane jet with a different thickness of 1 and 2 mm, covers the heated surface where rigorous boiling takes place. The experiment varies a jet velocity from 3 to 15 m/s, a subcooling from 0 to 60 K, and system pressure at 0.1 MPa for water and at 1.5 to 3.0 MPa for R22. It is found that the existing correlation for saturation can be applied to the CHF of water, but hardly to the CHF of R22 in spite of saturation condition. After the effects of jet velocity and subcooling on the CHF can be elucidated, a new correlation including the effect of subcooling is proposed to predict most of the CHF data within an accuracy of ±20 percent. This correlation for saturated condition is found to interestingly agree with that theoretically derived by applying the Katto and Haramura criterion to this system. Received on 8 January 1997     

A review of turbomachinery tip gap effects : Part 1: Cascades

This two part review covers experiments examining the effects of blade tip gaps encountered in turbomachines and the methods by which the synthesised data are currently used in turbomachine design and analysis. Data gained since the 1930's are subdivided for convenience into cascade (Part 1) and rotating machinery¹ (Part 2) data, with a further subdivision into diffusing, or compressor type flows and accelerating, or turbine type flows. The overall trend is that an increasing tip gap, whose effect can reach over most or all of the blade height, reduces turbomachine performance. There is some evidence among the compressor and compressor cascade data that an optimum gap exists when the opposing effects of secondary flows and tip leakage with rotor/wall relative movement tend to balance. Turbine data are, in general, more regular than the body of compressor data, possibly because of the enhanced effect of, usually, undefined boundary layers in diffusing flow in the latter. Comment is made in Part 2 on the predictive and design models reported in the literature     

A review of turbomachinery tip gap effects: Part 2: Rotating machinery

This two part review covers experiments examining the effects of blade tip gaps encountered in turbomachines and the methods by which the synthesised data are currentl used in turbomachine design and analysis. Data gained since the 1930's are subdivided for convenience into cascade (Part 1) and rotating machinery (Part 2) data, with a further subdivision into diffusing, or compressor type flows and accelerating, or turbine type flows. The overall trend is that an increasing tip gap, whose effect can reach over most or all of the blade height, reduces turbomachine performance. There is some evidence among the compressor and compressor cascade data that an optimum gap exists when the opposing effects of secondary flows and tip leakage with rotor/wall relative movement tend to balance. Turbine data are, in general, more regular than the body of compressor data, possibly because of the enhanced effect of, usually, undefined boundary layers in diffusing flow in the latter. Comment is made in Part 2 on the predictive and design models reported in the liturature     

The study of sound wave propagation in rarefied gases using unified gas-kinetic scheme

Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme (UGKS). The numerical calculations are carried out for a wide range of wave oscillating frequencies. The corresponding rarefaction parameter is defined as the ratio of sound wave frequency to the intermolecular particle collision frequency. The simulation covers the flow regime from the continuum to free molecule one. The treatment of the oscillating wall boundary condition and the methods for evaluating the absorption coefficient and sound wave speed are presented in detail. The simulation results from the UGKS are compared to the Navier-Stokes solutions, the direct simulation Monte Carlo (DSMC) simulation, and experimental measurements. Good agreement with the experimental data has been obtained in the whole flow regimes for the corresponding Knudsen number from 0.08 to 32. The current study clearly demonstrates the capability of the UGKS method in capturing the sound wave propagation and its usefulness for the rarefied flow study.     

Sensitivity Analysis of Problems of Elasticity with Unilateral Constraints*

ABSTRACT A unified approach is developed for sensitivity analyses of unilateral problems for discrete and continuous elastic structures. Sensitivity analyses are crucial in problems of redesign or optimization of structures. The topic covers, in this paper, the problem of determining the variation of structural response, subject to variations of ihe design, material, and loading. This type of problem is inherently nonlinear and nondifFerentiable for structures with unilateral constraints and, in general, only directional sensitivities can be obtained. Employing modern methods of functional analysis and the principle of minimum potential energy, a general result is presented for determination of sensitivities, and the implications for discrete or discretized structures are discussed in some detail. Four example problems are used to illustrate different aspects of the sensitivity analysis and to show how to handle variations of unilateral constraints.     

Toughening under non-uniform ferro-elastic domain switching

The existing models of switch-toughening seldom consider the effect of non-uniform ferro-elastic domain switching in the vicinity of a crack. To explore this issue, an evolution law for the volume fraction of the switched portion under applied electromechanical loading is established from the minimum energy principle. Based on this law, a switching model capable of dealing with the non-uniform distribution of switching strain is developed. The domain switching zone is divided into a saturated inner core and an active surrounding annulus. Mono-domain solution of ferro-elastic toughening is obtained under the model of small scale domain switching. Toughening for ferroelectrics with different poling states is estimated via Reuss type approximation. Two sets of solutions are obtained according to spherical and cylindrical inclusions. The interval of toughening defined by these two models covers the range of experimental data. The same conclusion is reached for the size of the switching zone.     

Biophilic fractals and the visual journey of organic screen-savers

Computers have led to the remarkable popularity of mathematically-generated fractal patterns. Fractals have also assumed a rapidly expanding role as an art form. Due to their growing impact on cultures around the world and their prevalence in nature, fractals constitute a central feature of our daily visual experiences throughout our lives. This intimate association raises a crucial question - does exposure to fractals have a positive impact on our mental and physical condition? This question raises the opportunity for readers of this journal to have some visual fun. Each year a different nonlinear inspired artist is featured on the front cover of the journal. This year, Scott Draves's fractal art works continues this tradition. In May 2007, we selected twenty of Draves's artworks and invited readers to vote for their favorites from this selection. The most popular images will feature on the front covers this year. In this article, we discuss fractal aesthetics and Draves's remarkable images.     

数值流形方法及其在岩石力学中的应用

数值流形方法是目前岩石力学分析的主要方法之一.该方法起源于不连续变形分析,主要用于统一求解连续和非连续问题,其核心技术是在分析时采用了双重网格:数学网格提供的节点形成求解域的有限覆盖和权函数;而物理网格为求解的积分域.数学网格被用来建立数学覆盖,数学覆盖与物理网格的交集定义为物理覆盖,由物理覆盖的交集形成流形单元.流形方法的优点在于它使用了独立的数学和物理网格,具有和有限元明显不同的定义形式,且数学网格对于同一问题不同的求解精度的需求可以很方便地细化.由于该方法考虑了块体运动学,可以模拟节理岩体裂隙的开裂和闭合过程,因而在岩石力学中得到了广泛应用,近年来许多学者对该方法进行了研究.本文简要叙述了节理岩体的数值方法从连续到非连续的发展过程,详细地介绍了数值流形方法的组成和数值流形方法在岩石力学及其相关领域的研究和发展概况,最后就作者所关心的一些问题,如三维问题的数值流形方法、数值流形方法在物理非线性问题和裂纹扩展问题中的应用、相关的耦合方法等进行了探讨.      

昆虫飞行参数测量实验研究进展

在昆虫飞行的实验研究中,可采用活体实验、模型实验和活体模型结合三种方法。活体实验可以客观反映自然界中昆虫的飞行规律,获得真实的实验数据,但可重复性差。模型实验作为机械装置可以重复进行试验,详细描述流场结构并定量各种参数大小,但与真实飞行存在一定差距。单独使用这两种中的任一方法均可对一些现象给出了解释。二者相结合的方法更易于准确描述昆虫的运动特征,通过对比模型与活体的结果来提出机理,尽管需要的实验周期较长,但结论往往更接近真实状态,基于该方法科学家们已提出了几种飞行机理。本文结合近几年文献报道,综述了昆虫飞行参数测量方法,并对以上几种方法在研究昆虫飞行机理中的作用进行了对比分析,认为模型和活体结合的研究方法更容易为一些飞行现象提出合理解释。     

A multi level approach to synthesis of planar mechanisms

A multi level approach to synthesis of planar mechanisms is presented. The approach covers both structural and dimensional synthesis of planar rigid body mechanisms containing revolute and translational joints. The synthesis is based on four different criteria. Firstly the type of mechanism is chosen with a view to get the simplest mechanism that satisfactorily fulfills the remaining three criteria. Two of these criteria are formulated as constraints on the kinematic behavior and the total area occupied by the mechanism, respectively. The fourth criteria is simply the desired minimization of the reactive forces/moments that appear in the mechanism. The desired kinematic behavior is based on a finite number, typically 1, ..., 6, of points in time (positions of the mechanism) where the position and orientation of up to two output bodies may be prescribed. The constraints on occupied areas are labelled territory constraints and formulated as a number of restricted areas (boxes). A synthesis is automatically performed at five levels. At the first level the structure of the mechanism is decided. At the second level initial dimensions for the given type of mechanism are found by random checking. At the third level the constraints on the kinematic behavior is fulfilled. At the fourth level the territory constraints are taken into account and, finally, at the fifth level the minimization of reactions is carried out. The entire approach has been implemented in a software package SYNMEC that runs on PCs and constitutes a way of performing the synthesis of a mechanism that is general and flexible with respect to both the type of mechanism that may be synthesized as well as the desired behavior upon which the synthesis is based.     

Symbolic dynamics of Belykh-type maps

The symbolic dynamics of a Belykh-type map (a two-dimensional discontinuous piecewise linear map) is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.