Topological classification of affine mappings from ℝ<Superscript>2</Superscript> into ℝ<Superscript>2</Superscript>

We investigate affine mappings from ℝ² into ℝ² and establish necessary and sufficient conditions for the topological conjugacy of these mappings. Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 472–480, October–December, 2008.     

Roughness effects in low-<Emphasis Type="Italic"> Re</Emphasis><Subscript><Emphasis Type="Italic"> θ</Emphasis></Subscript> open-channel turbulent boundary layers

This paper reports velocity measurements obtained on a smooth and two geometrically different types of rough surfaces in an open channel. The measurements were obtained using a laser-Doppler anemometer. The recent boundary layer theory proposed by George and Castillo (1997) and conventional scaling laws are used to analyze the data. The present flow shows a strong structural similarity to a canonical turbulent boundary layer in the inner layer. The results demonstrate that surface roughness increases the wake parameter. Surface roughness also enhances the levels of turbulence intensities, Reynolds shear stress and triple correlations over most of the boundary layer, but decreases the stress anisotropy.     

K F Jensen; E O Einset; D I Fotiadis; 董务民

<正> 1 引言 1.1薄膜沉积技术 把无机薄膜气相母体沉积到固定基体上,是广泛技术应用范围内的一个关键环节.这些技术应用包括制备微电子电路,光记录和磁记录介质,光学器件,以及高性能切割和研磨工具.沉积薄膜的厚度范围从几个纳米(nm),例如量子阱光学器件的活性层,到几十个微米(μm),例如耐磨镀层.生产薄膜时必须能够控制其性质(例如,纯度,组分,厚度,粘附力,晶体结构以及表面形态).此外,沉积不能对基体中已有的微结构有显著的影响.对薄膜的性质的容许限度范围随不同的应用而变,可是,严格的要求是电子和光学材料加工中的特征.在电子和光学材料加工这类应用中,要求的严格程度随集成度的提高、器件尺寸的减小和器件复杂程度的提高等而提高.薄膜厚度的均匀性一般要求很高,以便在穿越每个     

四川凉山州美姑县“6·1”泥石流灾害研究

四川凉山州美姑县“6.1”泥石流灾害实例研究表明,该泥石流约为20年一遇的中小规模的泥石流。流域上游短历时强降雨和冰雹天气过程是这次泥石流暴发的诱因,流域内退化的生态环境和中下两岸不稳定边坡以及沟道内大量的松散堆积物为这次泥石流提供了丰富的固体物质来源。泥石流堆积物具有典型的多峰型粒度特征,且有较高的粘粒含量。巨大的泥石流漂砾、石背石现象、龟裂现象、侧积堤和龙头堆积证实了这次泥石流为粘性泥石流。危险度评价表明,采莫洛沟属于高度危险的泥石流沟,危险度为0.67;乃托沟属于中度危险的泥石流沟,危险度为0.58。风险评估结果可知,两沟都属于泥石流高风险区风险度分别为0.52和0.45。高风险区的泥石流灾害给当地的经济社会造成了严重影响并直接造成了较大的人员伤亡和财产损失。     

论“岩体结构控制论”

经过长期实践和研究,作者于1984年提出岩体结构控制论是岩体力学的基础理论,并全面、系统地以岩体结构控制论为指导研究了岩体变形、岩体破坏及岩体力学性质的基本规律;提出岩体变形系山岩体材料变彤和岩体结构变形共同贡献的,岩体破坏系受岩体材料破坏和岩体结构破坏控制的;岩体力学性质不仅决定于岩体材料力学的性质,而且受控于岩体结构力学效应及环境因素力学效应。在此基础上,作者提出了岩体可以划分为连续介质、碎裂介质,块裂介质及板裂介质四种岩体力学介质,从而建立了完整的岩体结构力学理论体系。     

The Navier-Stokes Equations in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> with Linearly Growing Initial Data

Consider the equations of Navier-Stokes on ⁿ with initial data U₀ of the form U₀(x)=u₀(x)–Mx, where M is an n×n matrix with constant real entries and u₀ L^p(ⁿ). It is shown that under these assumptions the equations of Navier-Stokes admit a unique local solution in L^p(ⁿ). Moreover, if ||e^tM||1 for all t0, then this mild solution is even analytic in x. This is surprising since the underlying semigroup of Ornstein-Uhlenbeck type is not analytic, in contrast to the Stokes semigroup.Acknowledgement It is our pleasure to thank G. METAFUNE, E. PRIOLA and A. RHANDI for fruitful discussions on the Ornstein-Uhlenbeck     

80&#176;／65&#176;双三角翼摇滚特性风洞实验研究

介绍了在FL-23高速风洞中研究自由摇滚的装置、试验方法、数据采集等试验技术。在马赫数从0．3到0．6范围内,对应的雷诺数从0．56&#215;10^7／m至1．126&#215;10^7／m范围内,开展了双三角翼大迎角下的摇滚特性的研究,包括迎角、马赫数、初始释放等参数的影响,给出了典型的结果。结果表明,随着模型迎角的增加,双三角翼呈现不同的滚转运动形态,包括静态稳定、准极限环摇滚、双周期震荡等;试验中马赫数提高对翼摇滚起抑制作用;摇滚运动的最终平衡状态和摇滚幅值与初始状态无关。     

Elastic properties of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–NiAl: a modified version of Hashin–Shtrikman bounds

The modified nonlinear relations for the estimation of elastic constants of Al₂O₃–NiAl composite material are developed. The concept of microstructure and interconnectivity of phases at the interface is used. Hashin–Shtrikman relations are described in their actual form and modified version of Hashin–Shtrikman relations for bulk and shear moduli are discussed. These relations for elastic and mechanical properties are applied mainly for Al₂O₃–NiAl composite material. Theoretical predictions using modified relations are compared with Hashin–Shtrikman bounds and experimental results of elastic properties for Al₂O₃–NiAl matrix-inclusion-based composite. It is found that the predicted values of elastic and mechanical properties using modified relations are quite close to the experimental results.     

Synchronization of unified chaotic system by sliding mode/mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

This paper deals with the synchronization of uncertain unified chaotic system in the presence of two kinds of disturbances, white noise and bounded power signal. A sliding mode controller (SMC) is established to guarantee the sliding motion. Moreover, a proportional-integral (PI) switching surface is used to determine the performance of the system in the sliding motion. Also, by using a mixed H ₂/H _∞ approach, the effect of external disturbances on the sliding motion is reduced. The necessary parameters of constructing controller and switching surface are found via semidefinite programming (SDP) which can be solved effectively by a standard software. Finally, a numerical simulation is presented to show the effectiveness of the proposed method.     

A Global Foliation of Einstein–Euler Spacetimes with Gowdy-Symmetry on <Emphasis Type="Italic">T</Emphasis><Superscript>3</Superscript>

We investigate the initial value problem for the Einstein–Euler equations of general relativity under the assumption of Gowdy symmetry on T ³, and we construct matter spacetimes with low regularity. These spacetimes admit both impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularities propagating at light speed) and shock waves in the fluid (that is, discontinuities propagating at about the sound speed). Given an initial data set, we establish the existence of a future development, and we provide a global foliation in terms of a globally and geometrically defined time-function, closely related to the area of the orbits of the symmetry group. The main difficulty lies in the low regularity assumed on the initial data set which requires a distributional formulation of the Einstein–Euler equations.     

Two-Phase Problems for Linear Elliptic Operators with Variable Coefficients: Lipschitz Free Boundaries are <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">1,γ</Emphasis></Superscript>

We prove C ^1, regularity of Lipschitz free boundaries of two-phase problems for linear elliptic operators with Hölder continuous coefficients.     

Entropy Solutions in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">∞</Emphasis></Superscript> for the Euler Equations in Nonlinear Elastodynamics and Related Equations

A compactness framework is established for approximate solutions to the Euler equations in one-dimensional nonlinear elastodynamics by identifying new properties of the Lax entropies, especially the higher order terms in the Lax entropy expansions, and by developing ways to employ these new properties in the method of compensated compactness. Then this framework is applied to establish the existence, compactness, and decay of entropy solutions in L for the Euler equations in nonlinear elastodynamics with a more general stress-strain relation than those for the previous existence results. This compactness framework is further applied to solving the Euler equations of conservation laws of mass, momentum, and energy for a class of thermoelastic media, and the equations of motion of viscoelastic media with memory.     

Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response

In this paper, the global stability of virus dynamics model with Beddington–DeAngelis infection rate and CTL immune response is studied by constructing Lyapunov functions. We derive the basic reproduction number R ₀ and the immune response reproduction number R ⁰ for the virus infection model, and establish that the global dynamics are completely determined by the values of R ₀. We obtain the global stabilities of the disease-free equilibrium E ₀, immune-free equilibrium E ₁ and endemic equilibrium E ^∗ when R ₀≤1, R ₀>1, R ⁰>1, respectively.     

“工程地质基本理论”座谈综述

1　问题的提出任何学科都有自身的基本理论。鉴于过去对学科基本理论未作深究,更主要的是产业部门忙于繁重的生产任务,无暇顾及此类问题;科研部门埋头钻研专题研究,亦未触及此类问题;在教育部门的教学大纲中也缺乏这方面的要求。从而,在基本理论问题上似乎形成了“真空”。因此,有些工程地质工作者们,尖锐地提出了“工程地质学到底有没有基础理论 ?”为此,中国地质学会工程地质专业委员会从1999年 12月 14日起组织了 5次研讨会,分别是 :(1) 1999年 12月 14日议题———“2 1世纪工程地质学发展”。     

Multivalued penalty method for evolution variational inequalities with <Emphasis Type="Italic">λ</Emphasis><Subscript>0</Subscript>-pseudomonotone multivalued maps

We consider evolution variational inequalities with λ ₀-pseudomonotone maps. The main properties of these maps are investigated. By using the finite-difference method, we prove the property of strong solvability for the class of evolution variational inequalities with λ ₀-pseudomonotone maps. Using the penalty method for multivalued maps, we show the existence of weak solutions of evolution variational inequalities on closed convex sets. The class of multivalued penalty operators is constructed. We also consider a model example to illustrate this theory.     

Adaptive <Emphasis Type="Italic">Q</Emphasis>–<Emphasis Type="Italic">S</Emphasis> synchronization of non-identical chaotic systems with unknown parameters

This work investigates the adaptive Q–S synchronization of non-identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q–S synchronization of two different chaotic systems (including different dimensional systems) are derived, based on Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the non-identical chaotic systems are to have Q–S synchronization. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.     

Young’s modulus defect for the solid solution of hydrogen in palladium (PdH<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)

We use the internal friction method in the free vibration mode to study the temperature dependence of the spectra of dissipative losses and shear modulus in the Pd polycrystalline system, the PdH _x penetration solid solution, and in the dehydrogenized Pd system. Studying the spectra and shear moduli, we discovered that the hydrogen desorption from the α- and β-phases of the PdH _x system occurs completely after the first cycle of heating of this system. The temperature dependences of the shear modulus of the original and dehydrogenized systems coincide. The existence of dissipative processes in the solid solution is related to the mobility of hydrogen atoms in the face-centered cubic lattice of the Pd structure and provokes the appearance of peaks of losses on the modulus defect spectrum in the temperature region. We consider the possibility of describing the modulus defect in the framework of phenomenological models of elasticity. Dissolution of hydrogen atoms in a metal structure results in changes in the physical-mechanical characteristics of the obtained solid solutions compared with the original dehydrogenized metals.     

A Phase-Partitioning Model for CO<Subscript>2</Subscript>–Brine Mixtures at Elevated Temperatures and Pressures: Application to CO<Subscript>2</Subscript>-Enhanced Geothermal Systems

Correlations are presented to compute the mutual solubilities of CO₂ and chloride brines at temperatures 12–300°C, pressures 1–600 bar (0.1–60 MPa), and salinities 0–6 m NaCl. The formulation is computationally efficient and primarily intended for numerical simulations of CO₂-water flow in carbon sequestration and geothermal studies. The phase-partitioning model relies on experimental data from literature for phase partitioning between CO₂ and NaCl brines, and extends the previously published correlations to higher temperatures. The model relies on activity coefficients for the H₂O-rich (aqueous) phase and fugacity coefficients for the CO₂-rich phase. Activity coefficients are treated using a Margules expression for CO₂ in pure water, and a Pitzer expression for salting-out effects. Fugacity coefficients are computed using a modified Redlich–Kwong equation of state and mixing rules that incorporate asymmetric binary interaction parameters. Parameters for the calculation of activity and fugacity coefficients were fitted to published solubility data over the P–T range of interest. In doing so, mutual solubilities and gas-phase volumetric data are typically reproduced within the scatter of the available data. An example of multiphase flow simulation implementing the mutual solubility model is presented for the case of a hypothetical, enhanced geothermal system where CO₂ is used as the heat extraction fluid. In this simulation, dry supercritical CO₂ at 20°C is injected into a 200°C hot-water reservoir. Results show that the injected CO₂ displaces the formation water relatively quickly, but that the produced CO₂ contains significant water for long periods of time. The amount of water in the CO₂ could have implications for reactivity with reservoir rocks and engineered materials.