Pullback attractor of 2D non-autonomous <Emphasis Type="Italic">g</Emphasis>-Navier-Stokes equations on some bounded domains

The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes eauations is given.     

Pullback attractor of 2D nonautonomous <Emphasis Type="Italic">g</Emphasis>-Navier-Stokes equations with linear dampness

The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness are investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.     

Pullback attractor of 2D nonautonomous g-Navier-Stokes equations with linear dampness

The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness are investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given. Key words pullback attractor, g-Navier-Stokes equation, pullback asymptotic compactness, fractal dimension, linear dampness     

Pullback Attracting Inertial Manifolds for Nonautonomous Dynamical Systems

In this paper we present an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance and squeezing property, and two additional technical assumptions, called boundedness and coercivity property. Moreover we give conditions which ensure that the global pullback attractor is contained in the inertial manifold. In the second part of the paper we consider special nonautonomous dynamical systems, namely processes (or two-parameter semi-flows). As a first application of our abstract approach and for reason of comparison with known results we verify the assumptions for semilinear nonautonomous evolution equations whose linear part satisfies an exponential dichotomy condition and whose nonlinear part is globally bounded and globally Lipschitz.     

Discretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary Delay

We prove the existence of a stationary random solution to a delay random ordinary differential system, which attracts all other solutions in both pullback and forwards senses. The equation contains a one-sided dissipative Lipschitz term without delay, while the random delay appears in a globally Lipschitz one. The delay function only needs to be continuous in time. Moreover, we also prove that the split implicit Euler scheme associated to the random delay differential system generates a discrete time random dynamical system, which also possesses a stochastic stationary solution with the same attracting property, and which converges to the stationary solution of the delay random differential equation pathwise as the stepsize goes to zero.     

Pullback Attractors in Dissipative Nonautonomous Differential Equations Under Discretization

The effects of discretization on the nonautonomous pullback attractors of skew-product flows generated by a class of dissipative differential equations, are investigated, It is assumed that the vector, field of the differential equations varies in time due to the input of an autonomous dynamical system acting on a compact metric space. In particular, it is shown that the corresponding discrete time skew-product system generated by a one-step numerical scheme with variable timesteps also has a pullback attractor, the component subsets of which converge upper semicontinuously to their counterparts of the pullback attractor of the original continuous time system.     

Preface

This special issue of PARTICUOLOGY is devoted to the first UK-China Particle Technology Forum taking place in Leeds, UK, on 1-3 April 2007. The forum was initiated by a number of UK and Chinese leading academics and organised by the University of Leeds in collaboration with Chinese Society of Particuology, Particle Technology Subject Group （PTSG） of the Institution of Chemical Engineers （IChemE）, Particle Characterisation Interest Group （PCIG） of the Royal Society of Chemistry （RSC） and International Fine Particle Research Institute （IFPRI）. The forum was supported financially by the Engineering and Physics Sciences Research Council （EPSRC） of United Kingdom,     

Guide for authors

正Each of the sections below provides essential information for authors.We recommend that you take the time to read them before submitting a contribution to Acta Mechanica Sinica.We hope our guide to authors may help you navigate to the appropriate section.How to prepare a submission This document provides an outline of the editorial process involved in publishing a scientific paper in Acta Mechanica Sinica.     

The 7th International Conference on Fluid Mechanics May 24-27,2015,Qingdao,China

正http://www.icfm7.org First Announcement and Call for PapersThe objective of International Conference on Fluid Mechanics(ICFM)is to provide a forum for researchers to exchange new ideas and recent advances in the fields of theoretical,experimental,computational Fluid Mechanics as well as interdisciplinary subjects.It was successfully convened by the Chinese Society of Theoretical and Applied Mechanics(CSTAM)in Beijing(1987,     

INFORMATION FOR CONTRIBUTORS

Contributions： The Journal, Acta Mechanica Solida Sinica, is pleased to receive papers from engineers and scientists working in various aspects of solid mechanics. All contributions are subject to critical review prior to acceptance and publication.     

一种基于直接计算高阶奇异积分的断裂力学双边界积分方程分析法

相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.      

汶川地震诱发文家沟巨型滑坡 碎屑流基本特征及成因机制初步分析

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2008年5月12日,汶川M80地震在四川省绵竹市清平乡文家沟内诱发一巨型滑坡。通过现场调查得知,滑坡前后缘高差455m,厚度20～30m,滑面为基岩层面,初始方量2750×107m3。滑体在运动中转化为碎屑流。滑坡-碎屑流总的水平运动距离为4022m,垂直运动距离为1443m,遗留的堆积物体积达5×107m3。滑坡距映秀—北川断裂仅36km,位于其下盘,地震烈度达XI度。滑坡导致文家沟中48人遇害,并形成一条完整的地震次生地质灾害链。初步分析表明滑坡启动速度快,滑坡向碎屑流转化过程明显、地点明确。碎屑流运动过程复杂,伴有强烈的“气垫效应”和“前缘气浪冲击效应”。作者认为,文家沟滑坡的高启动速度是长持时强烈地震动作用的结果,与山体的猛烈碰撞是导致滑体解体并转化为碎屑流的原因。     

Preface: Orbits around asteroid

One of the core issues in modern celestial mechanics is the orbital dynamics in the near-regime gravitational field of as- teroids, which provides deep insights into the mathematical nature of a class of nonlinear systems, and plays as a critical basis for in situ explorations of different science goals. Lots of efforts have been made to reveal the characteristics of orbital motion in the vicinity of asteroids, and to improve the skills of asteroid research in methodology.