Numerical Energy Conservation for Multi-Frequency Oscillatory Differential Equations

The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with highly oscillatory solutions is studied in this paper. The numerical methods considered are symmetric trigonometric integrators and the St?rmer–Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system. A brief discussion of conservation properties in the continuous problem is also included. AMS subject classification (2000) 65L05, 65P10     

Uniform (Lp, Lq) boundedness of multilinear oscillatory

A class of multilinear oscillatory singular integrals with smooth phases is studied. And their uniform boundedness on Lebesgue space is proved.     

Pricing Behaviors on Networks: Some General Results for Two-way Networks

In this paper, we study monopolistic pricing behaviors within a two-way network. In this symbiotic production system, independent decision centers carry out an activity which concurs to the production of different system goods. The players are assumed to know the whole network. Due to this rationality, they try to capture a share of the profit of the firms who sell the system goods to the consumers. These double marginalization behaviors are studied within very general networks. Conditions with ensure existence and uniqueness are discussed. We even provided a complete characterization of an equilibrium. Potential applications are also discussed     

基于激光共聚焦显微镜模拟微合金钢连铸过程中第二相的析出行为

通过高温激光共聚焦显微镜模拟了微合金钢在不同冷却工艺下的凝固过程,并原位观察该过程样品表面的变化,探讨样品表面变化与第二相析出的关联性。研究结果表明：随着微合金钢钢液的凝固冷却,样品表面会出现细小浮凸;该浮凸出现的温度及分布位置与第二相的析出理论计算及透射电镜表征结果一致;通过原位观察该浮凸的产生,可间接表征第二相的析出,有利于分析第二相对基体组织演变的影响。     

低碳钢中纳米尺寸碳化物的相间析出行为

采用扫描电镜和透射电子显微镜对低碳Ti-Mo系的热轧板进行了组织分析,同时对其中的纳米粒子析出行为进行了研究.强化机理分析表明析出强化对于屈服强度的贡献值可达291 MPa.随着卷取温度的降低,纳米粒子相间析出的排间距会减小,相间析出的排间距与其在铁素体中形核点位置有一定的离散值,但基本上呈一定的固定值.α/γ界面的观察和采用不同理论的计算结果表明相间析出的产生主要与α/γ界面的台阶形成有关,相间析出的排间距大小由台阶高度、晶界扩散系数、等温温度、台阶面迁移速率等决定.     

多缩微智能车交互行为研究平台设计与实现

针对真实道路上开展智能汽车研究存在的风险和困难,提出了一种基于缩微城市道路环境的智能车交互行为研究平台. 该平台首先实现了具备视觉认知功能的缩微智能车,采用了一种基于特征和模型融合的嵌入式平台实时车道线和障碍物检测算法,通过本车可行驶区域的形式化描述,实现道路环境的感知,最后经过模糊决策控制方法控制缩微智能车产生拟人驾驶行为. 实验结果表明,文中提出的研究平台能够有效模拟智能车车间交互行为,环境感知算法和决策控制方法能够满足实时性和精度要求.     

触变性流体在振荡载荷作用下的响应

采用Moore型触变性流体本构方程，研究了振荡载荷作用下的应力响应．发现：(1)稳态情况下，描述流体内部结构状态的参量为时间的周期函数；(2)剪应力和剪应变率之间关系为一闭合的滞后环。     

Simulation of oscillatory flow in an aortic bifurcation using FVM and FEM: A comparative study of implementation strategies

Cardiovascular diseases are one of the major causes of long‐term morbidity and mortality in human beings. The nearly epidemic increase in prevalence of such diseases poses a serious threat to public health and calls for efficient methods of diagnosis and treatment. Non‐invasive diagnostic procedures such as MRI are often used in this context; however, these are limited in terms of spatial and temporal resolution and do not provide information on time‐dependent pressures and wall shear stresses—key quantities considered to be partially responsible for the formation and development of related pathologies. The present study is concerned with the numerical simulation of oscillatory flow through the abdominal aortic bifurcation. Computational fluid dynamics simulation of oscillatory flow in a branched geometry at high Reynolds numbers poses considerable challenges. The present study reports a detailed comparison of simulations performed with a finite volume and a finite element method, two approaches with significant differences in their discretization strategy, treatment of boundary conditions and other numerical aspects. Both solvers were parallelized, using loop parallelization of the BiCGStab linear solver for the finite volume and domain decomposition based on the Schur complement method for the finite element technique. The experience gained with these two approaches for the solution of flow in a bifurcation forms the focus of this study. Although similar results were obtained for both methods, the computation time required for convergence was found to be significantly smaller for the finite element approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.     

Implementation of physical boundary conditions into computational domain in modelling of oscillatory bottom boundary layers

This paper discusses the importance of realistic implementation of the physical boundary conditions into computational domain for the simulation of the oscillatory turbulent boundary layer flow over smooth and rough flat beds. A mathematical model composed of the Reynolds averaged Navier–Stokes equation, turbulent kinetic energy (k) and dissipation rate of the turbulent kinetic energy (ε) has been developed. Control‐volume approach is used to discretize the governing equations to facilitate the numerical solution. Non‐slip condition is imposed on the bottom surface, and irrotational main flow properties are applied to the upper boundary. The turbulent kinetic energy is zero at the bottom, whereas the dissipation rate is approaching to a constant value, which is proportional to the kinematic viscosity times the second derivative of the turbulent kinetic energy. The output of the model is compared with the available experimental studies conducted in oscillatory tunnels and wave flume. It is observed that the irrotational flow assumption at the upper boundary is not realistic in case of water tunnels. Therefore, new upper boundary conditions are proposed for oscillatory tunnels. The data of wave flume show good agreement with the proposed numerical model. Additionally, several factors such as grid aspect ratio, staggered grid arrangement, time‐marching scheme and convergence criteria that are important to obtain a robust, realistic and stable code are discussed. Copyright © 2009 John Wiley & Sons, Ltd.