Boundary conditions at the interface between fluid layer and fibrous medium

The flow through a channel partially filled with fibrous porous medium was analyzed to investigate the interfacial boundary conditions. The fibrous medium was modeled as a periodic array of circular cylinders, in a hexagonal arrangement, using the boundary element method. The area and volume average methods were applied to relate the pore scale to the representative elementary volume scale. The permeability of the modeled fibrous medium was calculated from the Darcy's law with the volume‐averaged Darcy velocity. The slip coefficient, interfacial velocity, effective viscosity and shear jump coefficients at the interface were obtained with the averaged velocities at various permeabilities or Darcy numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

模糊聚类分析方法在水平井开发指标预测中的应用

模糊聚类分析方法在实际中应用很广泛,采用模糊聚类的方法,以胜利油田已经大量投产的水平井的数据为基础,将同类油藏中已投产水平井进行分类,然后根据新设计井的有关参数将其归到相应类中,根据同类中已投产井的有关开发指标对新设计水平井的指标进行预测,取得了较好效果.     

On the Number of Cylinders Touching a Ball

In this note we prove an upper bound of seven for the maximum number of unit cylinders touching a unit ball in a packing. This improves a previous bound of eight by Heppers and Szab. The value conjectured by Kuperberg in 1990 is six.     

Existence of travelling wave solutions for the heat equation in infinite cylinders with a nonlinear boundary condition

The existence of travelling wave solutions for the heat equation ∂_t u –Δu = 0 in an infinite cylinder subject to the nonlinear Neumann boundary condition (∂u /∂n) = f (u) is investigated. We show existence of nontrivial solutions for a large class of nonlinearities f. Additionally, the asymptotic behavior at ∞ is studied and regularity properties are established. We use a variational approach in exponentially weighted Sobolev spaces. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thickness-shear vibration of a circular cylindrical ceramic cylinder with unattached electrodes and air gaps

We analyze thickness-shear vibration of an axially poled circular cylindrical tube with unattached electrodes and air gaps. Both free and electrically forced vibrations are studied. Exact solutions are obtained from the equations of linear piezoelectricity. Resonant frequencies and the impedance of the transducer are calculated from the solution. Results show that the resonant frequencies are sensitive to the dimensions of the air gaps when the gaps are thin. The impedance depends strongly on the air gaps. Supported by the National Natural Science Foundation of China (Grant No. 50778179)     

三维水平井最优控制系统及应用

建立了三维水平井井眼轨迹的非线性多阶段动力系统，论述了该系统解的存在性及其最优控制的可控性和多解性。以均匀设计方法选初始点，并依此把允许区域分解为有限多个子域，在每个子域上构造了改进的Hooke-Jeeves优化算法。将它用于多口水平井的实际生产中，表明了本文给出的模型、算法及软件的正确性与有效性。     

Meshfree weak–strong (MWS) form method and its application to incompressible flow problems

A meshfree weak–strong (MWS) form method has been proposed by the authors' group for linear solid mechanics problems based on a combined weak and strong form of governing equations. This paper formulates the MWS method for the incompressible Navier–Stokes equations that is non‐linear in nature. In this method, the meshfree collocation method based on strong form equations is applied to the interior nodes and the nodes on the essential boundaries; the local Petrov–Galerkin weak form is applied only to the nodes on the natural boundaries of the problem domain. The MWS method is then applied to simulate the steady problem of natural convection in an enclosed domain and the unsteady problem of viscous flow around a circular cylinder using both regular and irregular nodal distributions. The simulation results are validated by comparing with those of other numerical methods as well as experimental data. It is demonstrated that the MWS method has very good efficiency and accuracy for fluid flow problems. It works perfectly well for irregular nodes using only local quadrature cells for nodes on the natural boundary, which can be generated without any difficulty. Copyright © 2004 John Wiley & Sons, Ltd.     

The volume problem in calculus

Everyone knows that the area of the base of solid is A,and the height is h,then the volume of it is V=A·h.It＇s an experience on math class in primer or middle school.Although you have an intuitive idea of what volume means,however,you can make this idea precise by using calculus to give an exact definition of volume.You will know what the concept of volume is in the calculus.     

An experimental investigation of dual-resonant and non-resonant responses for vortex-induced vibration of a long slender cylinder

Experimental results of the dual-resonant and non-resonant responses are presented for vortex-induced vibrations(VIV)of a long slender cylinder.The cylinder has a diameter of 10mm and a length of 3.31 m,giving an aspect ratio of 331.The cylinder was towed by a carriage with the velocity up to 1.5 m/s,with the Reynolds number varying from 2500 to 38000.Three different weights were used to provide the initial tension.Dual resonance means that resonance occurs simultaneously in both the cross-flow(CF)and in-line(IL)directions.The experiments were conducted in two stages.At the first stage,dual-resonant dynamic features of the cylinder subjected to vortex-induced excitation were investigated.The features of CF and IL vibration amplitude,motion orbits,phase angle differences,dominant frequencies and mode order numbers are presented.At the second stage of the experiments,particular emphasis was placed on non-resonant dynamic features.The variation of multi-mode modal displacement amplitudes was investigated in detail.