A counterexample theorem in quasiconformal mapping theory

Given a quasisymmetric homeomorphismh of the unit circle onto itself, denote byK _n ^* ,H _h andK _h the extremal maximal dilatation, boundary dilatation and maximal dilatation ofh, respectively. It is proved that there exists a family of quasisymmetric homeomorphismsh such thatK _h <H _h =K _h ^* This gives a negative answer to a problem asked independently by Wu and Yang. Furthermore, some related topics are also discussed.     

Generalized Dirichlet Normal Ordering in Open Bosonic Strings

Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.     

A multigrid procedure for Cartesian ghost‐cell methods

This paper proposes a multigrid technique for Cartesian grid flow solvers. A recently developed ghost body‐cell method for inviscid flows is combined with a nested‐level local refinement procedure, which employs multigrid to accelerate convergence to steady state. Different from standard multigrid applications for body‐fitted grids, a fictitious residual needs to be defined in the ghost cells to perform a correct residual collection and thus to avoid possible stalling of the multigrid procedure. The efficiency of the proposed local refinement multigrid Cartesian method is demonstrated for the case of the inviscid subsonic flow past a circular body. Copyright © 2008 John Wiley & Sons, Ltd.     

Sign-changing solutions on a kind of fourth-order Neumann boundary value problem

In this paper, we consider the fourth-order Neumann boundary value problem u(4)(t)−2u^″(t)+u(t)=f(t,u(t)) for all t∈[0,1] and subject to u^′(0)=u^′(1)=u^?(0)=u^?(1)=0. Using the fixed point index and the critical group, we establish the existence theorem of solutions that guarantees the problem has at least one positive solution and two sign-changing solutions under certain conditions.     

Numerical analysis of turbulent flow separation in a rectangular duct with a sharp 180‐degree turn by algebraic Reynolds stress model

Turbulent flow in a rectangular duct with a sharp 180‐degree turn is difficult to predict numerically because the flow behavior is influenced by several types of forces, including centrifugal force, pressure‐driven force, and shear stress generated by anisotropic turbulence. In particular, this type of flow is characterized by a large‐scale separated flow, and it is difficult to predict the reattachment point of a separated flow. Numerical analysis has been performed for a turbulent flow in a rectangular duct with a sharp 180‐degree turn using the algebraic Reynolds stress model. A boundary‐fitted coordinate system is introduced as a method for coordinate transformation to set the boundary conditions next to complicated shapes. The calculated results are compared with the experimental data, as measured by a laser‐Doppler anemometer, in order to examine the validity of the proposed numerical method and turbulent model. In addition, the possibility of improving the wall function method in the separated flow region is examined by replacing the log‐law velocity profile for a smooth wall with that for a rough wall. The analysis results indicated that the proposed algebraic Reynolds stress model can be used to reasonably predict the turbulent flow in a rectangular duct with a sharp 180‐degree turn. In particular, the calculated reattachment point of a separated flow, which is difficult to predict in a turbulent flow, agrees well with the experimental results. In addition, the calculation results suggest that the wall function method using the log‐law velocity profile for a rough wall over a separated flow region has some potential for improving the prediction accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

CartGen: Robust,efficient and easy to implement uniform/octree/embedded boundary Cartesian grid generator

An efficient and easy to implement method to generate Cartesian grids is presented. The presented method generates various kinds of Cartesian grids such as uniform, octree and embedded boundary grids. It supports the variation of grid size along each spatial direction as well as anisotropic and non‐graded refinements. The efficiency and ease of implementation are the main benefits of the presented method in contrast to the alternative methods. Regarding octree grid generation, applying a simple and efficient data compression method permits to store all grid levels without considerable memory overhead. The presented method generates octree grids up to a 13‐level refinement (8192³ grids on the finest level) from a complicated geometry in a few minutes on the traditional desktop computers. The FORTRAN 90 implementation of the presented method is freely available under the terms of the GNU general public license. Copyright © 2007 John Wiley & Sons, Ltd.     

Evolution of 3-D crystals from supersaturated vapor with modified Stefan condition: Galerkin method approach

We examine the evolution of crystals in three dimensions. We assume that the Wulff shape is a prism with a hexagonal base. We include the Gibbs-Thomson law on the crystal surface and the so-called Stefan condition. We show local in time existence of solutions assuming that the initial crystal has admissible shape.     

Energy Estimate for the Type-Ⅱ Superconducting Film

We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high k, placed in an applied magnetic field hex, when hex is of the order of the ＂first critical field＂, i.e. of the order of ｜lnε｜. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.     

基于弹性波散射对二维障碍物边界的识别

给出了二维障碍物弹性波散射场的一种近似积分形式 ,基于 Fourier变换法建立了均匀障碍物特征函数与其远场散射振幅中形状因子的关系式 ,最后就基体为锌 ,对圆形和椭圆形截面铁夹杂进行了计算机模拟 ,结果表明该反演方法对定量无损检测技术具有应用价值。     

The Markov modulated regulated Brownian motion: A second-order fluid flow model of a finite buffer

A second-order fluid flow model of a queue with finite capacity buffer and variable net input process is presented, based on the previous work of Karandikar and Kulkarni (1995). Queue length is modelled as a Brownian motion whose parameters are controlled by a finite state Markov chain. The process, termed a Markov modulated regulated Brownian motion (MMRBM), provides analytical solutions for steady state queue length distributions, overflow losses and idleness probabilities using boundary regulators. Applications of the model include queues with failure-prone servers and ATM statistical multiplexers with variable traffic loads. This revised version was published online in June 2006 with corrections to the Cover Date.