Fine singularity analysis of solutions to the Laplace equation

We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann data on one component of the boundary. Our motivation is to study the so‐called Berg effect, which is explained in the introduction. Copyright © 2014 John Wiley & Sons, Ltd.     

Circumference and Pathwidth of Highly Connected Graphs

Birmele [J Graph Theory 2003] proved that every graph with circumference t has treewidth at most . Under the additional assumption of 2‐connectivity, such graphs have bounded pathwidth, which is a qualitatively stronger conclusion. Birmele's theorem was extended by Birmele et al. [Combinatorica 2007] who showed that every graph without k disjoint cycles of length at least t has treewidth . Our main result states that, under the additional assumption of ‐connectivity, such graphs have bounded pathwidth. In fact, they have pathwidth . Moreover, examples show that ‐connectivity is required for bounded pathwidth to hold. These results suggest the following general question: for which values of k and graphs H does every k‐connected H‐minor‐free graph have bounded pathwidth? We discuss this question and provide a few observations.     

Real analytic families of harmonic functions in a planar domain with a small hole

We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a real parameter ?   and we denote by _u?$u_{?}$ the corresponding solution. The behavior of _u?$u_{?}$ for ?   small and positive can be described in terms of real analytic functions of two variables evaluated at (?,1/log??)$(?,1/\log ??)$. We show that under suitable assumptions on the geometry and on the boundary data one can get rid of the logarithmic behavior displayed by _u?$u_{?}$ for ?   small and describe _u?$u_{?}$ by real analytic functions of ?. Then it is natural to ask what happens when ? is negative. The case of boundary data depending on ? is also considered. The aim is to study real analytic families of harmonic functions which are not necessarily solutions of a particular boundary value problem.     

等维Cartan-Hartogs域双全纯映射的特征

本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域Ω^Bm(μ)不是球,则它上面存在一函数X使得它在Ω^Bm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域Ω^Bm(μ)不是球,Ω^Bm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变.     

Series solutions for steady unsaturated flow in irregular porous domains

For the most part, analytical solutions for steady unsaturated infiltration have been restricted to infinite and semi-infinite seepage geometries, using the quasi-linear approximation for the hydraulic conductivity. We provide analytical series methods to solve the steady quasi-linear flow equations, in finite irregular seepage geometries. Unlike the classical approach, the series method has been modified, to cater for arbitrary boundary geometry and surface recharge distributions. The matrix flux potential and the stream function both satisfy the same governing partial differential equation, and the stream function formulation is used to estimate the series coefficients. For a finite vadose zone, the stream function solution does not uniquely determine the matrix flux potential, when flux boundary conditions are used. Consequently, the stream function solution applies to a range of moisture distributions, for given infiltration and evapotranspiration rates through the surface.     

间隔靶对射流侵彻影响的数值模拟和实验研究

对某聚能装药射流侵彻靶板的过程进行了数值模拟 ,得出其碰撞点附近应力分布与传统理论相符 ,侵彻深度与实验结果及工程计算结果基本相符 ;分别对该聚能装药侵彻连续靶和间隔靶的过程进行了数值模拟 ,数值模拟结果显示间隔靶的侵彻深度明显低于连续靶的侵彻深度 ,这说明侵彻开坑阶段的能耗侵深比远大于准定常阶段。为了验证间隔靶对射流侵彻的影响 ,用另一聚能装药分别对连续靶和间隔靶进行了侵彻实验 ,并排除了炸高的影响。实验结果也表明 ,间隔靶对射流侵彻的确存在着不利影响。还结合数值模拟及实验结果对传统的侵彻公式进行了修正。     

Formation and stability of a charged jet in a strong electric field

The shape of a charged jet is determined in the approximation of a strong electric field. The stability of the jet with respect to both axisymmetric and nonaxisymmetric perturbations of the sinusoidal type is investigated in the linear approximation. The domains of predominance of the axisymmetric and bending modes and the longitudinal partition mode are determined. Experimental data on the longitudinal partition of a polymeric jet into several daughter jets are given.     

边界元法边界层处理的一种新方法—拟多连域法

提出了处理边界元法边界层问题的新方法。这种方法在求得边界未知量后，在距边界较远的域中构造一工作边界，将实际边界与工作边界看作一多连域问题求得工作边界的未知量。再将工作边界与边界层边界视为一多连域问题求解，可得到满足精度要求的边界附近点的位移与应力。这种方法理论简洁、计算方便、有效、精度高，对于需求边界上多点的未知量问题很具优越性