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泥沙冲刷漏斗自由边界问题及其计算 总被引:1,自引:0,他引:1
本文分析了水库排沙孔前泥沙冲刷所形成的漏斗状自由边界问题,建立了二维不可压缩理想势流孔口泥沙冲刷漏斗自由边界问题的数学模型,并利用局部试验自由边界的有限元方法与边界元方法对这一问题作了计算,迭代收敛较快。计算结果与实验数据比较吻合,从而也验证了这一数学模型适用于坝前不出现降水曲线的泥沙冲刷问题。 相似文献
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可混溶驱动问题的超收敛性 总被引:3,自引:0,他引:3
本文讨论多孔介质中两相可混溶渗流驱动问题的有限元方法,采用一致网格剖分、指标为k的Raviart-Thomas空间对压力作混合有限元逼近,用正则剖分、逼近阶为l的标准有限元方法处理浓度方程,通过核函数对有限元解作卷积进行局部平均确定非线性项的系数,得到了浓度误差H1范数的超收敛估计,经高阶插值,得到了整体高精度的逼近. 相似文献
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地下水渗流自由边界问题的分裂隐处理方法 总被引:1,自引:0,他引:1
梁栋 《高等学校计算数学学报》1996,18(1):29-38
1 引言 地下水是一种极其重要的资源,也是人类赖以生存的环境,不仅水资源的开发利用情况直接关系到国民经济的发展,而且水资源的保护也是保护人类生存环境的重要组成部分.在地下水渗流过程中,自由潜水面、自由交界面问题的计算一直是非常困难的问题,本文讨论多孔介质饱和带中均质地下水渗流自由边界问题的一类数值方法:分裂—隐处理方法,对—维入渗补给问题给出严格的理论分析,证明了最优阶误差估计(L~2,H~1,H~2模). 2 数学模型 研究地下渗流问题的方法通常采用Euler方法.取体积元ΔV=ΔxΔyΔz,在该体积 相似文献
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本文证明了化学反应扩散过程中的一类周期自由边界问题古典解的存在唯一性,并且讨论了潜热L→0时周期Stefan问题古典解的渐近性态及误差估计. 相似文献
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本文处理带有两种流体的轴对称的一个自由边界问题,其中在渗流区域的上部都是油,下部是水,这是同时取油注水的一个数学模型。下面,我们将用复分析方法求出此自由边界问题的一个解,并证明其解的唯一性。 相似文献
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本文研究一个描述硅的氧化过程的自由边界问题.它的数学模型是一个可压缩的Navior-Stokes方程与一个抛物方程以及一个双曲方程的耦合,其中在自由边界上存在表面张力并且密度方程是非齐次的.本文将证明只要已知数据满足相容性条件,则上述问题有唯一局部强解. 相似文献
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具有抛物线边界的二维弹性介质的Green函数 总被引:2,自引:1,他引:1
文章求解了具有抛物线边界的二维弹性介质的两种Green函数,一种是自由边界问题,另一种是刚性边界问题。我们还求得了当抛物线边界退化成半无限裂纹或半无限刚性裂纹时裂纹尖端的奇异场,得到了集中力作用于边界的基本解,这个基本解使得我们可以通过沿边界积分确定任意分布荷载的弹性解. 相似文献
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ZHENG ShiJun 《分析论及其应用》2004,20(3)
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V. 相似文献
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One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows 相似文献
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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals. 相似文献
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Pankaj Mathur 《分析论及其应用》2006,22(2)
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x). 相似文献
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It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary. 相似文献
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《高校应用数学学报(英文版)》2014,29(4)
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with 相似文献
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《数学研究及应用》2014,(6)
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics. 相似文献
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A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6]. 相似文献