粘流—无粘干扰流动理论广义解的存在性和唯一性条件

本文证明了粘流-无粘干扰流动理论基本控制方程—简化Navier-Stokes方程原始变量变分形式广义解的存在性,给出了广义解的唯一性条件和Re数上限估计,得到与完全N-S方程的已知结果相应的一系列结论。一、预备知识和基本假设     

粘流－无粘干扰流动理论变分问题迭代序列的收敛性和算子方程性质

本文证明了粘流－无粘干扰流动理论［１，２］基本控制方程─—简化的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程变分问题几种迭代序列的收敛性，并探讨了其算子方程的性质。本文的结论对于简化Ｎ－Ｓ方程的数值计算具有指导意义。     

粘流—无粘干扰流动理论变分问题迭代序列的收敛性和算子方程…

本文证明了粘流－无粘干扰流动理论基本控制方程－简化的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程变分问题几种迭代序列的收敛性，并探讨了其算子方程的性质。本文的结论对于简化Ｎ－Ｓ方程的数值计算具有指导意义。     

粘弹流体的绕流特性研究

本文建立了分析粘弹流体平面流的基本方程,并采用摄动法和加权余量法.在小Deborah数条件下,进行了粘弹流体流动的有限元分析,探讨了粘弹流体的绕流特性,分析了粘弹流体在绕流中所表现的分离点滞后及减阻现象的机理.结果表明,本文的方法.对于粘弹流体流动特性的分析工作,具有简便和准确的优点.     

粘滑混合边界条件下平面边界前的Stokes流动

对具有粘滑混合边界条件的平面边界,建立一个Stokes流动的一般性定理,利用双调和函数A与调和函数B,表示了3维Stokes流动的速度场和压力场.关于无滑动平面边界前Stokes流动的早期定理,成为该一般性定理的一个特例.进一步地,从一般性定理导出了一个推论,根据该Stokes流函数,给出了粘滑边界条件时刚性平面轴对称Stokes流动问题的解,得到了流体作用在边界上的牵引力和扭矩公式.给出了一个说明性的例子.     

高弹粘流在三维变厚度狭缝流道中流动的数值模拟

用有限块法对高弹粘流在三维变厚度狭缝流道中的流动进行数值模拟.求出流体流量在流道中的分布规律;通过对实际板材挤出模鱼尾型流道中设置阻流块对流动影响的计算,证实有限块法是简易可行的,从而为挤出模的计算机辅助设计提供了一个重要手段.     

二维剪切流的粘性-无粘湍流干扰理论

对二维不可压缩近壁剪切湍流,本文提出一个粘性-无粘湍流干扰理论.主要内容有:从分子粘性考虑出发确定干扰湍流的流动结构及其物理尺度,导出空间为小尺度的局部流动结构随顺流距离的演变规律,导出支配干扰湍流流动的简化Reyno-lds(SR)方程和扩散抛物化K-ε方程.该SR方程是作者早先提出的简化Navier-Stokes(SNS)方程的湍流形式,它的重要性质是“简化运算”和时间Reynolds平均运算的顺序可以交换.关于最大湍流剪应力、本理论计算值与实验测量值很好相符.经典湍流边界层理论、Clauser平衡湍流边界层以及湍流分离Triple-deck理论均是本文理论的特例.证实了顺流方向长度尺度随干扰增强而显著减小的实验结论.     

拟流函数法——叶轮机械内三维流动分析问题和设计问题的一种求解方法

本文从动量方程的特点出发并满足连续方程,引入了两个拟流函数.每个拟流函数的主方程均只包含其自身的二阶偏导数,而不包含另一个拟流函数的二阶偏导数.这样,完全的三维解便可通过两个拟流函数主方程的分别单独求解和它们之间的相互迭代来获得.文中给出了在任意非正交坐标系中拟流函数的主方程和相应的边界条件.对叶轮机械内部三维气动分析问题和设计问题的求解进行了讨论和计算,并与解析解、其他数值解法做了比较.结果表明:这种拟流函数方法计算准确而简便,易于得到收敛结果,是求解三维无粘流动的好方法.     

关于绕任意机翼非常流动的一种无条件稳定的欧拉方程解

本给出了绕二维与三维刚性或弹性振动机翼非定常无粘流动的欧拉方程解。首先利用Ｊａｍｅｓｏｎ的有限体积方法建立了求解欧拉方程的Ｒｕｎｇｅ－Ｋｕｔｔａ方法，为了提高受Ｒｕｎｇｅ－Ｋｕｌｔｔａ法稳定性限制的时间步长，中采用了变系数的残值光顺方法，该方法避免了常系数残值光顺引起局部流场损失较大的问题。同时可在保证原计算格式精度要求下，大幅度提高计算时间步长，从而提高了计算效率。中以二维与三维矩形机翼为     

粘塑性流体在旋转圆盘上的流动

本文对两种情况导出了描述粘塑性流体在旋转圆盘上流动的基本方程.分别用摄动方法和数值方法得到了方程的解.这就有可能去计算薄膜的厚度分布.经计算发现有两种类型的厚度分布.对于粘度和屈服应力都与径向坐标r无关的粘塑性流体,厚度h随r的增加而减小.对于粘度和屈服应力都是时间和r的函数的Bingham流体,厚度h随r的增加而增加.     

Physicomechanical characteristics of a disperse-filled polytetrafluoroethylene

Composite polymer materials based on PTFE containing ultradisperse -sialon (1–10 wt.%) as the cross-linking agent are studied. It is shown that the injection of small amounts of fillers (1–2 wt.%) increases the degree of composite crystallinity. A correlation between the structure, element distribution on the surface layers of samples, and tribotechnical characteristics of composites is found. The change in the physicomechanical characteristics is associated with the effect of the interstructural plasticization.Ammosov Yakutsk State University, Yakutsk, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 797–806, November–December, 1999.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

On the weakening of the convergence of Newton’s method using recurrent functions

We use Newton’s method to approximate a locally unique solution of an equation in a Banach space setting. We introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton’s method than before [J. Appell, E. De Pascale, J.V. Lysenko, P.P. Zabrejko, New results on Newton–Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997) 1–17; I.K. Argyros, The theory and application of abstract polynomial equations, in: Mathematics Series, St. Lucie/CRC/Lewis Publ., Boca Raton, Florida, USA, 1998; I.K. Argyros, Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005) 179–194; I.K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer-Verlag Publ., New York, 2008; S. Chandrasekhar, Radiative Transfer, Dover Publ., New York, 1960; F. Cianciaruso, E. De Pascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003) 713–723; N.T. Demidovich, P.P. Zabrejko, Ju.V. Lysenko, Some remarks on the Newton–Kantorovich method for nonlinear equations with Hölder continuous linearizations, Izv. Akad. Nauk Belorus 3 (1993) 22–26. (in Russian); E. De Pascale, P.P. Zabrejko, Convergence of the Newton–Kantorovich method under Vertgeim conditions: A new improvement, Z. Anal. Anwendvugen 17 (1998) 271–280; L.V. Kantorovich, G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations, Dokl. Akad. Nauk BSSR 38 (1994) 20–24. (in Russian); B.A. Vertgeim, On conditions for the applicability of Newton’s method, (Russian), Dokl. Akad. Nauk., SSSR 110 (1956) 719–722; B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957) 166–169. (in Russian); English transl.:; Amer. Math. Soc. Transl. 16 (1960) 378–382] provided that the Fréchet-derivative of the operator involved is p$p$-Hölder continuous (p∈(0,1]$p\in (0,1]$).     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

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.     

Staircase transportation problems with superadditive rewards and cumulative capacities

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].     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Zero-dimensional subschemes of ruled varieties

Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method This research is part of the T.A.S.C.A. project of I.N.d.A.M., supported by P.A.T. (Trento) and M.I.U.R. (Italy)     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Superapproximation and Commutator Properties of Discrete Orthogonal Projections for Continuous Splines

This paper builds upon the L_p-stability results for discrete orthogonal projections on the spaces S_h of continuous splines of order r obtained by R. D. Grigorieff and I. H. Sloan in (1998, Bull. Austral. Math. Soc.58, 307–332). Properties of such projections were proved with a minimum of assumptions on the mesh and on the quadrature rule defining the discrete inner product. The present results, which include superapproximation and commutator properties, are similar to those derived by I. H. Sloan and W. Wendland (1999, J. Approx. Theory97, 254–281) for smoothest splines on uniform meshes. They are expected to have applications (as in I. H. Sloan and W. Wendland, Numer. Math. (1999, 83, 497–533)) to qualocation methods for non-constant-coefficient boundary integral equations, as well as to the wide range of other numerical methods in which quadrature is used to evaluate L₂-inner products. As a first application, we consider the most basic variable-coefficient boundary integral equation, in which the constant-coefficient operator is the identity. The results are also extended to the case of periodic boundary conditions, in order to allow appplication to boundary integral equations on closed curves.     

Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization

This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [M. Elad, Why simple shrinkage is still relevant for redundant representations? IEEE Trans. Inform. Theory 52 (12) (2006) 5559–5569], a new iterative method called parallel coordinate descent (PCD) was devised. We provide herein a convergence analysis of the PCD algorithm, and also introduce a form of the regularization function, which permits analytical solution to the coordinate optimization. Several other recent works [I. Daubechies, M. Defrise, C. De-Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. LVII (2004) 1413–1457; M.A. Figueiredo, R.D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Process. 12 (8) (2003) 906–916; M.A. Figueiredo, R.D. Nowak, A bound optimization approach to wavelet-based image deconvolution, in: IEEE International Conference on Image Processing, 2005], which considered the deblurring problem in a Bayesian methodology, also obtained element-wise optimization algorithms. We show that the last three methods are essentially equivalent, and the unified method is termed separable surrogate functionals (SSF). We also provide a convergence analysis for SSF. To further accelerate PCD and SSF, we merge them into a recently developed sequential subspace optimization technique (SESOP), with almost no additional complexity. A thorough numerical comparison of the denoising application is presented, using the basis pursuit denoising (BPDN) objective function, which leads all of the above algorithms to an iterated shrinkage format. Both with synthetic data and with real images, the advantage of the combined PCD-SESOP method is demonstrated.