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71.
B. Amaziane M. Goncharenko L. Pankratov 《Mathematical Methods in the Applied Sciences》2005,28(15):1847-1865
We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω(ε) of asymptotically degenerating measure, i.e. meas Ω(ε) → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω(ε) associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
72.
We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation. 相似文献
73.
Herbert Danninger Tayfun Kara Michael Ruhnow Hans -Jürgen Ullrich 《Mikrochimica acta》1990,101(1-6):219-229
Homogenization of Mo, W and Cr in alloyed P/M carbon steels during sintering with a transient liquid phase has been investigated by microscopic and microanalytical means. The reaction was found to start with carburization of the VIa metal, continues with the formation of different carbides, and generation of a liquid phase between the carbide and -Fe. The steady state equilibrium remains stable until all VIa metal has been consumed. Microprobe analysis was found to yield optimum results if selected model samples, in which homogenization should not proceed too fast, are investigated.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday 相似文献
74.
Given a subset E of convex functions from
into
which satisfy growth conditions of order p>1 and an open bounded subset
of
, we establish the continuity of a map μΦμ from the set of all Young measures on
equipped with the narrow topology into a set of suitable functionals defined in
and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization. 相似文献
75.
Roman Luis J. Zhang Xinsheng Zheng Weian 《Mathematical Physics, Analysis and Geometry》2003,6(2):113-124
We consider the solutions to /tu
(n)=a
(n)(x)u
(n) where {a
(n)(x)}
n=1,2,... are random fields satisfying a well-mixing condition (which is different to the usual strong mixing condition). In this paper we estimate the rate of convergence of u
(n) to the solution of a heat equation. Since our equation is of simple form, we get quite strong result which covers the previous homogenization results obtained on this equation. 相似文献
76.
在本文我们讨论了在等值面边值问题中的非线性边界条件的均匀化,推广了相应的边界条件均匀化结果,而且可应用到用于处理热敏电阻问题中的一类非线性非局部边值问题的边界条件均匀化问题。 相似文献
77.
We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction [0, max] (max is the maximum volume fraction of a spheres). As a starting point we use a perturbation approach for 0 and an asymptotic solution for max. Three different spatial arrangements of the spheres, simple cubic, body centred and face centred cubic arrays, are considered. Results obtained give a good agreement with numerical data. 相似文献
78.
A. A. Pan’kov 《Mechanics of Composite Materials》2000,36(1):19-36
A generalized self-consistent method [1, 2] is developed and applied to the boundary-value problems of composites with random
elastic properties of inclusions. The approach suggested makes it possible to allow for a random mutual arrangement, statistical
dispersion of elastic properties and sizes of the inclusions, and their mutual correlation in terms of special homogenized
indicator functions. For comparison, the analytical solutions and those obtained from a corresponding sequence of H+1 (H=0,1,…)
linked homogenized problems of the self-consistent method for the strain distribution in the inclusions and for the tensor
of effective elastic properties of the composite are given. A numerical calculation of the effective transversely isotropic
elastic characteristics for a unidirectional polydisperse fibrous composite is also presented.
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 33–58, January–February, 2000. 相似文献
79.
Constantin Năstăsescu Florin Panaite Freddy Van Oystaeyen 《Algebras and Representation Theory》1999,2(3):211-226
We apply to Hopf algebras a construction from graded rings, called the group ring of a graded ring. By using this construction we study the transfer of properties between certain categories of relative Hopf modules. As another application, we obtain a Maschke-type theorem for a Galois extension over a semisimple Hopf algebra. 相似文献
80.
We compute the -limit of a sequence obstacle functionals in the case of periodic obstacles. 相似文献