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1.
On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems
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D. Gómez M. Lobo M. E. Pérez T. A. Shaposhnikova M. N. Zubova 《Mathematical Methods in the Applied Sciences》2015,38(12):2606-2629
Let u? be the solution of the Poisson equation in a domain perforated by thin tubes with a nonlinear Robin‐type boundary condition on the boundary of the tubes (the flux here being β(?)σ(x,u?)), and with a Dirichlet condition on the rest of the boundary of Ω. ? is a small parameter that we shall make to go to zero; it denotes the period of a grid on a plane where the tubes/cylinders have their bases; the size of the transversal section of the tubes is O(a?) with a???. A certain nonperiodicity is allowed for the distribution of the thin tubes, although the perimeter is a fixed number a. Here, is a strictly monotonic function of the second argument, and the adsorption parameter β(?) > 0 can converge toward infinity. Depending on the relations between the three parameters ?, a?, and β(?), the effective equations in volume are obtained. Among the multiple possible relations, we provide critical relations, which imply different averages of the process ranging from linear to nonlinear. All this allows us to derive spectral convergence as ?→0 for the associated spectral problems in the case of σ a linear function of u?. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains
. Here, Ωɛ=ΩS
ɛ is a periodically perforated domain. We obtain the homogenized equation and corrector results. The homogenization of the
equations on a fixed domain was studied by the authors [15]. The homogenization for a fixed domain and
has been done by Jian [11]. 相似文献
4.
This paper discusses the spectral properties and numerical simulation for the second order elliptic operators with rapidly
oscillating coefficients in the domains which may contain small cavities distributed periodically with period ε. A multiscale
asymptotic analysis formula for this problem is obtained by constructing properly the boundary layer. Finally, numerical results
are given, which provide a strong support for the analytical estimates 相似文献
5.
开孔粘弹性薄板的非线性数学模型 总被引:2,自引:0,他引:2
应力函数的多值性和位移单值性要求,是开孔薄板大挠度问题中必须注意的两个方面。本文利用线粘性力学中的Boltzmann蠕变律,把开孔弹性薄板大挠度问题的一般数学理论推广到开孔弹性薄板。在考察应力函数的多值性和位移单值性条件的基础上,提出了开孔粘弹性薄板的控制方程和初、边值条件,系统地建立了开也粘弹性薄板非线性分析的三类初一边值问题。 相似文献
6.
We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a real parameter ? and we denote by u? the corresponding solution. The behavior of u? for ? small and positive can be described in terms of real analytic functions of two variables evaluated at (?,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? for ? small and describe 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. 相似文献
7.
In this paper, we consider a semilinear parabolic equation of second order with lower term a power function of the unknown function and prove that the sequence of solutions in a perforated cylinder tends to a solution in a unperforated cylinder if the radii of rejected balls in the parabolic metric tend to zero at the rate depending on the exponent of the power function in the lower term. 相似文献
8.
关于开孔薄板大挠度问题的一般数学理论(续) 总被引:2,自引:0,他引:2
本文讨论了作用在开孔薄板的各孔边上的外力自身不平衡吋的大挠度问题的应力函数的多值性,并给出了这种问题的一般数学模型,因此本文可以看成是[1]的继续和深入。 相似文献
9.
Perforated nanocap array: Facile fabrication process and efficient surface enhanced Raman scattering with fluorescence suppression
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Recently, individual reduced-symmetry metal nanostructures and their plasmonic properties have been studied extensively. However, little attention has been paid to the approach to fabricating ordered reduced-symmetry metal nanostructure arrays. In this paper, a novel perforated silver nanocap array with high surface-enhanced Raman scattering (SERS) activity and fluorescence suppression is reported. The array is fabricated by electron beam evaporating Ag onto the perforated barrier layer side of a hard anodization (HA) anodic aluminum oxide (AAO) template. The morphology and optical property of the perforated silver nanocap array are characterized by an atomic force microscope (AFM), a scanning electron microscope (SEM), and absorption spectra. The results of SERS measurements reveal that the perforated silver nanocap array offers high SERS activity and fluorescence suppression compared with an imperforated silver nanocap array. 相似文献
10.