一般不完全透射条件下复合材料的界面电位

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Zeitschrift fur Angewandte Mathematik und Physik Pub Date : 2023-09-20 DOI:10.1007/s00033-023-02094-7

M. Amar, D. Andreucci, C. Timofte

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引用次数: 1

摘要

摘要本文所分析的模型来源于对复合材料的描述，这种复合材料是由一层由两种不同材料的子层组成的薄层包裹的含有周期性夹杂物阵列的承载介质制成的。这种两相涂层材料在正交方向上具有较低的扩散系数，而在切向上具有较高的扩散系数。在之前的一篇论文(Amar In IFB 21:41-59, 2019)中，通过浓缩程序，内层被不完美的界面取代。本文通过周期展开的方法，研究了外涂层的浓度和均匀化问题，得到了一个远非标准的模型。尽管极限问题看起来像椭圆方程的经典狄利克雷问题，但在构造均匀矩阵和源项时，需要进行非常精细的分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Interface potential in composites with general imperfect transmission conditions

Abstract The model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction. In a previous paper (Amar in IFB 21:41–59, 2019), by means of a concentration procedure, the internal layer was replaced by an imperfect interface. The present paper is concerned with the concentration of the external coating layer and the homogenization, via the periodic unfolding method, of the resulting model, which is far from being a standard one. Despite the fact that the limit problem looks like a classical Dirichlet problem for an elliptic equation, in the construction of the homogenized matrix and of the source term, a very delicate analysis is required.

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来源期刊

Zeitschrift fur Angewandte Mathematik und Physik 数学-应用数学

CiteScore

2.90

自引率

10.00%

发文量

216

审稿时长

6-12 weeks

期刊介绍： The Journal of Applied Mathematics and Physics (ZAMP) publishes papers of high scientific quality in Fluid Mechanics, Mechanics of Solids and Differential Equations/Applied Mathematics. A paper will be considered for publication if at least one of the following conditions is fulfilled: The paper includes results or discussions which can be considered original and highly interesting. The paper presents a new method. The author reviews a problem or a class of problems with such profound insight that further research is encouraged. The readers of ZAMP will find not only articles in their own special field but also original work in neighbouring domains. This will lead to an exchange of ideas; concepts and methods which have proven to be successful in one field may well be useful to other areas. ZAMP attempts to publish articles reasonably quickly. Longer papers are published in the section "Original Papers", shorter ones may appear under "Brief Reports" where publication is particularly rapid. The journal includes a "Book Review" section and provides information on activities (such as upcoming symposia, meetings or special courses) which are of interest to its readers.