A Singularly Perturbed Nonideal Transmission Problem and Application to the Effective Conductivity of a Periodic Composite
A Singularly Perturbed Nonideal Transmission Problem and Application to the Effective Conductivity of a Periodic Composite
复制标题
奇扰动非理想传输问题及其在周期性复合材料有效电导率中的应用
DOI：
10.1137/120886637
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
P. Musolino
中科院分区：
文献类型：
--
作者：
M. D. Riva;P. Musolino
本文研究了在界面处具有热阻的两相复合材料的有效导热系数。该复合材料是通过在无限均匀矩阵中引入一组不同材料的周期性夹杂物而获得的。每个夹杂物的直径被假定成正比于一个积极的真实的参数$\displaystyle $\displaystyle $。在适当的假设下，我们表明，有效电导率可以继续真实的分析参数$\$周围的退化值$\=0$，在相应的夹杂物崩溃的点。部分结果已在[M. Dalla Riva和P. Musolino，AIP Conf.Proc.1493，美国物理研究所，梅尔维尔，纽约，2012年，pp. 264- 268]。
We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. The diameter of each inclusion is assumed to be proportional to a positive real parameter $\epsilon$. Under suitable assumptions, we show that the effective conductivity can be continued real analytically in the parameter $\epsilon$ around the degenerate value $\epsilon=0$, in correspondence of which the inclusions collapse to points. Part of the results presented here have been announced in [M. Dalla Riva and P. Musolino, AIP Conf. Proc. 1493, American Institute of Physics, Melville, NY, 2012, pp. 264--268].