Homogenization and Field Concentrations in Heterogeneous Media
Homogenization and Field Concentrations in Heterogeneous Media
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异质介质中的均匀化和场集中
DOI：
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发表时间：
2006
影响因子：
2
通讯作者：
R. Lipton
中科院分区：
文献类型：
--
作者：
R. Lipton
本文提出了复合介质和多晶介质中场浓度的多尺度表征方法。我们专注于梯度场与强度由温度和电势给出的量。在线性制度，这些量模拟的二阶椭圆型偏微分方程的振荡系数的解决方案。异质性相对于样本量的特征长度标度用$vareps $表示，强度用$u^{vareps}$表示。场浓度使用梯度场的$L^p$范数测量。|
阿夫拉·乌^{varepad}|_{L^p（D）}$对于$2 leq p < infty$。分析集中在$0 <varepill 1$的情况下。关于$limif_{vareps}的显式下界
八箭头0}|
阿夫拉乌瓦雷普什|_{L^p（D）}$。这些界限提供了一种方法来严格评估所产生的场浓度的微观几何形状，而不必计算实际的字段$u…
A multiscale characterization of the field concentrations inside composite and polycrystalline media is developed. We focus on gradient fields associated with the intensive quantities given by the temperature and the electric potential. In the linear regime these quantities are modeled by the solution of a second order elliptic partial differential equation with oscillatory coefficients. The characteristic length scale of the heterogeneity relative to the sample size is denoted by $varepsilon$ and the intensive quantity is denoted by $u^{varepsilon}$. Field concentrations are measured using the $L^p$ norm of the gradient field $|
abla u^{varepsilon}|_{L^p(D)}$ for $2 leq p < infty$. The analysis focuses on the case when $0 < varepsilon ll 1$. Explicit lower bounds on $liminf_{varepsilon
ightarrow 0} |
abla u^varepsilon|_{L^p(D)}$ are developed. These bounds provide a way to rigorously assess field concentrations generated by the microgeometry without having to compute the actual field $u...