论文标题
同心球的绝缘且完美的电导率问题的确切解决方案
Exact solutions for the insulated and perfect conductivity problems with concentric balls
论文作者
论文摘要
在所有维度上都考虑了由高对比度复合材料引起的绝缘和完美的电导率问题。解决方案及其梯度分别代表电势和场。本文的新颖性在于找到与同心球的绝缘且完美的电导率问题的精确解决方案。我们的结果表明，绝缘电导率问题没有电场浓度，而完美电导率问题的电场相对于内部和外部球之间的界面边界之间的较小距离表现出鲜明的奇异性。这种差异表明，同心球是绝缘复合材料的最佳结构，而不是超导复合材料的最佳结构。
The insulated and perfect conductivity problems arising from high-contrast composite materials are considered in all dimensions. The solution and its gradient, respectively, represent the electric potential and field. The novelty of this paper lies in finding exact solutions for the insulated and perfect conductivity problems with concentric balls. Our results show that there appears no electric field concentration for the insulated conductivity problem, while the electric field for the perfect conductivity problem exhibits sharp singularity with respect to the small distance between interfacial boundaries of the interior and exterior balls. This discrepancy reveals that concentric balls is the optimal structure of insulated composites, but not for superconducting composites.
