随机分布点缺陷连续极限的非度量性
Non-metricity in the continuum limit of randomly-distributed point defects
摘要：
我们提出了均匀化定理各向同性分布的点缺陷，通过考虑一系列的流形越来越密集的点缺陷。根据加权泊松点过程随机选择缺陷的位置，使其成为第一通道渗流模型的连续版本。我们证明了流形序列收敛到光滑的黎曼流形，而Levi-Civita联络收敛到极限流形上的非度量联络。因此，我们得到严格的出现的非度量张量，这是假设在文献中表示连续分布的点缺陷。
英文摘要：
We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defects are chosen randomly according to a weighted Poisson point process, making it a continuous version of the first passage percolation model. We show that the sequence of manifolds converges to a smooth Riemannian manifold, while the Levi-Civita connections converge to a non-metric connection on the limit manifold. Thus, we obtain rigorously the emergence of a non-metricity tensor, which was postulated in the literature to represent continuous distribution of point defects.
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