Abstract
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.
Original language | English |
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Pages (from-to) | 75-139 |
Number of pages | 65 |
Journal | Israel Journal of Mathematics |
Volume | 223 |
Issue number | 1 |
DOIs | |
State | Published - 1 Feb 2018 |
All Science Journal Classification (ASJC) codes
- General Mathematics