Non-metricity in the continuum limit of randomly-distributed point defects

Raz Kupferman*, Cy Maor, Ron Rosenthal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageAmerican English
Pages (from-to)75-139
Number of pages65
JournalIsrael Journal of Mathematics
Volume223
Issue number1
DOIs
StatePublished - 1 Feb 2018

Bibliographical note

Publisher Copyright:
© 2018, Hebrew University of Jerusalem.

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