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

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.

References in corpus (2)

• The emergence of torsion in the continuum limit of distributed edge-dislocations
• Riemannian surfaces with torsion as homogenization limits of locally-Euclidean surfaces with dislocation-type singularities

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