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arXiv · 1201.4836

Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation

Patrick W. Dondl·Michael Scheutzow·Sebastian Throm
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Abstract

For a model of a driven interface in an elastic medium with random obstacles we prove existence of a stationary positive supersolution at non-vanishing driving force. This shows the emergence of a rate independent hysteresis through the interaction of the interface with the obstacles, despite a linear (force=velocity) microscopic kinetic relation. We also prove a percolation result, namely the possibility to embed the graph of an only logarithmically growing function in a next-nearest neighbor site-percolation cluster at a non-trivial percolation threshold.

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Patrick W. Dondl, Michael Scheutzow, Sebastian Throm. 2012-01-23. Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation. https://arxiv.org/abs/1201.4836

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