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

Dondl, Patrick W.; Scheutzow, Michael; Throm, Sebastian

doi:10.1017/s0308210512001291

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

Dondl, Patrick W.; Scheutzow, Michael; Throm, Sebastian

Authors

Patrick W. Dondl

Michael Scheutzow

Sebastian Throm

Abstract

For a model of a driven interface in an elastic medium with random obstacles we prove the 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 neighbour site percolation cluster at a non-trivial percolation threshold.

Citation

Dondl, P. W., Scheutzow, M., & Throm, S. (2015). Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 145(3), 481-512. https://doi.org/10.1017/s0308210512001291

Journal Article Type	Article
Acceptance Date	Jan 24, 2014
Online Publication Date	Jun 3, 2015
Publication Date	Jun 3, 2015
Deposit Date	Oct 24, 2014
Publicly Available Date	Jun 15, 2015
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Print ISSN	0308-2105
Electronic ISSN	1473-7124
Publisher	Cambridge University Press
Peer Reviewed	Peer Reviewed
Volume	145
Issue	3
Pages	481-512
DOI	https://doi.org/10.1017/s0308210512001291
Related Public URLs	http://arxiv.org/abs/1201.4836