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Main Title: Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation
Author(s): Dondl, Patrick W.
Scheutzow, Michael
Throm, Sebastian
Type: Article
Language Code: en
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.
Issue Date: 2015
Date Available: 27-Oct-2017
DDC Class: 510 Mathematik
Journal Title: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Publisher: Cambridge University Press
Publisher Place: Cambridge
Volume: 145
Issue: 3
Publisher DOI: 10.1017/s0308210512001291
Page Start: 481
Page End: 512
EISSN: 1473-7124
ISSN: 0308-2105
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:FG Stochastische Analysis » Publications

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