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

DOI10.1017/S0308210512001291zbMath1326.35387arXiv1201.4836OpenAlexW2964232866MaRDI QIDQ5500277

Sebastian Throm, Michael K. R. Scheutzow, Patrick W. Dondl

Publication date: 5 August 2015

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.4836

zbMATH Keywords

percolationsemilinear fractional diffusion problemobstacklesrandom elastic medium

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) PDEs with randomness, stochastic partial differential equations (35R60) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11) PDEs in connection with statistical mechanics (35Q82)

Related Items (5)

A proof of Taylor scaling for curvature-driven dislocation motion through random arrays of obstacles ⋮ Bounds on precipitate hardening of line and surface defects in solids ⋮ Pinning of interfaces by localized dry friction ⋮ Pinning of interfaces in a random medium with zero mean ⋮ Threshold phenomenon for homogenized fronts in random elastic media

Cites Work

• Hitchhiker's guide to the fractional Sobolev spaces
• Lipschitz percolation
• Time-homogenization of a first order system arising in the modelling of the dynamics of dislocation densities
• A non-local regularization of first order Hamilton-Jacobi equations
• Fractal first-order partial differential equations
• A First-Order Perturbation Analysis of Crack Trapping by Arrays of Obstacles
• An Extension Problem Related to the Fractional Laplacian

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