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Phase Field Models for Thin Elastic Structures with Topological Constraint (2016)
Journal Article
Dondl, P. W., Lemenant, A., & Wojtowytsch, S. (2017). Phase Field Models for Thin Elastic Structures with Topological Constraint. Archive for Rational Mechanics and Analysis, 223(2), 693-736. https://doi.org/10.1007/s00205-016-1043-6

This article is concerned with the problem of minimising the Willmore energy in the class of connected surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi’s diffuse Willmore... Read More about Phase Field Models for Thin Elastic Structures with Topological Constraint.

Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation (2015)
Journal Article
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

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 interacti... Read More about Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation.