Surface energies emerging in a microscopic, two-dimensional two-well problem
In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyze the H...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
28 Sep 2015
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| In: |
Arxiv
Year: 2015, Pages: 1-50 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1509.08220
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| Author Notes: | Georgy Kitavtsev, Stephan Luckhaus, and Angkana Rüland |
| Summary: | In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyze the Hamiltonian which was introduced in \cite{KLR14}. It turns out that this class of Hamiltonians allows for a direct control of the discrete second order gradients and for a one-sided comparison with a two-dimensonal spin system. Using this and relying on the ideas of Conti and Schweizer \cite{CS06}, \cite{CS06a}, \cite{CS06c}, which were developed for a continuous analogue of the model under consideration, we derive a (first order) continuum limit. This shows the emergence of surface energy in the form of a sharp-interface limiting model as well the explicit structure of the minimizers to the latter. |
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| Item Description: | Gesehen am 27.05.2021 |
| Physical Description: | Online Resource |