Fin junction of ferroelectric thin films
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Luciano Carbone
Abstract
In this paper, starting from a non-convex and nonlocal 3D-variational model for the electric polarization in a ferroelectric material, and using an asymptotic process based on dimensional reduction, we analyze junction phenomena for two orthogonal joined ferroelectric thin films. We obtain three different 2D-variational models for joined thin films, depending on how the reduction happens. Indeed, a memory effect of the reduction process appears, and it depends on the competition of the relative thickness of the two films. The guide parameter is the limit of the ratio between these two small thickness.
Funding statement: The third author is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). He is also member of the Spanish project n. MTM2013-44883-P of MICINN. He wishes also to thank the Zhejiang University (Hangzhou, China), where he was visiting professor in 2015 and 2016 in the setting of project FP7-PEOPLE-2012-IRSES: EDWTGT, and where he had helpful discussions on ferroelectric materials.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the continuity of functionals defined on partitions
- Fin junction of ferroelectric thin films
- A class of shape optimization problems for some nonlocal operators
- Dichotomy of global capacity density in metric measure spaces
- Nonlinear diffusion in transparent media: The resolvent equation
Articles in the same Issue
- Frontmatter
- On the continuity of functionals defined on partitions
- Fin junction of ferroelectric thin films
- A class of shape optimization problems for some nonlocal operators
- Dichotomy of global capacity density in metric measure spaces
- Nonlinear diffusion in transparent media: The resolvent equation
