Crystalline evolutions in chessboard-like microstructures

Annalisa Malusa; Matteo Novaga; Annalisa Malusa; Matteo Novaga

doi:10.3934/nhm.2018022

Networks and Heterogeneous Media

2018, Volume 13, Issue 3: 493-513. doi: 10.3934/nhm.2018022

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Crystalline evolutions in chessboard-like microstructures

Annalisa Malusa ^{1
,},
Matteo Novaga ^{2
,}

1.
Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
2.
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56217 Pisa, Italy

Received: 01 November 2017 Revised: 01 March 2018
Primary: 53C44; Secondary: 35B27

We describe the macroscopic behavior of evolutions by crystalline curvature of planar sets in a chessboard-like medium, modeled by a periodic forcing term. We show that the underlying microstructure may produce both pinning and confinement effects on the geometric motion.
- Geometric evolutions,
- crystalline flows,
- homogenization,
- facet–breaking,
- pinning
Citation: Annalisa Malusa, Matteo Novaga. Crystalline evolutions in chessboard-like microstructures[J]. Networks and Heterogeneous Media, 2018, 13(3): 493-513. doi: 10.3934/nhm.2018022

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Abstract

We describe the macroscopic behavior of evolutions by crystalline curvature of planar sets in a chessboard-like medium, modeled by a periodic forcing term. We show that the underlying microstructure may produce both pinning and confinement effects on the geometric motion.

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