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Article Dans Une Revue Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Année : 2022

Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems

Résumé

We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, for finite range interactions, the homogenized energy density, identifying the effective limit, is crystalline, i.e. its Wulff crystal is a polytope, for which we can (exponentially) bound the number of vertices. This is achieved by deriving a dual representation of the energy density through a finite cell formula. This formula also allows easy numerical computations: we show a few experiments where we compute periodic patterns which minimize the anisotropy of the surface tension.
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Dates et versions

hal-03326337 , version 1 (25-08-2021)
hal-03326337 , version 2 (24-01-2022)
hal-03326337 , version 3 (10-10-2022)

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Antonin Chambolle, Leonard Kreutz. Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2022, 21 (1), pp.34--79. ⟨10.1137/21M1442073⟩. ⟨hal-03326337v3⟩
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