dorsal/arxiv
View SchemaDynamics and Topological Aspects of a Reconstructed Two-Dimensional Foam Time Series Using Potts Model on a Pinned Lattice
| Authors | Igor F. Vasconcelos, Isabelle Cantat, James A. Glazier |
|---|---|
| Categories | |
| ArXiv ID | physics/0303063 |
| URL | https://arxiv.org/abs/physics/0303063 |
| DOI | 10.1016/j.jcp.2003.06.001 |
| Journal | J. Comp. Phys. 192 (1) 1-20 (2003) |
Abstract
We discuss a method to reconstruct an approximate two-dimensional foam structure from an incomplete image using the extended Potts mode with a pinned lattice we introduced in a previous paper. The initial information consists of the positions of the vertices only. We locate the centers of the bubbles using the Euclidean distance-map construction and assign at each vertex position a continuous pinning field with a potential falling off as $1/r$. We nucleate a bubble at each center using the extended Potts model and let the structure evolve under the constraint of scaled target areas until the bubbles contact each other. The target area constraint and pinning centers prevent further coarsening. We then turn the area constraint off and let the edges relax to a minimum energy configuration. The result is a reconstructed structure very close to the simulation. We repeated this procedure for various stages of the coarsening of the same simulated foam and investigated the simulation and reconstruction dynamics, topology and area distribution, finding that they agree to good accuracy.
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"abstract": "We discuss a method to reconstruct an approximate two-dimensional foam\nstructure from an incomplete image using the extended Potts mode with a pinned\nlattice we introduced in a previous paper. The initial information consists of\nthe positions of the vertices only. We locate the centers of the bubbles using\nthe Euclidean distance-map construction and assign at each vertex position a\ncontinuous pinning field with a potential falling off as $1/r$. We nucleate a\nbubble at each center using the extended Potts model and let the structure\nevolve under the constraint of scaled target areas until the bubbles contact\neach other. The target area constraint and pinning centers prevent further\ncoarsening. We then turn the area constraint off and let the edges relax to a\nminimum energy configuration. The result is a reconstructed structure very\nclose to the simulation. We repeated this procedure for various stages of the\ncoarsening of the same simulated foam and investigated the simulation and\nreconstruction dynamics, topology and area distribution, finding that they\nagree to good accuracy.",
"arxiv_id": "physics/0303063",
"authors": [
"Igor F. Vasconcelos",
"Isabelle Cantat",
"James A. Glazier"
],
"categories": [
"physics.comp-ph"
],
"doi": "10.1016/j.jcp.2003.06.001",
"journal_ref": "J. Comp. Phys. 192 (1) 1-20 (2003)",
"title": "Dynamics and Topological Aspects of a Reconstructed Two-Dimensional Foam Time Series Using Potts Model on a Pinned Lattice",
"url": "https://arxiv.org/abs/physics/0303063"
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