dorsal/arxiv
View SchemaSquare Patterns and Quasi-patterns in Weakly Damped Faraday Waves
| Authors | Wenbin Zhang, Jorge Vinals |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9603005 |
| URL | https://arxiv.org/abs/patt-sol/9603005 |
| DOI | 10.1103/PhysRevE.53.R4283 |
| Journal | Phys. Rev. E 53, R4283 (1996) |
Abstract
Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude equation. Minimization of the associated Lyapunov function yields standing wave patterns of square symmetry for capillary waves, and hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold symmetry in the range of parameters predicted by the multiscale expansion.
{
"annotation_id": "8705b1ce-9552-42d3-80a2-0b377b2242b0",
"date_created": "2026-03-02T18:00:28.607000Z",
"date_modified": "2026-03-02T18:00:28.607000Z",
"file_hash": "2eb58cc0fb863fdff652c2578de93de741e8da3d04baf78b3d01fa7a8ded9afa",
"private": false,
"record": {
"abstract": "Pattern formation in parametric surface waves is studied in the limit of weak\nviscous dissipation. A set of quasi-potential equations (QPEs) is introduced\nthat admits a closed representation in terms of surface variables alone. A\nmultiscale expansion of the QPEs reveals the importance of triad resonant\ninteractions, and the saturating effect of the driving force leading to a\ngradient amplitude equation. Minimization of the associated Lyapunov function\nyields standing wave patterns of square symmetry for capillary waves, and\nhexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity\nwaves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold\nsymmetry in the range of parameters predicted by the multiscale expansion.",
"arxiv_id": "patt-sol/9603005",
"authors": [
"Wenbin Zhang",
"Jorge Vinals"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.53.R4283",
"journal_ref": "Phys. Rev. E 53, R4283 (1996)",
"title": "Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves",
"url": "https://arxiv.org/abs/patt-sol/9603005"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "f42a86aa-d058-416e-890a-366ecd7d45c9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}