dorsal/arxiv
View SchemaNew stability results for long-wavelength convection patterns
| Authors | Anne C. Skeldon, Mary Silber |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9712006 |
| URL | https://arxiv.org/abs/patt-sol/9712006 |
Abstract
We consider the transition from a spatially uniform state to a steady, spatially-periodic pattern in a partial differential equation describing long-wavelength convection. This both extends existing work on the study of rolls, squares and hexagons and demonstrates how recent generic results for the stability of spatially-periodic patterns may be applied in practice. We find that squares, even if stable to roll perturbations, are often unstable when a wider class of perturbations is considered. We also find scenarios where transitions from hexagons to rectangles can occur. In some cases we find that, near onset, more exotic spatially-periodic planforms are preferred over the usual rolls, squares and hexagons.
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"abstract": "We consider the transition from a spatially uniform state to a steady,\nspatially-periodic pattern in a partial differential equation describing\nlong-wavelength convection. This both extends existing work on the study of\nrolls, squares and hexagons and demonstrates how recent generic results for the\nstability of spatially-periodic patterns may be applied in practice. We find\nthat squares, even if stable to roll perturbations, are often unstable when a\nwider class of perturbations is considered. We also find scenarios where\ntransitions from hexagons to rectangles can occur. In some cases we find that,\nnear onset, more exotic spatially-periodic planforms are preferred over the\nusual rolls, squares and hexagons.",
"arxiv_id": "patt-sol/9712006",
"authors": [
"Anne C. Skeldon",
"Mary Silber"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "New stability results for long-wavelength convection patterns",
"url": "https://arxiv.org/abs/patt-sol/9712006"
},
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"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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