dorsal/arxiv
View SchemaUniversal algebraic relaxation of fronts propagating into an unstable state
| Authors | Ute Ebert, Wim van Saarloos |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9707004 |
| URL | https://arxiv.org/abs/patt-sol/9707004 |
| DOI | 10.1103/PhysRevLett.80.1650 |
| Journal | Phys. Rev. Lett. 80, 1650 (1998) (revised version). |
Abstract
We analyze ``pulled'' or ``linearly marginally stable'' fronts propagating into unstable states. While ``pushed'' fronts into meta- and unstable states relax exponentially, pulled fronts relax algebraically, and simultaneously the standard derivation of effective interface equations breaks down. We calculate all universal relaxation terms of uniformly translating pulled fronts. The leading $1/t$ and $1/t^{3/2}$ corrections to the velocity are determined by the dispersion relation of the linearized equation only. Our analysis sheds new light on the propagation mechanism of pulled fronts.
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"abstract": "We analyze ``pulled\u0027\u0027 or ``linearly marginally stable\u0027\u0027 fronts propagating\ninto unstable states. While ``pushed\u0027\u0027 fronts into meta- and unstable states\nrelax exponentially, pulled fronts relax algebraically, and simultaneously the\nstandard derivation of effective interface equations breaks down. We calculate\nall universal relaxation terms of uniformly translating pulled fronts. The\nleading $1/t$ and $1/t^{3/2}$ corrections to the velocity are determined by the\ndispersion relation of the linearized equation only. Our analysis sheds new\nlight on the propagation mechanism of pulled fronts.",
"arxiv_id": "patt-sol/9707004",
"authors": [
"Ute Ebert",
"Wim van Saarloos"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevLett.80.1650",
"journal_ref": "Phys. Rev. Lett. 80, 1650 (1998) (revised version).",
"title": "Universal algebraic relaxation of fronts propagating into an unstable state",
"url": "https://arxiv.org/abs/patt-sol/9707004"
},
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