dorsal/arxiv
View SchemaNoise and dynamical pattern selection
| Authors | Douglas A. Kurtze |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9511002 |
| URL | https://arxiv.org/abs/patt-sol/9511002 |
| DOI | 10.1103/PhysRevLett.77.63 |
Abstract
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will be realized in a given experiment appears to depend on unobservable details of the system's initial conditions. We show, however, that weak, Gaussian white noise drives such a system toward a preferred wave number which depends only on the system parameters and is independent of initial conditions. We give a prescription for calculating this wave number, analytically near the onset of instability and numerically otherwise.
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"abstract": "In pattern forming systems such as Rayleigh-Benard convection or directional\nsolidification, a large number of linearly stable, patterned steady states\nexist when the basic, simple steady state is unstable. Which of these steady\nstates will be realized in a given experiment appears to depend on unobservable\ndetails of the system\u0027s initial conditions. We show, however, that weak,\nGaussian white noise drives such a system toward a preferred wave number which\ndepends only on the system parameters and is independent of initial conditions.\nWe give a prescription for calculating this wave number, analytically near the\nonset of instability and numerically otherwise.",
"arxiv_id": "patt-sol/9511002",
"authors": [
"Douglas A. Kurtze"
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"categories": [
"patt-sol",
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"doi": "10.1103/PhysRevLett.77.63",
"title": "Noise and dynamical pattern selection",
"url": "https://arxiv.org/abs/patt-sol/9511002"
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