Comptes Rendus
Instabilities, patterns
Effect of neutral modes on the order of a transition
Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 475-487.

Neutral modes related to spontaneous broken symmetries at the onset of a pattern-forming instability can strongly modify the nature of secondary instabilities of the pattern. In particular these neutral modes can change the order of the secondary transition making it first order or subcritical in the language of bifurcation theory. We first discuss this phenomenon in the context of the drift bifurcation from stationary to traveling patterns. We then consider patterns that undergo a spatial period-doubling bifurcation like the Peierls transition in solid state physics.

Je rappelle comment une expérience réalisée par Yves Couder et son groupe a motivé des travaux théoriques qui ont montré que les modes de phase d’une structure cellulaire engendrée par instabilité peuvent affecter la nature des instabilités secondaires de cette structure, à savoir, le caractère propagatif ou non de l’instabilité secondaire et sa sous-criticalité. Je discute ensuite la sous-criticalité résultant du couplage avec les modes de phase sur d’autres exemples tels que la transition de Peierls en physique de la matière condensée.

Published online:
DOI: 10.5802/crmeca.21
Keywords: Instability, Symmetry, Neutral modes, Drifting patterns, Peierls transition

Stéphan Fauve 1

1 Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Stéphan Fauve. Effect of neutral modes on the order of a transition. Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 475-487. doi : 10.5802/crmeca.21. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.21/

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