Effect of neutral modes on the order of a transition

Stéphan Fauve

doi:10.5802/crmeca.21

Instabilities, patterns

Effect of neutral modes on the order of a 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

Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 475-487.

Résumé
Abstract

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.

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.

Publié le : 2020-11-16

DOI : 10.5802/crmeca.21

Mots clés : Instability, Symmetry, Neutral modes, Drifting patterns, Peierls transition

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Effect of neutral modes on the order of a transition},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {475--487},
     publisher = {Acad\'emie des sciences, Paris},
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     number = {6-7},
     year = {2020},
     doi = {10.5802/crmeca.21},
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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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