Subcriticality of the zigzag transition: A nonlinear bifurcation analysis

Abstract : When repelling particles are confined by a transverse potential in quasi-one-dimensional geometry, the straight line equilibrium configuration becomes unstable at small confinement, in favor of a staggered row that may be inhomogeneous or homogeneous. This conformational phase transition is a pitchfork bifurcation called the zigzag transition. We study the zigzag transition in infinite and periodic finite systems with short-range interactions. We provide numerical evidence that in this case the bifurcation is subcritical since it exhibits phase coexistence and hysteretic behavior. The physical mechanism responsible for the change in the bifurcation character is the nonlinear coupling between the transverse soft mode at the transition and the longitudinal Goldstone mode linked to the translational or rotational invariance of the zigzag pattern. An asymptotic analysis, near the bifurcation threshold and assuming an infinite system, gives an explicit expression for the normal form of the bifurcation. We establish the subcriticality, and we describe with excellent precision the inhomogeneous zigzag patterns observed in the simulations. A direct test of the physical mechanism responsible for the bifurcation character evidences a quantitative agreement.
Type de document :
Article dans une revue
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 91, pp.32917 - 32917. 〈10.1103/PhysRevE.91.032917〉
Liste complète des métadonnées

Littérature citée [39 références]  Voir  Masquer  Télécharger

https://hal-univ-diderot.archives-ouvertes.fr/hal-01404811
Contributeur : Christophe Coste <>
Soumis le : mardi 29 novembre 2016 - 11:52:49
Dernière modification le : jeudi 11 janvier 2018 - 06:23:15
Document(s) archivé(s) le : mardi 21 mars 2017 - 09:53:52

Fichier

2015_PRE_ZZNonLin.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

Collections

Citation

Tommy Dessup, Christophe Coste, Michel Saint Jean. Subcriticality of the zigzag transition: A nonlinear bifurcation analysis. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 91, pp.32917 - 32917. 〈10.1103/PhysRevE.91.032917〉. 〈hal-01404811〉

Partager

Métriques

Consultations de la notice

93

Téléchargements de fichiers

49