Comptes Rendus
Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique : hommage à Pierre Coullet
Pattern universes
Comptes Rendus. Mécanique, Volume 347 (2019) no. 4, pp. 318-331.

In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Defects in generic 3+1 stripe patterns carry an energy density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy.

Dans cet article, nous explorons plusieurs analogies entre la formation de structures périodiques macroscopiques, qui résultent de la succession de transitions de phase ou d'instabilités, et certains phénomènes similaires en cosmologie, où une suite de transitions de phase dans l'univers primordial aurait donné lieu à la séparation des forces fondamentales et à la formation des structures. Nous considérons trois analogies différentes : (i) les défauts et charges topologiques dans les structures macroscopiques sont analogues aux spins et charges des quarks et des leptons ; (ii) les défauts dans les structures périodiques génériques (en dimensions 3+1) ont une densité d'énergie qui donne lieu à certains phénomènes attribués à la présence de matière noire ; (iii) les structures spatio-temporelles résultant de l'interaction d'ondes non linéaires ont des comportements qui rappellent certains phénomènes quantiques, tels que l'inflation cosmique, l'enchevêtrement quantique et l'énergie noire.

Published online:
DOI: 10.1016/j.crme.2019.03.004
Keywords: Pattern formation, Cosmology, Phase transitions
Mot clés : Formation de motifs, Cosmologie, Transition de phase

Alan C. Newell 1; Shankar C. Venkataramani 1

1 Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
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     title = {Pattern universes},
     journal = {Comptes Rendus. M\'ecanique},
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     year = {2019},
     doi = {10.1016/j.crme.2019.03.004},
     language = {en},
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Alan C. Newell; Shankar C. Venkataramani. Pattern universes. Comptes Rendus. Mécanique, Volume 347 (2019) no. 4, pp. 318-331. doi : 10.1016/j.crme.2019.03.004.

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