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Stationary solutions to phase field crystal equations

2010; Wiley; Volume: 34; Issue: 3 Linguagem: Inglês

10.1002/mma.1355

1099-1476

Morgan Pierre, Arnaud Rougirel,

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Mathematical Methods in the Applied SciencesVolume 34, Issue 3 p. 278-308 Research Article Stationary solutions to phase field crystal equations Morgan Pierre, Corresponding Author Morgan Pierre [email protected] Laboratoire de Mathématiques et Applications (UMR 6086), Université de Poitiers & CNRS, Téléport 2—BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, FranceLaboratoire de Mathématiques et Applications (UMR 6086), Université de Poitiers & CNRS, Téléport 2—BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France===Search for more papers by this authorArnaud Rougirel, Arnaud Rougirel Laboratoire de Mathématiques et Applications (UMR 6086), Université de Poitiers & CNRS, Téléport 2—BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, FranceSearch for more papers by this author Morgan Pierre, Corresponding Author Morgan Pierre [email protected] Laboratoire de Mathématiques et Applications (UMR 6086), Université de Poitiers & CNRS, Téléport 2—BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, FranceLaboratoire de Mathématiques et Applications (UMR 6086), Université de Poitiers & CNRS, Téléport 2—BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France===Search for more papers by this authorArnaud Rougirel, Arnaud Rougirel Laboratoire de Mathématiques et Applications (UMR 6086), Université de Poitiers & CNRS, Téléport 2—BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, FranceSearch for more papers by this author First published: 08 November 2010 https://doi.org/10.1002/mma.1355Citations: 4Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract This paper is devoted to the analytical and numerical study of stationary solutions of the one-dimensional Phase Field Crystal Equation. This new model recently introduced by K. Elder and M. Grant describes phase transformations at the atomic level on large time scales. By using bifurcation methods, we investigate the quantitative and qualitative properties of these solutions: multiplicity, stability, and periodicity. Quite unusual bifurcation diagrams are obtained by numerical simulations. Copyright © 2010 John Wiley & Sons, Ltd. Citing Literature Volume34, Issue3February 2011Pages 278-308 RelatedInformation