Searching nontrivial magnetic equilibria using the deflated Newton method

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dc.coverageDOI: 10.1016/j.chaos.2024.114468
dc.creatorCisternas, Jaime
dc.creatorConcha, Andrés
dc.date2024
dc.date.accessioned2026-01-05T21:05:49Z
dc.date.available2026-01-05T21:05:49Z
dc.description<p>Nonlinear systems that model physical experiments often have many equilibrium configurations, and the number of these static solutions grows with the number of degrees of freedom and the presence of symmetries. It is impossible to know a priori how many equilibria exist and which ones are stable or relevant, therefore from the modeler's perspective, an exhaustive search and symmetry classification in the space of solutions are necessary. With this purpose in mind, the method of deflation (introduced by Farrell as a modification of the classic Newton iterative method) offers a systematic way of finding every possible solution of a set of equations. In this contribution we apply deflated Newton and deflated continuation methods to a model of macroscopic magnetic rotors, and find hundreds of new equilibria that can be classified according to their symmetry. We assess the benefits and limitations of the method for finding branches of solutions in the presence of a symmetry group, and explore the high-dimensional basins of attraction of the method in selected 2-dimensional sections, illustrating the effect of deflation on the convergence.</p>eng
dc.identifierhttps://investigadores.uandes.cl/en/publications/c5c3c69a-7e8f-4b3a-ab09-cac696e33a85
dc.identifier.urihttps://repositorio.uandes.cl/handle/uandes/62140
dc.languageeng
dc.rightsinfo:eu-repo/semantics/restrictedAccess
dc.sourcevol.179 (2024) p.1-11
dc.subjectBasins of attraction
dc.subjectDeflation
dc.subjectMagnets
dc.subjectNewton method
dc.subjectSymmetry
dc.titleSearching nontrivial magnetic equilibria using the deflated Newton methodeng
dc.typeArticleeng
dc.typeArtículospa
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