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Author (up) Cisternas, J.; Concha, A. doi  openurl
  Title Searching nontrivial magnetic equilibria using the deflated Newton method Type
  Year 2024 Publication Chaos Solitons & Fractals Abbreviated Journal Chaos Solitons Fractals  
  Volume 179 Issue Pages 114468  
  Keywords Magnets; Symmetry; Newton method; Deflation; Basins of attraction  
  Abstract 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.  
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  Series Volume Series Issue Edition  
  ISSN 0960-0779 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001155974400001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1939  
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