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Phys. A: Math. Theor."],"published-print":{"date-parts":[[2024,11,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivated by relativistic materials, we develop a numerical scheme to support existing or state new conjectures in the spectral optimisation of eigenvalues of the Dirac operator, subject to infinite-mass boundary conditions. We numerically study the optimality of the regular polygon (respectively, disk) among all polygons of a given number of sides (respectively, arbitrary sets), subject to area or perimeter constraints. We consider the three lowest positive eigenvalues and their ratios. Roughly, we find results analogous to known or expected for the Dirichlet Laplacian, except for the third eigenvalue which does not need to be minimised by the regular polygon (respectively, the disk) for all masses. In addition to the numerical results, a new, mass-dependent upper bound to the lowest eigenvalue in rectangles is proved and its extension to arbitrary quadrilaterals is conjectured.<\/jats:p>","DOI":"10.1088\/1751-8121\/ad8b01","type":"journal-article","created":{"date-parts":[[2024,10,24]],"date-time":"2024-10-24T22:54:51Z","timestamp":1729810491000},"page":"475203","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Numerical optimisation of Dirac eigenvalues"],"prefix":"10.1088","volume":"57","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1969-1860","authenticated-orcid":true,"given":"Pedro R S","family":"Antunes","sequence":"first","affiliation":[]},{"given":"Francisco","family":"Bento","sequence":"additional","affiliation":[]},{"given":"David","family":"Krej\u010di\u0159\u00edk","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2024,11,6]]},"reference":[{"key":"aad8b01bib1","article-title":"Problem List","author":"Krej\u010di\u0159\u00edk","year":"2019"},{"key":"aad8b01bib2","doi-asserted-by":"publisher","first-page":"1348","DOI":"10.1016\/j.enganabound.2009.05.007","article-title":"On the choice of source points in the method of fundamental solutions","volume":"33","author":"Alves","year":"2009","journal-title":"Eng. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2024-07-05","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-10-24","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-11-06","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}