{"paper":{"title":"Pseudo-Spectrum of the Resistive Magneto-hydrodynamics Operator: Resolving the Resistive Alfven Paradox","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA","math.SP","physics.flu-dyn"],"primary_cat":"physics.plasm-ph","authors_text":"D.Borba, G.T.A. Huysmans, K.S. Riedel, M. Ottaviani, P.J. Schmid, W. Kerner","submitted_at":"2018-03-25T18:22:43Z","abstract_excerpt":"The `Alfv\\'en Paradox' is that as resistivity decreases, the discrete eigenmodes do not converge to the generalized eigenmodes of the ideal Alfv\\'en continuum. To resolve the paradox, the $\\epsilon$-pseudospectrum of the RMHD operator is considered. It is proven that for any $\\epsilon$, the $\\epsilon$- pseudospectrum contains the Alfv\\'en continuum for sufficiently small resistivity. Formal $\\epsilon-pseudoeigenmodes$ are constructed using the formal Wentzel-Kramers-Brillouin-Jeffreys solutions, and it is shown that the entire stable half-annulus of complex frequencies with $\\rho{|\\omega|^2}=|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09303","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1803.09303/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}