{"paper":{"title":"Adaptive homotopy continuation for robust dispersion curve computation in viscoelastic waveguides: guaranteed branch identity continuity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Method ensures one-to-one branch match in viscoelastic dispersion curves","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Dong Xiao, M. H. Aliabadi, Zahra Sharif Khodaei","submitted_at":"2026-05-14T17:10:12Z","abstract_excerpt":"This paper presents the first systematic application of a material homotopy continuation framework for efficient, automated computation of dispersion curves in viscoelastic waveguides of arbitrary cross-section. A material homotopy continuously maps the original lossy problem to an auxiliary lossless one via an attenuation parameter s in [0,1], addressing the core challenges of the non-Hermitian eigenvalue problem. Grounded in analytic perturbation theory, the method guarantees branch identity continuity--a one-to-one correspondence between solutions at s=0 and s=1--provided the real-parameter"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The method guarantees branch identity continuity--a one-to-one correspondence between solutions at s=0 and s=1--provided the real-parameter path does not cross any exceptional points, yielding the characteristic real-part veering with imaginary-part crossing without post-processing.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The real-parameter path does not cross any exceptional points (or follows Type I exceptional point topology), so that physical mode labels established at the elastic stage remain valid at the viscoelastic stage.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A material homotopy continuation framework computes dispersion curves in viscoelastic waveguides by continuously mapping to an elastic problem while guaranteeing branch identity continuity under non-crossing exceptional points.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Method ensures one-to-one branch match in viscoelastic dispersion curves","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"be522eda8e6999bef8ca8e96541c7892decdb7e6c8fd59ca250be90109abde06"},"source":{"id":"2605.15089","kind":"arxiv","version":1},"verdict":{"id":"2d4a151a-bb90-47f0-b393-64cf543886cf","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:59:52.904916Z","strongest_claim":"The method guarantees branch identity continuity--a one-to-one correspondence between solutions at s=0 and s=1--provided the real-parameter path does not cross any exceptional points, yielding the characteristic real-part veering with imaginary-part crossing without post-processing.","one_line_summary":"A material homotopy continuation framework computes dispersion curves in viscoelastic waveguides by continuously mapping to an elastic problem while guaranteeing branch identity continuity under non-crossing exceptional points.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The real-parameter path does not cross any exceptional points (or follows Type I exceptional point topology), so that physical mode labels established at the elastic stage remain valid at the viscoelastic stage.","pith_extraction_headline":"Method ensures one-to-one branch match in viscoelastic dispersion curves"},"references":{"count":58,"sample":[{"doi":"","year":2014,"title":"Rose.Ultrasonic Guided Waves in Solid Media","work_id":"108c1224-6fa1-4290-b80f-064c98e1f5d8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Victor Giurgiutiu.Structural Health Monitoring with Piezoelectric Wafer Active Sensors. 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