{"id":"W4285075589","doi":"","title":"Direct Characterization of Spectral Stability of Small Amplitude Periodic Waves in Scalar Hamiltonian Problems Via Dispersion Relation","year":2019,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Nonlinear Photonic Systems","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Dispersion relation; Floquet theory; Amplitude; Eigenvalues and eigenvectors; Mathematics; Mathematical analysis; Hamiltonian (control theory); Instability; Complex plane; Scalar (mathematics); Physics; Nonlinear system; Wavenumber; Classical mechanics; Quantum mechanics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0007981771,0.0006133274,0.001301874,0.000424993,0.0001030981,0.00004419037,0.0006796939,0.0004489221,0.0002865024],"category_scores_gemma":[0.0000182176,0.0007373624,0.0005800767,0.0008234702,0.0003431265,0.0003804381,0.0005384392,0.0006958923,0.00004238463],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006089785,"about_ca_system_score_gemma":0.0004978443,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00248765,"about_ca_topic_score_gemma":0.0002076517,"domain_scores_codex":[0.996006,0.000624412,0.001176511,0.001458798,0.0001966987,0.0005376345],"domain_scores_gemma":[0.9962909,0.0001337027,0.00169592,0.001398902,0.0003196875,0.000160945],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.000309527,0.001029057,0.8082927,0.001309041,0.0002181982,0.000005086276,0.002363183,0.04891851,0.1355433,0.001600452,1.874067e-7,0.0004107394],"study_design_scores_gemma":[0.002026443,0.0002791766,0.6776692,0.001624696,0.0002721798,8.920958e-7,0.000656741,0.2894756,0.02635662,0.0006826494,0.0001056896,0.0008500974],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9761996,0.00003345033,0.01906825,0.00001016626,0.000490075,0.002183959,0.0003744327,0.00002626929,0.001613765],"genre_scores_gemma":[0.9986041,0.0001064373,0.0001208222,0.000001908301,0.0001480177,0.000003227713,0.0006674592,0.0000553435,0.0002927026],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2405571,"threshold_uncertainty_score":0.9995077,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03500949575310666,"score_gpt":0.1769521960897226,"score_spread":0.1419427003366159,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}