{"id":"W2090129097","doi":"10.1016/j.jde.2009.11.014","title":"Bounds on the tight-binding approximation for the Gross–Pitaevskii equation with a periodic potential","year":2009,"lang":"en","type":"article","venue":"Journal of Differential Equations","topic":"Nonlinear Photonic Systems","field":"Physics and Astronomy","cited_by":32,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"Deutsche Forschungsgemeinschaft","keywords":"Mathematics; Limit (mathematics); Piecewise; Gross–Pitaevskii equation; Context (archaeology); Mathematical analysis; Work (physics); Space (punctuation); Nonlinear system; Applied mathematics; Mathematical physics; Quantum mechanics; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006391139,0.002439127,0.003510948,0.003398713,0.003680867,0.005437705,0.005814433,0.004741859,0.01152347],"category_scores_gemma":[0.02652435,0.001328385,0.00166668,0.002480321,0.008543648,0.01121049,0.007377539,0.01174087,0.00198946],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00394592,"about_ca_system_score_gemma":0.002570683,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004874763,"about_ca_topic_score_gemma":0.003601847,"domain_scores_codex":[0.9979928,0.0006678225,0.00007631032,0.0002047256,0.0006286555,0.000429857],"domain_scores_gemma":[0.9860918,0.009313953,0.0007085222,0.00130638,0.001202897,0.001376437],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003921965,0.00002594793,0.00006834765,0.00005926205,0.00001530188,0.00003440731,0.00006649008,0.009809243,0.0002443328,0.9868211,0.001714082,0.001102279],"study_design_scores_gemma":[0.00001481774,0.000008008353,0.00008617809,0.00004278515,0.0000120936,0.00002073104,0.00003002246,0.1404054,0.0001071992,0.8585474,0.0007045527,0.00002079064],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.132208,0.0104546,0.5857067,0.02080488,0.002051677,0.0001417482,0.0006102567,0.0008249705,0.2471972],"genre_scores_gemma":[0.8811188,0.004665943,0.06641318,0.003113776,0.001599271,0.0004704835,0.0007705219,0.0008514482,0.04099657],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01152347,"threshold_uncertainty_score":0.03854978,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02394798181031047,"score_gpt":0.2575688698543246,"score_spread":0.2336208880440142,"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."}}