{"id":"W4391546707","doi":"10.3934/cam.2024009","title":"Well-posedness and stability for a nonlinear Euler-Bernoulli beam equation","year":2024,"lang":"en","type":"article","venue":"Communications in Analysis and Mechanics","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Polytechnique Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Bernoulli's principle; Nonlinear system; Stability (learning theory); Beam (structure); Euler's formula; Mathematics; Mathematical analysis; Applied mathematics; Physics; Computer science; Thermodynamics; Optics","routes":{"ca_aff":true,"ca_fund":true,"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":[],"consensus_categories":[],"category_scores_codex":[0.0006131196,0.000113601,0.0002470113,0.0002353052,0.0001286129,0.0001121755,0.0001966267,0.00008500091,0.00003078293],"category_scores_gemma":[0.0001499248,0.0001180661,0.0001088365,0.0006949743,0.00005235455,0.0001254365,0.00008480165,0.0001503287,0.000002262438],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006308102,"about_ca_system_score_gemma":0.00002395998,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000063282,"about_ca_topic_score_gemma":0.002276092,"domain_scores_codex":[0.9991822,0.00005997254,0.0003277862,0.0002159522,0.00008280021,0.0001313244],"domain_scores_gemma":[0.9983937,0.0007270299,0.00002032326,0.000736282,0.00007084329,0.0000517883],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00009857842,0.00140382,0.005587383,0.002430422,0.004491473,9.819979e-7,0.01308629,0.0213702,0.01720426,0.4994507,0.0001013241,0.4347746],"study_design_scores_gemma":[0.0001880996,0.0000205304,0.0004472286,0.00001990205,0.0004644654,2.232294e-7,0.0004131852,0.9836923,0.0002866449,0.01246032,0.00188715,0.0001199497],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3201048,0.006856508,0.6703582,0.001382886,0.0001511332,0.0005717243,0.0001652876,0.000204664,0.0002047272],"genre_scores_gemma":[0.9917579,0.00166445,0.006214535,0.00001499481,0.0000152866,0.0001353915,0.0001759239,0.00001235349,0.000009208371],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9623221,"threshold_uncertainty_score":0.4814596,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04233421645129582,"score_gpt":0.2845773061083605,"score_spread":0.2422430896570646,"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."}}