{"id":"W2049258558","doi":"10.4006/1.3141024","title":"The dynamic bi-Laplacian equation in polar coordinates and the magic numbers of atomic nucleus","year":2009,"lang":"en","type":"article","venue":"Physics Essays","topic":"Elasticity and Wave Propagation","field":"Engineering","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Physics; Nucleus; Polar coordinate system; Polar; Laplace operator; Quantum mechanics; Geometry; Mathematics; Biology","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001820913,0.00006930593,0.00008984831,0.00001732499,0.00006568708,0.00002697782,0.00007694864,0.00002543355,8.598386e-7],"category_scores_gemma":[0.00002109221,0.00004733834,0.00002207567,0.0001317736,0.00007113186,0.0001007017,0.000009770346,0.0001109691,0.000006414945],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003085458,"about_ca_system_score_gemma":0.000005352142,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004425727,"about_ca_topic_score_gemma":0.00003964033,"domain_scores_codex":[0.9995959,0.00003360835,0.0001257063,0.00006139268,0.00007645084,0.0001069378],"domain_scores_gemma":[0.9996936,0.0001465423,0.00003514583,0.00009459115,0.00001778767,0.00001231914],"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":[0.00008719622,0.00005558956,0.001741967,0.0000855988,0.00004476502,0.000001141263,0.002714031,0.03959709,0.01258982,0.8782953,0.00006954495,0.06471797],"study_design_scores_gemma":[0.0004884286,0.0000130324,0.002101946,0.00002387602,0.00001257241,6.16662e-7,0.00009143445,0.5945541,0.001381865,0.4012517,0.0000138659,0.00006662137],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.956812,0.0005146031,0.0307702,0.0007253909,0.0001215572,0.0002608325,0.0000108729,0.00006472314,0.01071985],"genre_scores_gemma":[0.9997374,0.0001242095,0.00007055455,0.00002086477,0.00001910446,0.000002694557,0.000006352361,0.000008017147,0.00001075474],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.554957,"threshold_uncertainty_score":0.1930401,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005676560299059604,"score_gpt":0.2006596163016596,"score_spread":0.1949830560026,"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."}}