{"id":"W4221057333","doi":"10.1016/j.physd.2022.133258","title":"Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows","year":2022,"lang":"en","type":"article","venue":"Physica D Nonlinear Phenomena","topic":"Navier-Stokes equation solutions","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Fundamental Research Funds for the Central Universities; National Key Research and Development Program of China; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Vortex; Mathematics; Rotational symmetry; Euler equations; Vortex ring; Compressibility; Euler's formula; Mathematical analysis; Flow (mathematics); Polynomial; Nonlinear system; Physics; Geometry; Mechanics; Quantum mechanics","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":[0.0006977957,0.0002896688,0.0003775479,0.0002658417,0.001041323,0.00006821893,0.0007412932,0.00003359298,0.0006007109],"category_scores_gemma":[0.0001696814,0.0002446554,0.0002010454,0.001697547,0.00004747762,0.0001441038,0.0007217097,0.0005458267,0.0004583543],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002458352,"about_ca_system_score_gemma":0.0001182186,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004849267,"about_ca_topic_score_gemma":0.00004636004,"domain_scores_codex":[0.9972939,0.0001968105,0.0005464582,0.0005006021,0.0009434942,0.0005187151],"domain_scores_gemma":[0.9977267,0.0008723519,0.0002413396,0.0008484271,0.0001425686,0.00016857],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.001058384,0.01481342,0.001069124,0.0005824258,0.002279129,0.00006470623,0.03247455,0.5431765,0.03352546,0.1399261,0.1174922,0.113538],"study_design_scores_gemma":[0.001775082,0.0003010696,0.0009655087,0.00004429704,0.0001992303,0.00001658671,0.0004739949,0.7632551,0.0007256041,0.04898871,0.1823118,0.0009429328],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.917547,0.0006413918,0.05540351,0.009149824,0.001972375,0.003412642,0.0007903395,0.0007007223,0.01038214],"genre_scores_gemma":[0.9496131,0.000002576958,0.04517871,0.001149222,0.001734852,0.0004889847,0.00009363501,0.000133835,0.001605092],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2200786,"threshold_uncertainty_score":0.9976759,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06196600199309898,"score_gpt":0.3035210586653658,"score_spread":0.2415550566722668,"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."}}