{"id":"W2082353165","doi":"10.1007/s00220-007-0370-8","title":"Tensor Invariants of the Poisson Brackets of Hydrodynamic Type","year":2007,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Computational Fluid Dynamics and Aerodynamics","field":"Engineering","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Tensor field; Lie derivative; Poisson bracket; Poisson manifold; Lie algebra; Mathematics; Symmetric tensor; Invariant (physics); Mathematical physics; Tensor (intrinsic definition); Lie group; Manifold (fluid mechanics); Pure mathematics; Vector field; Scalar (mathematics); Poisson algebra; Poisson distribution; Rank (graph theory); Combinatorics; Mathematical analysis; Geometry; Exact solutions in general relativity; Lie conformal algebra; Symplectic 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001422465,0.000987576,0.001011238,0.004168188,0.001701387,0.003251114,0.001063994,0.001080213,0.01178722],"category_scores_gemma":[0.00321607,0.000530182,0.001022998,0.001866211,0.002816252,0.006373452,0.002295457,0.00270338,0.001779985],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001288776,"about_ca_system_score_gemma":0.0008896578,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006898969,"about_ca_topic_score_gemma":0.0005943627,"domain_scores_codex":[0.999057,0.0002055983,0.0000649061,0.0001698265,0.0003464273,0.0001562025],"domain_scores_gemma":[0.9976258,0.0003015092,0.000514936,0.000295165,0.0007681822,0.000494471],"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":[0.00001763389,0.00001422042,0.000106076,0.00001599921,0.000005455765,0.00003777334,0.0001168392,0.0003124756,0.0009792779,0.9934088,0.001224783,0.003760748],"study_design_scores_gemma":[0.0000104172,0.00003553658,0.0003945934,0.00001164012,0.000008261237,0.0001855462,0.0000818995,0.005122902,0.0008261186,0.9872563,0.006039481,0.00002728303],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2835885,0.003825079,0.4934618,0.004698198,0.006115433,0.0001334995,0.0009134922,0.0008588231,0.2064052],"genre_scores_gemma":[0.8719106,0.002461655,0.0374654,0.001064277,0.005543612,0.00009422719,0.0005938962,0.0006874372,0.08017875],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01178722,"threshold_uncertainty_score":0.03943211,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02170125328884976,"score_gpt":0.2736132483028036,"score_spread":0.2519119950139538,"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."}}