{"id":"W4401835308","doi":"10.1016/j.cherd.2024.08.026","title":"Largest Lyapunov exponent and Shannon entropy: Two indices to analyze mixing in fluidized beds","year":2024,"lang":"en","type":"article","venue":"Process Safety and Environmental Protection","topic":"Granular flow and fluidized beds","field":"Engineering","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lyapunov exponent; Mathematics; Entropy (arrow of time); Fluidized bed; Exponent; Statistical physics; Mixing (physics); Thermodynamics; Statistics; Physics; Nonlinear system; 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":[0.000206542,0.0001906374,0.0001729643,0.0001961262,0.0001061203,0.000073232,0.00004883235,0.000083527,0.00004367425],"category_scores_gemma":[0.000004816311,0.0001882412,0.00002847657,0.0002096347,0.00003522052,0.0002994444,0.00004209486,0.0002167607,0.00002041051],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001095459,"about_ca_system_score_gemma":0.000004074426,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005642275,"about_ca_topic_score_gemma":0.00002613005,"domain_scores_codex":[0.99905,0.00002457374,0.0002286671,0.0003082622,0.0001489887,0.0002395026],"domain_scores_gemma":[0.9998026,0.00001215747,0.00001294622,0.00007547748,0.000001771159,0.00009507754],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0003919819,0.00010154,0.004975156,0.001222308,0.00009972429,0.00004380646,0.003871486,0.006314819,0.8942205,0.0001010404,0.00001007517,0.0886476],"study_design_scores_gemma":[0.005825178,0.0006330667,0.02177801,0.001366355,0.0002135213,0.000245349,0.002054786,0.5676877,0.3774808,0.001930159,0.01858896,0.002196113],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9665974,0.005159923,0.0270408,0.0001649849,0.0001633899,0.0005586352,0.00002327267,0.0001866572,0.0001048768],"genre_scores_gemma":[0.9984705,0.001134284,0.0001108924,0.00002132266,0.000070482,0.000119845,0.00002752122,0.00003174122,0.00001344741],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5613729,"threshold_uncertainty_score":0.7676255,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005067173707171269,"score_gpt":0.2018579915640451,"score_spread":0.1967908178568739,"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."}}