{"id":"W1993892019","doi":"10.4171/ifb/148","title":"Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems","year":2006,"lang":"en","type":"article","venue":"Interfaces and Free Boundaries Mathematical Analysis Computation and Applications","topic":"Block Copolymer Self-Assembly","field":"Materials Science","cited_by":40,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada; University of Minnesota; National Science Foundation","keywords":"Isoperimetric inequality; Mathematics; Cahn–Hilliard equation; Torus; Mean curvature; Constant (computer programming); Mathematical analysis; Convergence (economics); Curvature; Minification; Applied mathematics; Mathematical optimization; Geometry; Computer science; Differential equation","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":["sts","scholarly_communication"],"consensus_categories":[],"category_scores_codex":[0.0002698686,0.0001983567,0.000352467,0.0001603439,0.001398951,0.002178372,0.0001901545,0.00006196171,0.0001440176],"category_scores_gemma":[0.00001849345,0.0001373156,0.00006041504,0.0007142593,0.00114533,0.0001942109,0.0001563189,0.00009583947,0.00003046605],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001863731,"about_ca_system_score_gemma":0.00004416047,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002343424,"about_ca_topic_score_gemma":0.0002296359,"domain_scores_codex":[0.9986189,0.00006638582,0.000475784,0.0004019091,0.0002430012,0.0001940135],"domain_scores_gemma":[0.9991369,0.0001990361,0.0001755203,0.0002841807,0.0001135681,0.00009077586],"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":[0.0001342404,0.002287913,0.002702033,0.0009581977,0.001364995,0.000005736117,0.01996364,0.004442027,0.08243614,0.8068332,0.005252273,0.07361958],"study_design_scores_gemma":[0.003391981,0.0005709612,0.00392849,0.00009149323,0.003904566,0.0001695122,0.004798775,0.6503662,0.01442786,0.2532788,0.06355669,0.001514745],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5678088,0.003762163,0.4254378,0.001792309,0.00002215486,0.0004215135,0.00004250708,0.00008104188,0.0006316735],"genre_scores_gemma":[0.9955414,0.00004618049,0.003805208,0.0000971992,0.00005557354,0.0001749266,0.00002630531,0.00001080684,0.0002424071],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6459242,"threshold_uncertainty_score":0.9999011,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01216353325931011,"score_gpt":0.2818517223247937,"score_spread":0.2696881890654836,"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."}}