{"id":"W4404674634","doi":"10.1007/s00205-024-02070-z","title":"Boundary Behavior of Limit-Interfaces for the Allen–Cahn Equation on Riemannian Manifolds with Neumann Boundary Condition","year":2024,"lang":"en","type":"article","venue":"Archive for Rational Mechanics and Analysis","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Young Scientists Fund; Research Grants Council, University Grants Committee; National Natural Science Foundation of China; Chinese University of Hong Kong; Stryker","keywords":"Neumann boundary condition; Mathematical analysis; Limit (mathematics); Mathematics; Boundary value problem; Boundary (topology); Allen–Cahn equation","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":[0.000787173,0.000608082,0.0006414225,0.001689255,0.0009841232,0.001726532,0.001084437,0.001296587,0.003497715],"category_scores_gemma":[0.003189954,0.0003519776,0.0005831803,0.0002482521,0.002155683,0.00214587,0.002021147,0.001065468,0.0002756224],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001358773,"about_ca_system_score_gemma":0.000506528,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002167132,"about_ca_topic_score_gemma":0.001084322,"domain_scores_codex":[0.9997677,0.00006299456,0.000009943395,0.00003877897,0.00005748638,0.000063158],"domain_scores_gemma":[0.9992563,0.0001889594,0.0001482302,0.00003971538,0.0001379104,0.0002288518],"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":[0.0002599905,0.0001315788,0.005606258,0.0001296167,0.00003934321,0.0008905547,0.0006823876,0.04083156,0.01769885,0.9268624,0.001589515,0.005277895],"study_design_scores_gemma":[0.00006368958,0.0001475664,0.004123768,0.00006691392,0.00002111061,0.0004538942,0.0005479591,0.6618824,0.004666864,0.3264462,0.001512818,0.00006681903],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9185655,0.0004817544,0.06664836,0.0005475719,0.00005048013,0.00004432793,0.00007251952,0.0001217988,0.01346776],"genre_scores_gemma":[0.9884631,0.0001274916,0.006854226,0.00007114052,0.00003061207,0.00004218334,0.0001078137,0.00004614854,0.004257369],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003497715,"threshold_uncertainty_score":0.01170105,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02258445034831451,"score_gpt":0.2744572146732138,"score_spread":0.2518727643248992,"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."}}