{"paper":{"title":"Surface Growth Driven by an Optimality Criterion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Surface growth is determined by minimizing structural mean compliance subject to a global mass constraint at each discrete step.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Marco Picchi Scardaoni, Roberto Paroni, Rohan Abeyaratne","submitted_at":"2026-05-13T14:36:19Z","abstract_excerpt":"We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a constrained minimization problem. Growth is modeled as an irreversible surface deposition process subject to a global mass constraint, while the driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance.\n  The approach is illustrated on a linearly elastic cantilever beam whose cross-sectional height evolves thro"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Through a formal limiting procedure, we derive from the time-discrete formulation a time-continuous limit in the form of a constrained gradient flow.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance; growth is modeled as an irreversible surface deposition process subject to a global mass constraint.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A time-discrete variational model for accretive surface growth minimizes mean compliance subject to a global mass constraint and yields a constrained gradient flow in the continuous-time limit.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Surface growth is determined by minimizing structural mean compliance subject to a global mass constraint at each discrete step.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1e221625045ca76f0b7c57b73c91972ecad518378a399a9e234f364c243553d5"},"source":{"id":"2605.13602","kind":"arxiv","version":1},"verdict":{"id":"25d4f002-77cc-4c3b-9e47-0a6e5f0e9ccc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:52:11.250111Z","strongest_claim":"Through a formal limiting procedure, we derive from the time-discrete formulation a time-continuous limit in the form of a constrained gradient flow.","one_line_summary":"A time-discrete variational model for accretive surface growth minimizes mean compliance subject to a global mass constraint and yields a constrained gradient flow in the continuous-time limit.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance; growth is modeled as an irreversible surface deposition process subject to a global mass constraint.","pith_extraction_headline":"Surface growth is determined by minimizing structural mean compliance subject to a global mass constraint at each discrete step."},"references":{"count":38,"sample":[{"doi":"10.1007/s00158-022-","year":2022,"title":"Akerson, A., Bourdin, B., Bhattacharya, K. (2022). Optimal design of responsive structures.Structural and Multidisciplinary Optimization, 65. doi:10.1007/s00158-022- 03202-0","work_id":"4c1f754b-9c05-4c10-998d-03fef692c400","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/bs.hna.2020.10.004","year":2021,"title":"doi:10.1016/bs.hna.2020.10.004 , author =","work_id":"0e516fd2-0f49-4af9-b4b7-7078e4bdb896","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"Ambrosi, D., Mollica, F. (2002). On the mechanics of a growing tumor.International Journal of Engineering Science, 40(12), 1297–1316","work_id":"6a63b289-777f-45a2-acdb-ae5f7437bdae","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1177/1081286505059739","year":2007,"title":"Ambrosi, D., Guana, F. (2007). Stress-modulated growth.Mathematics and Mechanics of Solids, 12(3), 319–342. doi:10.1177/1081286505059739","work_id":"d82252f3-8052-456b-8dbd-d368e29cc640","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/978-3-7643-8722-8","year":2005,"title":"Gradient Flows: In Metric Spaces and in the Space of Probability Measures","work_id":"66948f4c-bf3b-4a10-a642-af9d3f03c777","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":38,"snapshot_sha256":"84172aced24e6736a92474916133dcbe57d786e2eb3b2eed2f695280298a08ce","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}