{"paper":{"title":"The Lennard-Jones Potential Minimization Problem for Prion AGAAAAGA Amyloid Fibril Molecular Modeling","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","math.OC","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"Jiapu Zhang","submitted_at":"2011-06-08T15:40:04Z","abstract_excerpt":"The simplified Lennard-Jones (LJ) potential minimization problem is minimize f(x)=4\\sum_{i=1}^N \\sum_{j=1,j<i}^N (\\tau_{ij}^{-6} -\\tau_{ij}^{-3})   subject to   x\\in \\mathbb{R}^n, where $\\tau_{ij}=(x_{3i-2}-x_{3j-2})^2 +(x_{3i-1}-x_{3j-1})^2+(x_{3i} -x_{3j})^2$, $(x_{3i-2},x_{3i-1},x_{3i})$ is the coordinates of atom $i$ in $\\mathbb{R}^3$, $i,j=1,2,...,N(\\geq 2 \\quad \\text{integer})$, $n=3N$ and $N$ is the whole number of atoms. The nonconvexity of the objective function and the huge number of local minima, which is growing exponentially with $N$, interest many mathematical optimization expert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1584","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}