{"paper":{"title":"Finding All the Stationary Points of a Potential Energy Landscape via Numerical Polynomial Homotopy Continuation Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DS"],"primary_cat":"cond-mat.stat-mech","authors_text":"Dhagash Mehta","submitted_at":"2011-04-28T20:00:08Z","abstract_excerpt":"The stationary points (SPs) of a potential energy landscape play a crucial role in understanding many of the physical or chemical properties of a given system. Unless they are found analytically, there is, however, no efficient method to obtain 'all' the SPs of a given potential. We introduce a novel method, called the numerical polynomial homotopy continuation (NPHC) method, which numerically finds all the SPs, and is 'embarrassingly parallelizable'. The method requires the non-linearity of the potential to be polynomial-like, which is the case for almost all of the potentials arising in phys"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5497","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"}