{"paper":{"title":"A Mathematical Model for Flash Sintering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"math.AP","authors_text":"Andrew A. Lacey, Ian J. Hewitt, Richard I. Todd","submitted_at":"2015-12-14T13:38:20Z","abstract_excerpt":"A mathematical model is presented for the Joule heating that occurs in a ceramic powder compact during the process of flash sintering. The ceramic is assumed to have an electrical conductivity that increases with temperature, and this leads to the possibility of runaway heating that could facilitate and explain the rapid sintering seen in experiments. We consider reduced models that are sufficiently simple to enable concrete conclusions to be drawn about the mathematical nature of their solutions. In particular we discuss how different local and non-local reaction terms, which arise from speci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04307","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"}