{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BLVDUZQQSX6RYR7A24UQNJBRFN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"eb8ac60740eac7d26d3e1716ca984d4310c9ae56eb6ccfd9894c52bd510df7ad","cross_cats_sorted":["cond-mat.stat-mech","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-09-11T19:50:58Z","title_canon_sha256":"6444aba841914a48099fc488d144b2add8ca878d19d088a56939550ffe8aced8"},"schema_version":"1.0","source":{"id":"1109.2344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2344","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2344v1","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2344","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"BLVDUZQQSX6R","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BLVDUZQQSX6RYR7A","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BLVDUZQQ","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:2e65d9ea65f9731415ae9549b0c0fa70ac31a6cffc7636eac54bf6a207a1892a","target":"graph","created_at":"2026-05-18T03:32:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displace","authors_text":"Ad\\'erito Ara\\'ujo, Amal K. Das, Cid\\'alia Neves, Erc\\'ilia Sousa","cross_cats":["cond-mat.stat-mech","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-09-11T19:50:58Z","title":"Numerical solution for a non-Fickian diffusion in a periodic potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2344","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8859dc86f1b88c63e2f2951ea19ad6acbeb739b258d7bcb85de46d65dda3f557","target":"record","created_at":"2026-05-18T03:32:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"eb8ac60740eac7d26d3e1716ca984d4310c9ae56eb6ccfd9894c52bd510df7ad","cross_cats_sorted":["cond-mat.stat-mech","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-09-11T19:50:58Z","title_canon_sha256":"6444aba841914a48099fc488d144b2add8ca878d19d088a56939550ffe8aced8"},"schema_version":"1.0","source":{"id":"1109.2344","kind":"arxiv","version":1}},"canonical_sha256":"0aea3a661095fd1c47e0d72906a4312b4b250e492c3aaaa76102e883e37045af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aea3a661095fd1c47e0d72906a4312b4b250e492c3aaaa76102e883e37045af","first_computed_at":"2026-05-18T03:32:31.972789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:31.972789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dFTCIGVPKE2SBGFt7QGbAo2p1ybBtH95HulRXVLxnSgdSEXNyc307ArB+vJQEDJHxwcycEOfIkrWHKFqXFfUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:31.973545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8859dc86f1b88c63e2f2951ea19ad6acbeb739b258d7bcb85de46d65dda3f557","sha256:2e65d9ea65f9731415ae9549b0c0fa70ac31a6cffc7636eac54bf6a207a1892a"],"state_sha256":"b09bc35b07326721faa4d3bb3c2423694fdf70231e2aa6b90519371492a2ae3e"}