{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:K37FX6KUPZZR5QNUJAPHERQIX4","short_pith_number":"pith:K37FX6KU","schema_version":"1.0","canonical_sha256":"56fe5bf9547e731ec1b4481e724608bf0c00f6665227fe7f2f3fa6cbe94f686a","source":{"kind":"arxiv","id":"1005.0444","version":2},"attestation_state":"computed","paper":{"title":"A double scale fast algorithm for the transient evolution of a resonant tunneling diode","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Ali Faraj, Naoufel Ben Abdallah (IMT)","submitted_at":"2010-05-04T06:26:47Z","abstract_excerpt":"The simulation of the time-dependent evolution of the resonant tunneling diode is done by a multiscale algorithm exploiting the existence of resonant states. After revisiting and improving the algorithm developed in [N. Ben Abdallah, O. Pinaud, J. Comp. Phys. 213 (2006) 288-310] for the stationary case, the time-dependent problem is dealt with. The wave function is decomposed into a non resonant part and a resonant one. The projection method to compute the resonant part leads to an accurate algorithm thanks to a suitable interpolation of the non resonant one. The simulation times are largely r"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1005.0444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-04T06:26:47Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"ce9fe513b73d6cb49af0ec1b39a0738b7e983ed3124e93c1a1d3ea2b33b37e1e","abstract_canon_sha256":"a38ec1476d8717e59cea6c8865efe27e8e6d490b594255ccd195dbc865730234"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:51.026303Z","signature_b64":"jL/HE52LSM+t90SjPhjXJn3HOIJNrtNd9KejvLyQNE4Fhrmfci7P5gJtU1M3/ZqyROaZBhxOt5N3xHqoG1mPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56fe5bf9547e731ec1b4481e724608bf0c00f6665227fe7f2f3fa6cbe94f686a","last_reissued_at":"2026-05-18T01:59:51.025682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:51.025682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A double scale fast algorithm for the transient evolution of a resonant tunneling diode","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Ali Faraj, Naoufel Ben Abdallah (IMT)","submitted_at":"2010-05-04T06:26:47Z","abstract_excerpt":"The simulation of the time-dependent evolution of the resonant tunneling diode is done by a multiscale algorithm exploiting the existence of resonant states. After revisiting and improving the algorithm developed in [N. Ben Abdallah, O. Pinaud, J. Comp. Phys. 213 (2006) 288-310] for the stationary case, the time-dependent problem is dealt with. The wave function is decomposed into a non resonant part and a resonant one. The projection method to compute the resonant part leads to an accurate algorithm thanks to a suitable interpolation of the non resonant one. The simulation times are largely r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0444","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1005.0444","created_at":"2026-05-18T01:59:51.025787+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.0444v2","created_at":"2026-05-18T01:59:51.025787+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0444","created_at":"2026-05-18T01:59:51.025787+00:00"},{"alias_kind":"pith_short_12","alias_value":"K37FX6KUPZZR","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"K37FX6KUPZZR5QNU","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"K37FX6KU","created_at":"2026-05-18T12:26:09.077623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4","json":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4.json","graph_json":"https://pith.science/api/pith-number/K37FX6KUPZZR5QNUJAPHERQIX4/graph.json","events_json":"https://pith.science/api/pith-number/K37FX6KUPZZR5QNUJAPHERQIX4/events.json","paper":"https://pith.science/paper/K37FX6KU"},"agent_actions":{"view_html":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4","download_json":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4.json","view_paper":"https://pith.science/paper/K37FX6KU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.0444&json=true","fetch_graph":"https://pith.science/api/pith-number/K37FX6KUPZZR5QNUJAPHERQIX4/graph.json","fetch_events":"https://pith.science/api/pith-number/K37FX6KUPZZR5QNUJAPHERQIX4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4/action/storage_attestation","attest_author":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4/action/author_attestation","sign_citation":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4/action/citation_signature","submit_replication":"https://pith.science/pith/K37FX6KUPZZR5QNUJAPHERQIX4/action/replication_record"}},"created_at":"2026-05-18T01:59:51.025787+00:00","updated_at":"2026-05-18T01:59:51.025787+00:00"}