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For an array of NCs with the diameter $d$ and the distance $D$ between their centers, which are separated by the small distance $s=D-d \\ll d$ or touch each other by small facets with radius $\\rho\\ll d$ what is equivalent to $s < 0$, $|s| \\ll d$ we derive two analytical asymptotics of the function $\\varepsilon_a(s)$ in the limit $\\varepsilon/\\varepsilo"},"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":"1512.05720","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-12-17T18:56:36Z","cross_cats_sorted":[],"title_canon_sha256":"02e2dba402639887b9e0b21115749dd5252315eb5ac1c1192ec793093b20ae7f","abstract_canon_sha256":"9fda3c5da99898765fca7a9bde61a6fe66381eb39eab0f26f4f6060c864f1419"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:54.009379Z","signature_b64":"OeuUkFLvv+qHaJpMEloAlMF1C3P9fNQdiQljlV7oaAOJ6Y7Slew6JsIyRK+Vz7su4ODjWbm29u4SV9CebrAJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59465065eeaa44bf53c7a446a512ef943666cd77bcb33fa35c8895c1914f4410","last_reissued_at":"2026-05-18T01:18:54.008742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:54.008742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dielectric Constant and Charging Energy in Array of Touching Nanocrystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"B. 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