{"paper":{"title":"Staggering domino-like blast front motion in a one-dimensional cold gas","license":"http://creativecommons.org/licenses/by/4.0/","headline":"For an infinite family of special mass ratios, a one-dimensional alternating particle chain with equidistant spacing admits an exact solution where the blast front advances ballistically because only one triplet of particles moves at any时刻.","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Krzysztof Pilorz, Taras Holovatch, Yurij Holovatch, Yuri Kozitsky","submitted_at":"2026-05-15T16:10:07Z","abstract_excerpt":"One-dimensional alternating particle systems are widely used to study interconnections between the hydrodynamics of blast waves in a gas-like medium and the Newtonian dynamics of its corpuscular constituents. We study the model in which point particles with masses $m,\\mu, m,\\mu,\\dots, (m\\geq\\mu)$ are distributed on the positive half-line $\\mathbb{R}_{+}$. Their dynamics are initiated by giving a positive velocity to the leftmost particle; in its course, the particles undergo elastic collisions. For this model with $m/\\mu=2$, it has previously been established that the dynamics that start from "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For an infinite family of mass ratios M_k the dynamics admit an exact solution in which at each moment only a single triplet m, μ, m is in motion, all other particles are at rest, and the shock front moves ballistically with average velocity equal to the initial one.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The initial positions are exactly equidistant (or otherwise non-random) and the mass ratio is tuned precisely to one of the discrete values M_k; any deviation from these exact conditions is assumed to destroy the staggered-triplet regime.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact solution for specific mass ratios in 1D alternating-mass elastic chain shows ballistic shock-front motion via staggered triplet dynamics instead of hydrodynamic scaling.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For an infinite family of special mass ratios, a one-dimensional alternating particle chain with equidistant spacing admits an exact solution where the blast front advances ballistically because only one triplet of particles moves at any时刻.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"da9a63da7de221a48183108f8c256d2be52ae2c24d024c4390bb78814c55a084"},"source":{"id":"2605.16125","kind":"arxiv","version":1},"verdict":{"id":"71303943-61c5-4e7c-be73-ad339b0c9743","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:42:32.318419Z","strongest_claim":"For an infinite family of mass ratios M_k the dynamics admit an exact solution in which at each moment only a single triplet m, μ, m is in motion, all other particles are at rest, and the shock front moves ballistically with average velocity equal to the initial one.","one_line_summary":"Exact solution for specific mass ratios in 1D alternating-mass elastic chain shows ballistic shock-front motion via staggered triplet dynamics instead of hydrodynamic scaling.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The initial positions are exactly equidistant (or otherwise non-random) and the mass ratio is tuned precisely to one of the discrete values M_k; any deviation from these exact conditions is assumed to destroy the staggered-triplet regime.","pith_extraction_headline":"For an infinite family of special mass ratios, a one-dimensional alternating particle chain with equidistant spacing admits an exact solution where the blast front advances ballistically because only one triplet of particles moves at any时刻."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16125/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.958986Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:51:36.093171Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:33.381686Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.469787Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e792e7699b5eca7be078628e6319fcc8286c1b6430f00f7ef8898080ead7081e"},"references":{"count":52,"sample":[{"doi":"","year":null,"title":"The exponents corresponding to other observables, obtained in a similar way, are also listed in Table I","work_id":"2d1bc623-2303-442e-9d29-0c7f17c24609","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Note that H(t) = 0 for all t > 0 for the degenerate domino dynamics","work_id":"01e4c214-6a00-4526-8e8b-2e9bafb1fd39","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"By combining the latter with (","work_id":"ad37581d-8221-4d2d-a060-ad4d3be61160","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Note that for m = 2, α is much smaller than γ, which means that the increase of the latter sum is much slower than that of ∑ l≥ 0 ml|ul(t)|","work_id":"c6dd63ea-05fa-4c52-9552-7653be428d87","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Then A := A1A0 =    θ 1 − θ 0 − θ(1 + θ) θ2 1 + θ 1 − θ2 − θ(1 − θ) θ    (16) 8 describes the complete round of collisions","work_id":"8beaf7f2-1585-4067-91e9-e6263810bc5e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":52,"snapshot_sha256":"cea13674940922c5547f1015e8ebb493bfce47512d67a702c8b8186dd54ec4e6","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e95df3e4dcac749a59bf57209f13b4116ccaa9005578abb070b4351736b885af"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}