{"paper":{"title":"Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Agata Fronczak, Micha{\\l} {\\L}epek, Pawe{\\l} Kukli\\'nski, Piotr Fronczak","submitted_at":"2018-09-11T21:19:36Z","abstract_excerpt":"The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability $W(Q,t)$ to find the system in a given mass spectrum $Q=\\{n_1,n_2,\\dots,n_g\\dots\\}$, with $n_g$ being the number of particles of size $g$. The exact expression for the average number of particles, $\\langle n_g(t)\\rangle$, at arbitrary time $t$ is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04172","kind":"arxiv","version":5},"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"}