{
  "abstract": "A scale-separated monopole method is developed for full-field prediction of precipitation under conditions where particle-scale diffusion fields coexist with solute variations over much larger distances. Precipitates are represented by monopole Green's-function solutions, providing a particle-based description of interacting particle growth and dissolution. The direct quasistatic formulation is validated against transient finite-difference calculations and a conventional Kampmann--Wagner numerical model, but becomes inappropriate when spatially heterogeneous particle populations generate slowly relaxing long-wavelength concentration fields. An Ewald decomposition is therefore used to separate the diffusion field by spatial scale. Screened particle-scale fields are treated quasistatically, while the complementary long-range field evolves by transient diffusion. The resulting hybrid formulation retains explicit particle-level precipitation kinetics while allowing mesoscale solute redistribution to evolve on its physical timescale. Application to Al--Sc demonstrates that a transient depletion field generated by localized precipitation can suppress subsequent nucleation and produce persistent spatial variations in precipitate number density and volume fraction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05436",
  "author_total": 1,
  "authors": [
    {
      "name": "C. W. Sinclair"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c45bb3gnbhje6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05436",
  "fulltext_url": null,
  "id": "c45bb3gnbhje6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05436",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "2505|Solidification and crystal growth phenomena"
    ]
  ],
  "openalex": "W7220662361",
  "pdf_url": "https://arxiv.org/pdf/2610.05436",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c45bb3gnbhje6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05436",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05436"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A Scale-Separated Full-Field Monopole Method for Precipitation Modelling",
  "title_text": "A Scale-Separated Full-Field Monopole Method for Precipitation Modelling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/c45bb3gnbhje6",
  "venue": "arXiv",
  "versions": []
}