{
  "abstract": "We present a direct simulation Monte Carlo (DSMC) method for the kinetic theory of ordered fluids recently introduced by the authors. The microscopic constituents of these fluids carry an order parameter belonging to a manifold. The method applies Strang splitting to couple a Monte Carlo treatment of the binary collisions with a symplectic integration of the mean-field Vlasov transport on the order-parameter manifold. We use the Nanbu-Babovsky approach for Maxwellian collision kernels, and Bird's acceptance-rejection method for general ones. The mean-field Vlasov force is reconstructed from the particle ensemble at each time step. We also include a Bhatnagar-Gross-Krook (BGK) / Andersen thermostat to control the system temperature. We formulate the method for a generic order-parameter manifold, and specialize it to two-dimensional calamitic (rod-like) molecules. Numerical tests validate the method. We confirm the relaxation to the Maxwellian distribution predicted by the H-theorem, and simulate the mean-field alignment driven by quadratic, Kuramoto, and Onsager interaction potentials. With the Onsager potential we successfully capture the isotropic-nematic phase transition at the correct critical temperature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31072",
  "author_total": 4,
  "authors": [
    {
      "name": "José A. Carrillo"
    },
    {
      "name": "Patrick E. Farrell"
    },
    {
      "name": "Andrea Medaglia"
    },
    {
      "name": "Umberto Zerbinati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/de2hb23r717s9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31072",
  "fulltext_url": null,
  "id": "de2hb23r717s9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31072",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7214585950",
  "pdf_url": "https://arxiv.org/pdf/2609.31072",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/de2hb23r717s9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.31072",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31072"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A Kinetic Theory Approach To Ordered Fluids: Direct Simulation Monte Carlo Methods",
  "title_text": "A Kinetic Theory Approach To Ordered Fluids: Direct Simulation Monte Carlo Methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/de2hb23r717s9",
  "venue": "arXiv",
  "versions": []
}