{
  "abstract": "We show that a single Lagrangian trajectory encodes not only temporal but also spatial cascade structure--recoverable without access to a spatially resolved Eulerian velocity field. We report a Markov-Switching Multifractal (MSM) framework that infers hidden multi-scale cascade states directly from single-particle trajectories. Kolmogorov scaling fixes the model's switching rates, leaving a single calibrated intermittency parameter; exact Bayesian filtering then returns the posterior of the layer-resolved cascade state along the trajectory. When we apply the MSM framework independently to each trajectory of a particle pair, we find that the inferred states carry genuine spatial information: consistent with Richardson's locality picture, the Kolmogorov $r^{1/3}$ scaling is preserved when fine-scale layers are randomized, but collapses once the randomization crosses the layer set by the pair separation. Single trajectories thus encode the spatial organization of the cascade, opening a route to cascade diagnostics for turbulent flows accessible primarily through sparse or individual Lagrangian trajectories--from particle-tracking velocimetry to atmospheric and oceanographic tracking--where the instantaneous Eulerian field is out of reach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08971",
  "author_total": 2,
  "authors": [
    {
      "name": "Ziang Yang"
    },
    {
      "name": "Lei Fang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ck57f0cez40ft.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08971",
  "fulltext_url": null,
  "id": "ck57f0cez40ft",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08971",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7220985572",
  "pdf_url": "https://arxiv.org/pdf/2610.08971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ck57f0cez40ft.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.08971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08971"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Inferring Multi-Scale Cascade Structure from a Single Lagrangian Trajectory via Hidden Markov Switching",
  "title_text": "Inferring Multi-Scale Cascade Structure from a Single Lagrangian Trajectory via Hidden Markov Switching",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/ck57f0cez40ft",
  "venue": "arXiv",
  "versions": []
}