{
  "abstract": "How much data does a memory kernel need before a fit is meaningful? For a distributed-order model, the answer is about 3.1 decades of observation, more than standard battery-degradation tests provide. Battery capacity fade and corrosion-film growth depend on their history, so they are often modelled using general fractional calculus (GFC), where memory is described by an arbitrary Sonine kernel rather than a single power law. We tested this using two mechanistic models without fractional operators and de Levie's porous-electrode model, whose high-frequency order is exactly 0.5; our estimator recovered 0.500. A single aging curve can recover an effective order, alpha, to within 5% noise using a weak formulation, while separating the tempered parameters (alpha, lambda) requires several Arrhenius conditions, with errors improving from (0.25, 0.43) with one condition to (0.04, 0.07) with four. A distributed-order memory needs 3.1 decades of data to be resolved to 90%; below that, a two-order memory can collapse into one intermediate order that fits the data better than the true spectrum. For saturating passivation, however, a general kernel improves the fit substantially, raising R2 from 0.862 to 0.998. Across 20 cells from two public datasets, observation windows span only 1.23 to 2.24 decades, making the 3.1-decade result a practical design rule: it defines what must be measured before fitting a memory kernel, not only what cannot be fitted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05426",
  "author_total": 1,
  "authors": [
    {
      "name": "Conrard Giresse Tetsassi Feugmo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bxbawxwezexx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05426",
  "fulltext_url": null,
  "id": "2bxbawxwezexx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05426",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "physics.data-an"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bxbawxwezexx.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05426"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "How much data does a memory kernel need? Measurement requirements for fractional models of battery and corrosion degradation",
  "title_text": "How much data does a memory kernel need? Measurement requirements for fractional models of battery and corrosion degradation",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:18Z",
  "url": "https://research.draconitic.com/paper/2bxbawxwezexx",
  "venue": "arXiv",
  "versions": []
}