{
  "abstract": "We study the temporal maximum of a boundary response generated by a coupled diffusion system in a half-space with Robin boundary conditions and a point fluorophore. The fluorescence lifetime enters through a one-sided exponential time convolution. Previous peak-time approximations were derived under separate short- and long-lifetime scalings. We construct a single reduced peak-time formula for every positive ratio of lifetime to the intrinsic width of the transport peak, thereby describing the transition between these regimes without switching formulas. Starting from a known large-distance approximation of the zero-lifetime response, we normalize at its unique maximum and approximate its logarithm quadratically. The resulting scalar mode equation has a unique solution, expressed through the inverse scaled complementary error function. Its endpoint expansions recover the leading structures of the earlier approximations in the corresponding joint large-distance regimes. A cubic correction accounts for the leading local asymmetry. Under a stated bound on the normalized cubic coefficient, we prove uniqueness of its positive mode and agreement with the exact reduced-profile peak expansion through second order in the lifetime. A conditional peak-location stability estimate is combined with a decomposition into transport-profile and local truncation errors. Numerical comparisons with the full diffusion response support the accuracy of the construction. The lifetime-unified formula is distinguished from the fixed-geometry, infinite-lifetime limit, in which the transport tail yields a different peak-time growth law.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21443",
  "author_total": 1,
  "authors": [
    {
      "name": "Junyong Eom"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxywxhbk024kt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21443",
  "fulltext_url": null,
  "id": "cxywxhbk024kt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21443",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2741|Optical Imaging and Spectroscopy Techniques"
    ]
  ],
  "openalex": "W7222465338",
  "pdf_url": "https://arxiv.org/pdf/2610.21443",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxywxhbk024kt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21443",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21443"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lifetime-unified quadratic and cubic approximations of fluorescence peak time for a time-domain diffuse-light response",
  "title_text": "Lifetime-unified quadratic and cubic approximations of fluorescence peak time for a time-domain diffuse-light response",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/cxywxhbk024kt",
  "venue": "arXiv",
  "versions": []
}