{
  "abstract": "We analyze the trapping of diffusing ligands, modeled as Brownian particles, by a sphere that has [Formula: see text] partially reactive boundary patches, each of small area and arbitrary shape, on an otherwise reflecting boundary. For such a structured target, the partial reactivity of each boundary patch is characterized by a Robin boundary condition, with a local boundary reactivity [Formula: see text] for [Formula: see text]. For any spatial arrangement of well-separated patches on the surface of the sphere, the method of matched asymptotic expansions is used to derive explicit results for the capacitance [Formula: see text] of the structured target, which is valid for any [Formula: see text]. This target capacitance [Formula: see text] is defined in terms of a Green’s matrix, which depends on the spatial configuration of patches, the local reactive capacitance [Formula: see text] of each patch and another coefficient that depends on the local geometry near a patch. The analytical dependence of [Formula: see text] on [Formula: see text] is uncovered via a spectral expansion over Steklov eigenfunctions. For circular patches, the latter are readily computed numerically and provide an accurate fully explicit sigmoidal approximation for [Formula: see text]. In the homogenization limit of [Formula: see text] identical uniformly-spaced patches with [Formula: see text], we derive an explicit scaling law for the effective capacitance and the effective reactivity of the structured target that is valid in the limit of small patch area fraction. From a comparison with numerical simulations, we show that this scaling law provides a highly accurate approximation over the full range [Formula: see text], even when there is only a moderately large number of reactive patches.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2509.26381",
  "author_total": 2,
  "authors": [
    {
      "name": "Denis S Grebenkov"
    },
    {
      "name": "Michael Ward"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22bavjzay06g8.bib",
  "cited_by": 0,
  "doi": "10.1137/25m180562x",
  "fulltext_url": null,
  "id": "22bavjzay06g8",
  "issns": [
    "1540-3459",
    "1540-3467"
  ],
  "landing_url": "https://hal.science/hal-05765236v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "1312|Diffusion and Search Dynamics"
    ]
  ],
  "openalex": "W7161992652",
  "pdf_url": "https://hal.science/hal-05765236/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-21",
  "publisher": "Society for Industrial and Applied Mathematics",
  "ris": "https://research.draconitic.com/paper/22bavjzay06g8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05765236",
      "source": "hal",
      "url": "https://hal.science/hal-05765236v1"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "openalex:1312|Diffusion and Search Dynamics",
      "subfield": "molecular-biology"
    }
  ],
  "title": "The Effective Reactivity for Capturing Brownian Motion by Partially Reactive Patches on a Spherical Surface",
  "title_text": "The Effective Reactivity for Capturing Brownian Motion by Partially Reactive Patches on a Spherical Surface",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/22bavjzay06g8",
  "venue": "Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal",
  "versions": []
}