{
  "annotation_id": "d09e3e77-2abb-4f5f-b21a-c503cc968e16",
  "date_created": "2026-03-02T18:01:17.174000Z",
  "date_modified": "2026-03-02T18:01:17.174000Z",
  "file_hash": "203588c15c89d326595efca19586c84b46194cda92c8ea62da27d89fa38946fc",
  "private": false,
  "record": {
    "abstract": "Analysing an application in liquid film dynamics, a guide for obtaining the\ncorresponding constrained functional derivatives for constraints coupling the\nfunctional variables is given. The use of constrained derivatives makes the\nproper account for constraints possible in time-dependent, nonequilibrium\nphysical theories, with physical equations not emerging as Euler-Lagrange\nequations, which is especially relevant with respect to the dynamics of complex\nliquids.",
    "arxiv_id": "physics/0701145",
    "authors": [
      "Tamas Gal"
    ],
    "categories": [
      "physics.flu-dyn",
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "doi": "10.1063/1.2737265",
    "journal_ref": "J. Math. Phys. 48, 053520 (2007)",
    "title": "Differentiation of functionals with variables coupled by constraints:   Analysis through a fluid-dynamical model",
    "url": "https://arxiv.org/abs/physics/0701145"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bb321681-d25a-43a2-bb48-d1c0eccd2d58",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}