Pith Number

pith:FNAAPFHP

pith:2026:FNAAPFHPDOFFY2EQH77RSOWKQQ

not attested not anchored not stored refs resolved

Turbulent stretching of FENE dumbbell polymer model via special stochastic scaling and singular limits

Federico Butori, Yassine Tahraoui

Under a scaling where turbulent eddies shrink as one over N, the stochastic density equation for FENE polymers converges pathwise to a deterministic equation with an added second-order operator for average turbulent stretching.

arxiv:2605.15742 v1 · 2026-05-15 · math.PR · math-ph · math.AP · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FNAAPFHPDOFFY2EQH77RSOWKQQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Under suitable scaling assumption, the polymer density equation, initially a stochastic Fokker-Planck equation in the presence of transport-stretching noise, converges weakly as N↑∞ to a limit deterministic equation with a new extra term, a second order operator. This operator express a sort of average 'turbulent stretching' effect. The deterministic limit is obtained pathwise, without having to take averages with respect to different realizations of the random flow.

C2weakest assumption

The suitable scaling assumption on the turbulent model (dominant space-scale ℓ∼N^{-1}, time-scale τ, white in time) together with the choice of weighted spaces that handle the FENE force singularity near the boundary and the no-flux boundary condition; if these do not hold the convergence to the claimed deterministic limit with the second-order operator may fail.

C3one line summary

Derives pathwise deterministic limit for FENE polymer density in white-in-time turbulent flow via stochastic scaling, adding a second-order stretching operator, then takes singular limit for stationary polymer length distribution.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Nonlinear elastic polymers in random flow 2005

[2] A. Agresti, F. Butori, and E. Luongo. Global smooth solutions by high mode Lie-Transport noise for loga- rithmically hyperdissipative Navier-Stokes equations. 2026+, In preparation 2026

[3] Turbulent dynamics of polymer solutions 2000

[4] Le Bris and T 2009

[5] F. Butori, F. Flandoli, and E. Luongo. On the Itˆ o-Stratonovich Diffusion Limit for the Magnetic Field in a 3D Thin Domain. arXiv preprint arXiv:2401.15701, 2024 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:15.824436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b400794ef1b8a5c68903fff193aca842a049bbca495ce10f3ee3083847ae959

Aliases

arxiv: 2605.15742 · arxiv_version: 2605.15742v1 · doi: 10.48550/arxiv.2605.15742 · pith_short_12: FNAAPFHPDOFF · pith_short_16: FNAAPFHPDOFFY2EQ · pith_short_8: FNAAPFHP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FNAAPFHPDOFFY2EQH77RSOWKQQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2b400794ef1b8a5c68903fff193aca842a049bbca495ce10f3ee3083847ae959

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "141c21ee6762559075c61ccdf6f4bc588e7d063e2fb8273a8473e2aef4d0772f",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-15T08:52:04Z",
    "title_canon_sha256": "1c8cf1d3b6d3aebfb90462b6df482e7146f3c9e6ae2dfeedbfccd63f6de6e951"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15742",
    "kind": "arxiv",
    "version": 1
  }
}