L1 ⚛ L1-477 ⊙ Testnet

Oldroyd-B Viscoelastic Constitutive Model

Polymer Physics · Viscoelastic flow

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-477.md

# ⚛ L1 Principle — Oldroyd-B Viscoelastic Constitutive Model **ID:** `L1-477` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Polymer Physics — *Viscoelastic flow* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** stress tensor field > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555300 --- ## 🧠 1. Introduction **Oldroyd-B Viscoelastic Constitutive Model** is a **nonlinear inverse problem** whose unknown lives in **stress tensor field** space, within the **Viscoelastic flow** sub-domain of **Polymer Physics**. Measurements consist of none via a **rheometry plus velocimetry** sensing mechanism. The forward operator applies, in order: E · momentum operator; E · UCM stress operator; a fixed-point or gradient iteration on the unknown; O · stress field operator. Observations are corrupted by additive Gaussian noise. High-Weissenberg number problem (HWNP); stress singularities near geometric corners; log-conformation reformulation needed for Wi>10. ## ⚙ 2. Forward Model Physical chain: **x** → E · momentum → E · UCM stress → O · stress field → **y** (detector). ``` y = `O.stress_field` `E.UCM_stress` `E.momentum` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.momentum` | E · momentum operator | | `E.UCM_stress` | E · ucm stress operator | | `O.stress_field` | O · stress field operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.iter` | A fixed-point or gradient iteration on the unknown | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Polymer Physics | | Sub domain | Viscoelastic flow | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | stress_tensor_field | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 5 | | L dag | 3.6 | ## 📡 4. Measurement Model High-Weissenberg number problem (HWNP); stress singularities near geometric corners; log-conformation reformulation needed for Wi>10. | Metric | Value | |---|---| | Metric | N1_N2_relative_error | | Secondary | velocity_profile_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `viscoelastic_parameter_inversion` · **Forward operator:** `oldroyd_b_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Re | — | 0.1 | | Wi | — | 1 | | Mesh n | N | 32 | | Geometry | — | 4to1_contraction | | Beta eta s over eta total | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Re | — | 0.0 – 100.0 | | Wi | — | 0.1 – 20.0 | | Mesh n | N | 16 – 256 | | Beta eta s over eta total | — | 0.05 – 0.95 | ## 🎯 6. Tolerance (ε) **Center tolerance:** N1 relative error <= 0.05 | Metric | Range | |---|---| | N1 n2 relative error | 0.02 – 0.4 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **N1_N2_relative_error**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xa50db07913dec22c16ef6efaa491371a451618d9267f4a9e00c628a14bc3ad0d` - **Chain tx hash:** `0xdbbaee78ff2caf4205f3c7c4624ea1cf07552e059453b6278e1f223e76984686` - **Chain block:** `41555300` --- ## File Mapping This bundle consists of: `L1-477.md`, `L1-477.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-477.md` | Source of truth — edit this | Human or LLM | | `L1-477.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-477`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-477.md).
Regenerate L1-477.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-477-001 Oldroyd-B Viscoelastic Constitutive Model Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-477",
  "chain_block": 41555300,
  "chain_hash": "0xa50db07913dec22c16ef6efaa491371a451618d9267f4a9e00c628a14bc3ad0d",
  "chain_tx_hash": "0xdbbaee78ff2caf4205f3c7c4624ea1cf07552e059453b6278e1f223e76984686",
  "domain": "Polymer Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "N1_N2_relative_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "N1_N2_relative_error",
    "regime": "High-Weissenberg number problem (HWNP); stress singularities near geometric corners; log-conformation reformulation needed for Wi\u003e10.",
    "secondary": "velocity_profile_RMSE"
  },
  "physics_fingerprint": {
    "L_DAG": 3.6,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Polymer Physics",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "E.momentum",
      "E.UCM_stress",
      "O.iter",
      "O.stress_field"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "rheometry_plus_velocimetry",
    "solution_space": "stress_tensor_field",
    "sub_domain": "Viscoelastic flow",
    "title": "Oldroyd-B Viscoelastic Constitutive Model"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "oldroyd_b_forward"
    ],
    "allowed_omega_dimensions": [
      "Wi",
      "Re",
      "beta_eta_s_over_eta_total",
      "geometry",
      "mesh_N"
    ],
    "allowed_problem_classes": [
      "viscoelastic_parameter_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "N1 relative error \u003c= 0.05",
      "forward_operator": "oldroyd_b_forward",
      "input_format": "measurement_only",
      "omega": {
        "Re": 0.1,
        "Wi": 1.0,
        "beta_eta_s_over_eta_total": 0.5,
        "geometry": "4to1_contraction",
        "mesh_N": 32
      },
      "problem_class": "viscoelastic_parameter_inversion"
    },
    "epsilon_bounds": {
      "N1_N2_relative_error": [
        0.02,
        0.4
      ]
    },
    "omega_bounds": {
      "Re": [
        0.0,
        100.0
      ],
      "Wi": [
        0.1,
        20.0
      ],
      "beta_eta_s_over_eta_total": [
        0.05,
        0.95
      ],
      "mesh_N": [
        16,
        256
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Viscoelastic flow",
  "title": "Oldroyd-B Viscoelastic Constitutive Model"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.