L1 ⚛ L1-198 ⊙ Testnet

Natural Convection — buoyancy-driven flow heat transfer

Heat Transfer · Rayleigh-Benard / cavity free convection

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⬇ L1-198.md

# ⚛ L1 Principle — Natural Convection — buoyancy-driven flow heat transfer **ID:** `L1-198` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Heat Transfer — *Rayleigh-Benard / cavity free convection* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D temp velocity fields > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034 --- ## 🧠 1. Introduction **Natural Convection — buoyancy-driven flow heat transfer** is a **nonlinear inverse problem** whose unknown lives in **3D temp velocity fields** space, within the **Rayleigh-Benard / cavity free convection** sub-domain of **Heat Transfer**. Measurements consist of thermal radiation / temperature measurements via a **piv shadowgraph ir** sensing mechanism. The forward operator applies, in order: L · boussinesq operator; L · buoyancy operator; L · heat transport operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Unstable above Ra > 10^8 (turbulent); chaotic sensitivity to IC. ## ⚙ 2. Forward Model Physical chain: **x** → L · boussinesq → L · buoyancy → L · heat transport → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.heat_transport` `L.buoyancy` `L.boussinesq` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.boussinesq` | L · boussinesq operator | | `L.buoyancy` | L · buoyancy operator | | `L.heat_transport` | L · heat transport operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Heat Transfer | | Sub domain | Rayleigh-Benard / cavity free convection | | Carrier | thermal | | Problem class | nonlinear_inverse | | Solution space | 3D_temp_velocity_fields | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Unstable above Ra > 10^8 (turbulent); chaotic sensitivity to IC. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `natural_convection` · **Forward operator:** `natural_convection_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Pr | — | 0.7 | | Ra | — | 1e+06 | | Snr db | dB | 30 | | Pr error | — | 0 | | Ra error | — | 0 | | Beta error | — | 0 | | Wall t error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 2048 | | W | px | 64 – 2048 | | Z | — | 32 – 1024 | | Pr | — | 0.01 – 1000 | | Ra | — | 1000.0 – 1000000000000.0 | | Snr db | dB | 0 – 40 | | Pr error | — | 0.0 – 0.1 | | Ra error | — | 0.0 – 0.2 | | Beta error | — | 0.0 – 0.1 | | Wall t error | — | 0.0 – 2.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb63bbe18ce6e080651614d95c3978226ddca0f8e042faa771cf50616afa5ca7d` - **Chain tx hash:** `0x699055fb200c7a8feaaa313820e24679124a2063697654c28ad46ebf363bb80e` - **Chain block:** `41554034` --- ## File Mapping This bundle consists of: `L1-198.md`, `L1-198.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-198.md` | Source of truth — edit this | Human or LLM | | `L1-198.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 `L1-198`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-198.md).
Regenerate L1-198.json so every field matches the Markdown.
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L2-198-001 Natural Convection — buoyancy-driven flow heat transfer Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-198",
  "chain_block": 41554034,
  "chain_hash": "0xb63bbe18ce6e080651614d95c3978226ddca0f8e042faa771cf50616afa5ca7d",
  "chain_tx_hash": "0x699055fb200c7a8feaaa313820e24679124a2063697654c28ad46ebf363bb80e",
  "domain": "Heat Transfer",
  "hardness_fn": {
    "delta": 5,
    "kappa": 1000,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
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    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Unstable above Ra \u003e 10^8 (turbulent); chaotic sensitivity to IC.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "thermal",
    "difficulty_delta": 5,
    "domain": "Heat Transfer",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.boussinesq",
      "L.buoyancy",
      "L.heat_transport",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "piv_shadowgraph_ir",
    "solution_space": "3D_temp_velocity_fields",
    "sub_domain": "Rayleigh-Benard / cavity free convection",
    "title": "Natural Convection \u2014 buoyancy-driven flow heat transfer"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "natural_convection_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "Ra",
      "Pr",
      "SNR_dB",
      "Ra_error",
      "beta_error",
      "Pr_error",
      "wall_T_error",
      "Ra_error",
      "beta_error",
      "Pr_error",
      "wall_T_error"
    ],
    "allowed_problem_classes": [
      "natural_convection"
    ],
    "center_spec": {
      "epsilon_fn_center": "20.0",
      "forward_operator": "natural_convection_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "Pr": 0.7,
        "Pr_error": 0.0,
        "Ra": 1000000.0,
        "Ra_error": 0.0,
        "SNR_dB": 30,
        "W": 256,
        "Z": 128,
        "beta_error": 0.0,
        "wall_T_error": 0.0
      },
      "problem_class": "natural_convection"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        2048
      ],
      "Pr": [
        0.01,
        1000
      ],
      "Pr_error": [
        0.0,
        0.1
      ],
      "Ra": [
        1000.0,
        1000000000000.0
      ],
      "Ra_error": [
        0.0,
        0.2
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        64,
        2048
      ],
      "Z": [
        32,
        1024
      ],
      "beta_error": [
        0.0,
        0.1
      ],
      "wall_T_error": [
        0.0,
        2.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Rayleigh-Benard / cavity free convection",
  "title": "Natural Convection \u2014 buoyancy-driven flow heat transfer"
}

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