L1 ⚛ L1-185 ⊙ Testnet

Eulerian-Lagrangian — dispersed-phase particle tracking

Fluid Dynamics · Euler-Lagrange DPM / two-way coupling

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⬇ L1-185.md

# ⚛ L1 Principle — Eulerian-Lagrangian — dispersed-phase particle tracking **ID:** `L1-185` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Euler-Lagrange DPM / two-way coupling* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** particle trajectories in flow > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553967 --- ## 🧠 1. Introduction **Eulerian-Lagrangian — dispersed-phase particle tracking** is a **linear inverse problem** whose unknown lives in **particle trajectories in flow** space, within the **Euler-Lagrange DPM / two-way coupling** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **ptv laser** sensing mechanism. The forward operator applies, in order: L · fluid eulerian operator; L · particle drag operator; L · two way coupling operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · fluid eulerian → L · particle drag → L · two way coupling → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.two_way_coupling` `L.particle_drag` `L.fluid_eulerian` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.fluid_eulerian` | L · fluid eulerian operator | | `L.particle_drag` | L · particle drag operator | | `L.two_way_coupling` | L · two way coupling operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Euler-Lagrange DPM / two-way coupling | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | particle_trajectories_in_flow | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `dpm` · **Forward operator:** `dpm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Snr db | dB | 30 | | N times | — | 500 | | N particles | — | 100000 | | Collision error | — | 0 | | Drag model error | — | 0 | | Turbulent dispersion error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Snr db | dB | 0 – 40 | | N times | — | 50 – 100000 | | N particles | — | 100.0 – 1000000000.0 | | Collision error | — | 0.0 – 0.2 | | Drag model error | — | 0.0 – 0.3 | | Turbulent dispersion error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe6c2a26b531749858168d5f474fa96ae174190495f203807403902091def0129` - **Chain tx hash:** `0x946909d4015b665976193a48b7519586e540f29a19824649be451a889025bb23` - **Chain block:** `41553967` --- ## File Mapping This bundle consists of: `L1-185.md`, `L1-185.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-185.md` | Source of truth — edit this | Human or LLM | | `L1-185.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 `L1-185`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-185.md).
Regenerate L1-185.json so every field matches the Markdown.
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L2-185-001 Eulerian-Lagrangian — dispersed-phase particle tracking Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-185",
  "chain_block": 41553967,
  "chain_hash": "0xe6c2a26b531749858168d5f474fa96ae174190495f203807403902091def0129",
  "chain_tx_hash": "0x946909d4015b665976193a48b7519586e540f29a19824649be451a889025bb23",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.fluid_eulerian",
      "L.particle_drag",
      "L.two_way_coupling",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "ptv_laser",
    "solution_space": "particle_trajectories_in_flow",
    "sub_domain": "Euler-Lagrange DPM / two-way coupling",
    "title": "Eulerian-Lagrangian \u2014 dispersed-phase particle tracking"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "dpm_forward"
    ],
    "allowed_omega_dimensions": [
      "N_particles",
      "H",
      "W",
      "N_times",
      "SNR_dB",
      "drag_model_error",
      "collision_error",
      "turbulent_dispersion_error",
      "drag_model_error",
      "collision_error",
      "turbulent_dispersion_error"
    ],
    "allowed_problem_classes": [
      "dpm"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "dpm_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "N_particles": 100000.0,
        "N_times": 500,
        "SNR_dB": 30,
        "W": 256,
        "collision_error": 0.0,
        "drag_model_error": 0.0,
        "turbulent_dispersion_error": 0.0
      },
      "problem_class": "dpm"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        2048
      ],
      "N_particles": [
        100.0,
        1000000000.0
      ],
      "N_times": [
        50,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "collision_error": [
        0.0,
        0.2
      ],
      "drag_model_error": [
        0.0,
        0.3
      ],
      "turbulent_dispersion_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Euler-Lagrange DPM / two-way coupling",
  "title": "Eulerian-Lagrangian \u2014 dispersed-phase particle tracking"
}

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