L1 ⚛ L1-474 ⊙ Testnet

Dissipative Particle Dynamics (DPD)

Polymer Physics · Mesoscale soft-matter dynamics

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⬇ L1-474.md

# ⚛ L1 Principle — Dissipative Particle Dynamics (DPD) **ID:** `L1-474` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Polymer Physics — *Mesoscale soft-matter dynamics* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D coarse grained trajectory > **📡 Carrier:** none · **🌫 Noise:** thermal langevin > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555300 --- ## 🧠 1. Introduction **Dissipative Particle Dynamics (DPD)** is a **nonlinear inverse problem** whose unknown lives in **3D coarse grained trajectory** space, within the **Mesoscale soft-matter dynamics** sub-domain of **Polymer Physics**. Measurements consist of none via a **mesoscale coarse grained dynamics** sensing mechanism. The forward operator applies, in order: F · conservative operator; F · dissipative operator; F · random operator; D · time · symplectic operator; O · structural operator. Observations are corrupted by Langevin-type thermal fluctuations. Well-posed forward; inverse (parameter recovery from g(r) / S(q)) is ill-conditioned due to near-degenerate parameter combinations (a_ij vs rho_bead trade-off). ## ⚙ 2. Forward Model Physical chain: **x** → F · conservative → F · dissipative → F · random → D · time · symplectic → O · structural → **y** (detector). ``` y = `O.structural` `D.time.symplectic` `F.random` `F.dissipative` `F.conservative` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `F.conservative` | F · conservative operator | | `F.dissipative` | F · dissipative operator | | `F.random` | F · random operator | | `D.time.symplectic` | D · time · symplectic operator | | `O.structural` | O · structural operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Polymer Physics | | Sub domain | Mesoscale soft-matter dynamics | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | 3D_coarse_grained_trajectory | | Noise model | thermal_langevin | | Integration axis | time | | Difficulty delta | 5 | | L dag | 4.2 | ## 📡 4. Measurement Model Well-posed forward; inverse (parameter recovery from g(r) / S(q)) is ill-conditioned due to near-degenerate parameter combinations (a_ij vs rho_bead trade-off). | Metric | Value | |---|---| | Metric | structure_factor_RMSE | | Secondary | g_r_integrated_L1 | ## 📏 5. Operating Range (Ω) **Center problem class:** `dpd_parameter_inversion` · **Forward operator:** `dpd_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Dt | — | 0.04 | | R c | — | 1 | | Gamma | — | 4.5 | | N beads | — | 10000 | | N steps | — | 200000 | | A ij aa | — | 15 | | A ij ab | — | 25 | | Rho bead | — | 3 | | T reduced | — | 1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Dt | — | 0.01 – 0.05 | | R c | — | 0.8 – 1.5 | | Gamma | — | 1.0 – 10.0 | | N beads | — | 1000 – 200000 | | N steps | — | 20000 – 500000 | | A ij aa | — | 10.0 – 30.0 | | A ij ab | — | 15.0 – 60.0 | | Rho bead | — | 1.0 – 6.0 | | T reduced | — | 0.5 – 1.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** S(q) RMSE <= 0.02 | Metric | Range | |---|---| | Structure factor rmse | 0.005 – 0.15 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **structure_factor_RMSE**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x96b77244071dd1abca8a38062d1efddb0da96f3ad29906f1cabd58a72de176c8` - **Chain tx hash:** `0x1c6321201c1aaee6b13ca6a100299302ca249a7350c06e5e31d318b0a32b8f68` - **Chain block:** `41555300` --- ## File Mapping This bundle consists of: `L1-474.md`, `L1-474.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-474.md` | Source of truth — edit this | Human or LLM | | `L1-474.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 `L1-474`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-474-001 Dissipative Particle Dynamics (DPD) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-474",
  "chain_block": 41555300,
  "chain_hash": "0x96b77244071dd1abca8a38062d1efddb0da96f3ad29906f1cabd58a72de176c8",
  "chain_tx_hash": "0x1c6321201c1aaee6b13ca6a100299302ca249a7350c06e5e31d318b0a32b8f68",
  "domain": "Polymer Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "structure_factor_RMSE",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "structure_factor_RMSE",
    "regime": "Well-posed forward; inverse (parameter recovery from g(r) / S(q)) is ill-conditioned due to near-degenerate parameter combinations (a_ij vs rho_bead trade-off).",
    "secondary": "g_r_integrated_L1"
  },
  "physics_fingerprint": {
    "L_DAG": 4.2,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Polymer Physics",
    "integration_axis": "time",
    "noise_model": "thermal_langevin",
    "primitives": [
      "F.conservative",
      "F.dissipative",
      "F.random",
      "D.time.symplectic",
      "O.structural"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "mesoscale_coarse_grained_dynamics",
    "solution_space": "3D_coarse_grained_trajectory",
    "sub_domain": "Mesoscale soft-matter dynamics",
    "title": "Dissipative Particle Dynamics (DPD)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "dpd_forward"
    ],
    "allowed_omega_dimensions": [
      "N_beads",
      "rho_bead",
      "r_c",
      "a_ij_AB",
      "a_ij_AA",
      "gamma",
      "dt",
      "T_reduced",
      "N_steps"
    ],
    "allowed_problem_classes": [
      "dpd_parameter_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "S(q) RMSE \u003c= 0.02",
      "forward_operator": "dpd_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_beads": 10000,
        "N_steps": 200000,
        "T_reduced": 1.0,
        "a_ij_AA": 15.0,
        "a_ij_AB": 25.0,
        "dt": 0.04,
        "gamma": 4.5,
        "r_c": 1.0,
        "rho_bead": 3.0
      },
      "problem_class": "dpd_parameter_inversion"
    },
    "epsilon_bounds": {
      "structure_factor_RMSE": [
        0.005,
        0.15
      ]
    },
    "omega_bounds": {
      "N_beads": [
        1000,
        200000
      ],
      "N_steps": [
        20000,
        500000
      ],
      "T_reduced": [
        0.5,
        1.5
      ],
      "a_ij_AA": [
        10.0,
        30.0
      ],
      "a_ij_AB": [
        15.0,
        60.0
      ],
      "dt": [
        0.01,
        0.05
      ],
      "gamma": [
        1.0,
        10.0
      ],
      "r_c": [
        0.8,
        1.5
      ],
      "rho_bead": [
        1.0,
        6.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Mesoscale soft-matter dynamics",
  "title": "Dissipative Particle Dynamics (DPD)"
}

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