L1 ⚛ L1-330 ⊙ Testnet

Discrete Dislocation Dynamics

Materials Science · Mesoscale plasticity

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⬇ L1-330.md

# ⚛ L1 Principle — Discrete Dislocation Dynamics **ID:** `L1-330` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Mesoscale plasticity* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** dislocation line configurations > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554127 --- ## 🧠 1. Introduction **Discrete Dislocation Dynamics** is a **nonlinear inverse problem** whose unknown lives in **dislocation line configurations** space, within the **Mesoscale plasticity** sub-domain of **Materials Science**. Measurements consist of none via a **bulk mechanical test** sensing mechanism. The forward operator applies, in order: E · elastic field operator; E · peach koehler operator; time evolution of the state; O · stress strain operator. Observations are corrupted by additive Gaussian noise. Well-posed locally; chaotic dynamics in bulk; inversion poorly conditioned due to dense dislocation interactions. ## ⚙ 2. Forward Model Physical chain: **x** → E · elastic field → E · peach koehler → Time derivative → O · stress strain → **y** (detector). ``` y = `O.stress_strain` ∂_t `E.peach_koehler` `E.elastic_field` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.elastic_field` | E · elastic field operator | | `E.peach_koehler` | E · peach koehler operator | | `D.time` | Time evolution of the state | | `O.stress_strain` | O · stress strain operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Mesoscale plasticity | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | dislocation_line_configurations | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Well-posed locally; chaotic dynamics in bulk; inversion poorly conditioned due to dense dislocation interactions. | Metric | Value | |---|---| | Metric | stress_strain_L2_error_MPa | | Secondary | dislocation_density_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `dislocation_dynamics` · **Forward operator:** `ddd_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 300 | | N nodes | — | 10000 | | Rho 0 m2 | — | 1e+12 | | Volume um3 | — | 1 | | Strain rate | — | 0.001 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 4 – 2000 | | N nodes | — | 1000 – 1000000 | | Rho 0 m2 | — | 1000000000.0 – 1000000000000000.0 | | Volume um3 | — | 0.001 – 1000 | | Strain rate | — | 1e-06 – 1000.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** stress-strain L2 <= 5 MPa | Metric | Range | |---|---| | Stress strain l2 error mpa | 1.0 – 100.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **stress_strain_L2_error_MPa**, with κ = `700` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x90cafee1b6bfa583a5123222f6b61bbe112d8b03ebe7d1aea6b3810faabf1cc7` - **Chain tx hash:** `0xf29f34fe8fa0e653dba0c75daee829e9716cc196b0a6495241cb5429b108a435` - **Chain block:** `41554127` --- ## File Mapping This bundle consists of: `L1-330.md`, `L1-330.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-330.md` | Source of truth — edit this | Human or LLM | | `L1-330.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 `L1-330`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-330.md).
Regenerate L1-330.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-330-001 Discrete Dislocation Dynamics Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554127,
  "chain_hash": "0x90cafee1b6bfa583a5123222f6b61bbe112d8b03ebe7d1aea6b3810faabf1cc7",
  "chain_tx_hash": "0xf29f34fe8fa0e653dba0c75daee829e9716cc196b0a6495241cb5429b108a435",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 700,
    "metric": "stress_strain_L2_error_MPa",
    "type": "epsilon_fn"
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      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "stress_strain_L2_error_MPa",
    "regime": "Well-posed locally; chaotic dynamics in bulk; inversion poorly conditioned due to dense dislocation interactions.",
    "secondary": "dislocation_density_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Materials Science",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "E.elastic_field",
      "E.peach_koehler",
      "D.time",
      "O.stress_strain"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "bulk_mechanical_test",
    "solution_space": "dislocation_line_configurations",
    "sub_domain": "Mesoscale plasticity",
    "title": "Discrete Dislocation Dynamics"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ddd_forward"
    ],
    "allowed_omega_dimensions": [
      "volume_um3",
      "rho_0_m2",
      "strain_rate",
      "T_K",
      "N_nodes"
    ],
    "allowed_problem_classes": [
      "dislocation_dynamics"
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    "center_spec": {
      "epsilon_fn_center": "stress-strain L2 \u003c= 5 MPa",
      "forward_operator": "ddd_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_nodes": 10000,
        "T_K": 300,
        "rho_0_m2": 1000000000000.0,
        "strain_rate": 0.001,
        "volume_um3": 1.0
      },
      "problem_class": "dislocation_dynamics"
    },
    "epsilon_bounds": {
      "stress_strain_L2_error_MPa": [
        1.0,
        100.0
      ]
    },
    "omega_bounds": {
      "N_nodes": [
        1000,
        1000000
      ],
      "T_K": [
        4,
        2000
      ],
      "rho_0_m2": [
        1000000000.0,
        1000000000000000.0
      ],
      "strain_rate": [
        1e-06,
        1000.0
      ],
      "volume_um3": [
        0.001,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Mesoscale plasticity",
  "title": "Discrete Dislocation Dynamics"
}

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