# ⚛  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._