# ⚛  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`

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## 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._