Dissipative Particle Dynamics (DPD) L1-474

Polymer PhysicsMesoscale soft-matter dynamicsδ=5 · challengingL_DAG = 4.2📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

d r_{i} / d t = v_{i}; m \cdot d v_{i} / d t = j! = i \sum [F_{C} (r_{i} j) + F_{D} (r_{i} j, v_{i} j) + F_{R} (r_{i} j)]; σ^{2} = 2 \cdot g amma \cdot k_{B} \cdot T

Groot-Warren DPD: coarse-grained beads evolve under conservative (soft-repulsive), dissipative, and random pairwise forces; fluctuation-dissipation links gamma and sigma to k_B T.

L-DAG

F.conservative -> F.dissipative -> F.random -> D.time.symplectic -> O.structural

F.conservativeF.dissipativeF.randomD.time.symplecticO.structural

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 400

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).

Solvability C

Solver class:: Velocity-Verlet + Lowe-Andersen thermostat; parameter inversion via Bayesian optimization or ensemble-averaged gradient-matching
Convergence rate q:: 2
Complexity:: O(N_beads * N_steps) per sweep with linked-cell neighbor lists

Specs (0)

No L2 specs registered yet for this principle.