de Gennes-Doi-Edwards Reptation Theory L1-476

Polymer PhysicsEntangled melt dynamicsδ=5 · challengingL_DAG = 3.5📋 Stub — not mineable

📋

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.

Read the contribution guide →Open a claim issue →

Forward model E

G (t) = G_{N}^{0} \cdot p \sum p s i_{p} (t) \cdot e x p (- p^{2} t / t a u_{d}) + G_{R} o u se (t); e t a_{0} = in t e g r a l_{0}^{i} n f G (t) d t

Doi-Edwards tube model: each chain reptates through a tube of entanglements with disengagement time tau_d ~ N^3.4; linear viscoelastic response G(t), G'(omega), G''(omega) follows double-reptation with contour-length fluctuations (CLF) and constraint release (CR).

L-DAG

E.doi_edwards_tube -> O.composite_method -> int.rheology -> O.viscoelastic_spectrum

E.doi_edwards_tubeO.composite_methodint.rheologyO.viscoelastic_spectrum

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 300

Well-posed for monodisperse melts; polydisperse inversion is ill-conditioned in the transition zone between Rouse and terminal regimes.

Solvability C

Solver class:: Tikhonov-regularized Laplace inversion (CONTIN, GEX); tube model fits via Marquardt-Levenberg
Convergence rate q:: 2
Complexity:: O(N_modes * N_freq)

Specs (0)

No L2 specs registered yet for this principle.