Pull (cooperative reptation)

Keyword:

MOVE_PULL

Move code:

11

Status:

stable

How it works

The pull move is a cooperative, local reptation of a sub-segment of a chain. An interior bead is displaced to a nearby empty site, and the beads following it are “pulled” along one after another - each taking the site just vacated by its predecessor - until connectivity is restored. The perturbation propagates bead-by-bead along the chain rather than moving it rigidly, so it needs almost no free volume: it can rearrange chains in dense/condensed systems where rigid translate/rotate moves simply clash. Chain identity and bonding are preserved throughout. Requires chains of length \(\ge 3\).

Like the slither, a pull step is a megamove: every eligible chain is pulled PULL_SUBSTEPS times, each with its own accept/reject. The two chain termini are not displaced by a pull, so it is best paired with the crankshaft/slither, which do move the ends.

Why detailed balance holds

The cascade starts by moving the chosen bead to a site drawn uniformly from a first-target set \(S\) of valid empty sites; once that first step is fixed, the rest of the cascade is determined. The size of this set differs between the forward move and its reverse, \(n_\text{fwd}=|S_\text{fwd}|\) and \(n_\text{rev}=|S_\text{rev}|\), so as with reptation the proposal is asymmetric and the move uses the Metropolis-Hastings acceptance

\[A(x\to y) = \min\!\left(1,\; \frac{n_\text{rev}}{n_\text{fwd}}\; e^{-\Delta E / T}\right).\]

The cascade is constructed so that the reverse move retraces exactly the forward path (the “didn’t-stop” conditions of the forward cascade force the reverse to stop at the same place), which is what guarantees reversibility and makes the multiplicity ratio the correct Hastings factor. The energy change uses the same telescoping per-bead decomposition as the slither. The construction is verified by the detailed-balance test suite.

Configuration

MOVE_PULLfloat

Probability of selecting a pull megamove (all MOVE_* must sum to 1.0).

PULL_SUBSTEPSint

Number of pull moves applied to each (length \(\ge 3\)) chain per megamove (default 10).

Pull is aimed squarely at dense-phase rearrangement; for moving whole correlated groups of chains see Virtual-Move Monte Carlo (VMMC).

Along with the crankshaft and slither, pull has a multi-threaded kernel: see PARALLELIZE. As a whole-chain move it uses the same chain-level block decomposition as the slither (a chain parallelizes only if all its beads fit in a block interior); in addition its cooperative-reptation target search is restricted to the block interior so the Metropolis-Hastings multiplicity ratio stays self-consistent.