Cluster translate

Keyword:

MOVE_CLUSTER_TRANSLATE

Move code:

7

Status:

core

How it works

A cluster move operates on a whole connected cluster of chains at once. PIMMS first identifies the cluster: starting from the selected chain it grows the set of all chains connected to it through contacts (a connected component). The entire cluster is then translated as a rigid body by a random displacement, exactly like a single-chain translation but applied to every chain in the cluster together.

This lets a whole aggregate or droplet diffuse as a unit - motion that no single-chain move can produce. It is comparatively expensive (identifying and moving the cluster, and checking for clashes against the rest of the system), so it is normally used at a small fraction of the move budget.

Why detailed balance holds

Two ingredients make the move balanced:

  1. Symmetric displacement. As for Chain translate, a shift by \(+v\) and the reverse \(-v\) are equally likely.

  2. Cluster preservation. After the rigid move PIMMS re-identifies the connected component and requires it to be the same set of chains. This guarantees that the reverse move would select and translate the identical cluster, keeping the proposal symmetric (\(g(x\to y)=g(y\to x)\)) and the move reversible.

Because the cluster moves rigidly, all intra-cluster contacts are unchanged; only the cluster-environment interface contributes to \(\Delta E\). The move is accepted with the plain Metropolis criterion \(A = \min(1, e^{-\Delta E/T})\) on that interfacial energy change, satisfying detailed balance (see the primer).

Configuration

MOVE_CLUSTER_TRANSLATEfloat

Probability of selecting a cluster-translation step (all MOVE_* must sum to 1.0). Keep small (e.g. 0.01-0.05); these moves are expensive.

Note

The cluster here is the geometric connected component, so in a single fully-connected droplet the “cluster” is the entire condensate and the move simply diffuses it bodily. To rearrange chains within a dense phase, use the energy-gradient collective move Virtual-Move Monte Carlo (VMMC), which recruits and moves sub-clusters.