Open versus closed systems
This protocol is extracted from research article:
How crystals form: A theory of nucleation pathways
Sci Adv, Apr 5, 2019; DOI: 10.1126/sciadv.aav7399

Physically, nucleation of a dense phase from a weak phase is very different in finite volumes for the cases of fixed and variable numbers of particles because, in the former case, the ambient density can drop substantially as the material is incorporated into the dense phase. The present approach can be applied to either case. The deterministic dynamics (Eq. 5) conserves particle number except at the boundary, where the behavior depends on the applied boundary conditions. In general, the interpolation step may or may not preserve particle number depending on the implementation used, but here, to be applicable to both open and closed systems, a conservative interpolation scheme was used. In this study, attention has been restricted to the case of an open system (at fixed chemical potential) as this is the more generic case (the results for finite systems vary according to their volume). In principle, the open system—even with a finite computational cell—should give results close to what one would obtain for an infinite system (for which the fixed/variable particle number distinction becomes irrelevant). Technical details can be found in the Supplementary Text.

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