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Many problems in materials science and biology involve particles interactingwith strong, short-ranged bonds, that can break and form on experimentaltimescales. Treating such bonds as constraints can significantly speed upsampling their equilibrium distribution, and there are several methods tosample probability distributions subject to fixed constraints. We introduce aMonte Carlo method to handle the case when constraints can break and form. Moregenerally, the method samples a probability distribution on a stratification: acollection of manifolds of different dimensions, where the lower-dimensionalmanifolds lie on the boundaries of the higher-dimensional manifolds. We showseveral applications of the method in polymer physics, self-assembly ofcolloids, and volume calculation in high dimensions.

Simulating sticky particles: A Monte Carlo method to sample a stratification