  The non-linear evolution of one-dimensional perturbations in a
three-dimensional expanding Universe is considered. A general Lagrangian scheme
is derived, and compared to two previously introduced approximate models. These
models are simulated with heap-based event-driven numerical procedure, that
allows for the study of large systems, averaged over many realizations of
random initial conditions. One of the models is shown to be qualitatively, and,
in some respects, concerning mass aggregation, quantitatively similar to the
adhesion model.
