Transients in time-dependent abrasion processes

In unidirectional abrasion processes, such as the erosion of a riverbed by sediment transport, nearly all initial shapes evolve toward the same final form. For an initially elliptical shape, the abrasion process ultimately produces a geometry that preserves its form under further wear. However, it remains an open question through which intermediate shapes this final form is reached and on what timescale. The process is analogous to purely damped dynamical systems, because the key factor is the energy dissipated through collisions during abrasion.

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