Acceleration of one-dimensional mixing by discontinuous mappings

Abstract

The paper considers a simple class of models for mixing of a passive tracer into a bulk material that is essentially one dimensional. We examine the relative rates of mixing due to diffusion, stretch and fold operations and permutation of sections of the sample. In particular we show how a combination of diffusion with permutation of sections of the sample (‘chopping and shuffling’) can achieve a faster rate of mixing than pure diffusion. This is done by numerical approximation of eigenvalues of certain linear operators.