41 research outputs found
Mixing and Un-mixing by Incompressible Flows
We consider the questions of efficient mixing and un-mixing by incompressible
flows which satisfy periodic, no-flow, or no-slip boundary conditions on a
square. Under the uniform-in-time constraint we
show that any function can be mixed to scale in time
, with for and
for . Known lower bounds show
that this rate is optimal for . We also show that
any set which is mixed to scale but not much more than that can be
un-mixed to a rectangle of the same area (up to a small error) in time
. Both results hold with scale-independent finite
times if the constraint on the flow is changed to with some . The constants in all our results are
independent of the mixed functions and sets.Comment: 37 pages, 5 figure