horse shoe map?????mixing device

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horse shoe map?????mixing device
Scönfeld, F., Hessel, V. and Hofmann, C., An
optimised split-and reconbine micro-mixer with
uniform chaotioc mixing, Lab Chip 4(2000),
65-69.
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split-and-recombine (SAR) ?mixing ???
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Stremler-Chen???
Stremler, M., Chen, J., Generating topological
chaos in lid-driven cavity flow, PHYSICS OF FLUID
19 (2007), 103602-1103602-6
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Kin-Sakajo?computer simulation
Kin, E., Sakajo, T., Efficient topological chaos
embeded in the blinking vortex system, Chaos
15(2005), 023111 023111-1023111-9
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pA type ?BSD
Kobayashi T. and Umeda, S, Realizing
pseudo-Anosov egg beaters with simple mechanisms,
Proc. of the Int. Workshop on Knot theory for
Sci. Objects, March(2006), 97-109, 2007.
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Thiffeault-Finn?BSD
Thiffeault,J.L., Finn, M.D., Topology, Braids,
and Mixing in Fluids, Math, Phys. and Eng. Sci.
364 (2006), 3251-3266
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hypotrochoid curve
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hypotrochoid curve ?????BSD
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Example
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Example
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????braid
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0bservation If it is reducible, lk( ) lk(
). for any inside
tube outside tube
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Table of Linking number

1 1 1 1
0 1 1 1
0 0 1 1
0 0 0 1
lk( ) ( ?1, 2, 3, 4) lk( )
0 ( ?a, b, c, d)
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PHYSICAL REVIEW E73 Topological mixing with
ghost rods Gouillart, Thiffeault and Finn
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ghost rods
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PHYSICS OF FLUID 19 Gnerating topological
chaos in lid-driven cavity flow Stremler, Chen
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lid-driven cavity flow