horse shoe mapmixing device Scnfeld F Hessel V

horse shoe mapを利用したmixing device Scönfeld, F. , Hessel, V. and Hofmann, C. , An optimised splitand reconbine micro-mixer with uniform ‘chaotioc’ mixing, Lab Chip 4(2000), 65 -69.

split-and-recombine (SAR) のmixing の様子

Stremler-Chenの実験 Stremler, M. , Chen, J. , Generating topological chaos in lid-driven cavity flow, PHYSICS OF FLUID 19 (2007), 103602 -1— 103602 -6

Kin-Sakajoのcomputer simulation Kin, E. , Sakajo, T. , Efficient topological chaos embeded in the blinking vortex system, Chaos 15(2005), 023111 -1— 023111 -9

p. A type の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.

Thiffeault-FinnのBSD Thiffeault, J. L. , Finn, M. D. , Topology, Braids, and Mixing in Fluids, Math, Phys. and Eng. Sci. 364 (2006), 3251 -3266

hypotrochoid curve

hypotrochoid curve を利用したBSD

Example

Example

0 bservation: If it is reducible, lk( ) = lk( for any : inside tube : outside tube ).

Table of Linking number 1 1 0 1 1 1 0 0 0 1 lk( )= ( ∈｛ 1, 2, 3, 4｝) lk( )= 0 （ ∈｛a, b, c, d｝）

PHYSICAL REVIEW E 73 Topological mixing with ghost rods Gouillart, Thiffeault and Finn

ghost rods

PHYSICS OF FLUID 19 Gnerating topological chaos in lid-driven cavity flow Stremler, Chen

lid-driven cavity flow