奈良女子大学人間文化研究科 博士課程後期２回 梅田早希 位相的カオスを利用した 流体のかき混ぜ 奈良女子大学人間文化研究科 博士課程後期２回 梅田早希
horse shoe mapを利用した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.
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 023111-1—023111-9
pA 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
対応するbraid
0bservation: If it is reducible, lk( ) = lk( ). for any : inside tube :outside tube
Table of Linking number 1 lk( ) = ( ∈｛1, 2, 3, 4｝) lk( ) = 0 （ ∈｛a, b, c, d｝）
実験
Topological mixing with ghost rods PHYSICAL REVIEW E73 Topological mixing with ghost rods Gouillart, Thiffeault and Finn 1919
ghost rods
Gnerating topological chaos in lid-driven cavity flow PHYSICS OF FLUID 19 Gnerating topological chaos in lid-driven cavity flow Stremler, Chen
lid-driven cavity flow