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

21, ll

il

ill ,2ill ,1

c

1 1 1 1

0 1 1 1

0 0 1 1

0 0 0 1

ji,

Table of Linking number

lk( 　　 ) = 　　 ( 　∈｛ 1, 2, 3, 4 ｝ )

lk( 　　 ) = 0 （ 　　 ∈｛ a, b, c, d ｝）

yx,

al bl cl dl

1l

2l

3l

4l

ji ll ,

yx ll ,

3

実験

PHYSICAL REVIEW E73

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