位相的カオスを利用した 流体のかき混ぜ
DESCRIPTION
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. Sc ö nfeld, 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. - PowerPoint PPT PresentationTRANSCRIPT
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