메뉴 건너뛰기




Volumn 364, Issue 1849, 2006, Pages 3251-3266

Topology, braids and mixing in fluids

Author keywords

Braids; Chaotic mixing; Topological chaos

Indexed keywords


EID: 33845667563     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2006.1899     Document Type: Article
Times cited : (63)

References (35)
  • 1
    • 0021443337 scopus 로고
    • Stirring by chaotic advection
    • (doi:10.1017/S0022112084001233)
    • Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1-21. (doi:10.1017/S0022112084001233)
    • (1984) J. Fluid Mech. , vol.143 , pp. 1-21
    • Aref, H.1
  • 2
    • 0022533713 scopus 로고
    • Chaotic advection in a Stokes flow
    • (doi:10.1063/1.865828)
    • Aref, H. & Balachandar, S. 1986 Chaotic advection in a Stokes flow. Phys. Fluids 29, 3515-3521. (doi:10.1063/1.865828)
    • (1986) Phys. Fluids , vol.29 , pp. 3515-3521
    • Aref, H.1    Balachandar, S.2
  • 4
    • 0001354876 scopus 로고
    • Train-tracks for surface homeomorphisms
    • (doi:10.1016/0040-9383(94)E0009-9)
    • Bestvina, M. & Handel, M. 1995 Train-tracks for surface homeomorphisms. Topology 34, 109-140. (doi:10.1016/0040-9383(94)E0009-9)
    • (1995) Topology , vol.34 , pp. 109-140
    • Bestvina, M.1    Handel, M.2
  • 6
    • 0002371966 scopus 로고
    • Entropy and the fundamental group
    • Lecture Notes in Mathematics, 668, New York, NY: Springer
    • Bowen, R. 1978 Entropy and the fundamental group. In Structure of attractors. Lecture Notes in Mathematics, 668, pp. 21-29. New York, NY: Springer.
    • (1978) Structure of Attractors , pp. 21-29
    • Bowen, R.1
  • 7
    • 0001482567 scopus 로고
    • Topological methods in surface dynamics
    • (doi:10.1016/0166-8641(94)00147-2)
    • Boyland, P. L. 1994 Topological methods in surface dynamics. Topol. Appl. 58, 223-298. (doi:10.1016/0166-8641(94)00147-2)
    • (1994) Topol. Appl. , vol.58 , pp. 223-298
    • Boyland, P.L.1
  • 8
    • 23844516823 scopus 로고    scopus 로고
    • Dynamics of two-dimensional time-periodic Euler fluid flows
    • (doi:10.1016/j.topol.2004.08.017)
    • Boyland, P. L. 2005 Dynamics of two-dimensional time-periodic Euler fluid flows. Topol. Appl. 152, 87-106. (doi:10.1016/j.topol.2004.08.017)
    • (2005) Topol. Appl. , vol.152 , pp. 87-106
    • Boyland, P.L.1
  • 9
    • 0033946678 scopus 로고    scopus 로고
    • Topological fluid mechanics of stirring
    • (doi:10.1017/S0022112099007107)
    • Boyland, P. L., Aref, H. & Stremler, M. A. 2000 Topological fluid mechanics of stirring. J. Fluid Mech. 403, 277-304. (doi:10.1017/ S0022112099007107)
    • (2000) J. Fluid Mech. , vol.403 , pp. 277-304
    • Boyland, P.L.1    Aref, H.2    Stremler, M.A.3
  • 10
    • 0037437759 scopus 로고    scopus 로고
    • Topological fluid mechanics of point vortex motions
    • (doi:10.1016/S0167-2789(02)00692-9)
    • Boyland, P. L., Stremler, M. A. & Aref, H. 2003 Topological fluid mechanics of point vortex motions. Physica D 175, 69-95. (doi:10.1016/S0167- 2789(02)00692-9)
    • (2003) Physica D , vol.175 , pp. 69-95
    • Boyland, P.L.1    Stremler, M.A.2    Aref, H.3
  • 11
    • 0023045012 scopus 로고
    • Experimental study of Lagrangian turbulence in a Stokes flow
    • Chaiken, J., Chevray, R., Tabor, M. & Tan, Q. M. 1986 Experimental study of Lagrangian turbulence in a Stokes flow. Proc. R. Soc. A 408, 165-174.
    • (1986) Proc. R. Soc. A , vol.408 , pp. 165-174
    • Chaiken, J.1    Chevray, R.2    Tabor, M.3    Tan, Q.M.4
  • 12
    • 0033337185 scopus 로고    scopus 로고
    • Control of mixing in fluid flow: A maximum entropy approach
    • (doi:10.1109/9.793724)
    • D'Alessandro, D., Dahleh, M. & Mezić, I. 1999 Control of mixing in fluid flow: a maximum entropy approach. IEEE Trans. Autom. Control 44, 1852-1863. (doi:10.1109/9.793724)
    • (1999) IEEE Trans. Autom. Control , vol.44 , pp. 1852-1863
    • D'Alessandro, D.1    Dahleh, M.2    Mezić, I.3
  • 13
    • 0036558752 scopus 로고    scopus 로고
    • On a Yang-Baxter map and the Dehornoy ordering
    • (doi:10.1070/RM2002v057n03ABEH000519)
    • Dynnikov, I. A. 2002 On a Yang-Baxter map and the Dehornoy ordering. Russ. Math. Surv. 57, 592-594. (doi:10.1070/RM2002v057n03ABEH000519)
    • (2002) Russ. Math. Surv. , vol.57 , pp. 592-594
    • Dynnikov, I.A.1
  • 14
    • 0002304365 scopus 로고
    • Travaux de Thurston sur les surfaces
    • Fathi, A., Laundenbach, F. & Poenaru, V. 1979 Travaux de Thurston sur les surfaces. Astérisque 66-67, 1-284.
    • (1979) Astérisque , vol.66-67 , pp. 1-284
    • Fathi, A.1    Laundenbach, F.2    Poenaru, V.3
  • 16
    • 0242594648 scopus 로고    scopus 로고
    • Topological chaos in inviscid and viscous mixers
    • (doi:10.1017/S0022112003005858)
    • Finn, M. D., Cox, S. M. & Byrne, H. M. 2003a Topological chaos in inviscid and viscous mixers. J. Fluid Mech. 493, 345-361. (doi:10.1017/ S0022112003005858)
    • (2003) J. Fluid Mech. , vol.493 , pp. 345-361
    • Finn, M.D.1    Cox, S.M.2    Byrne, H.M.3
  • 17
    • 0344468066 scopus 로고    scopus 로고
    • Chaotic advection in a braided pipe mixer
    • (doi:10.1063/1.1616555)
    • Finn, M. D., Cox, S. M. & Byrne, H. M. 2003b Chaotic advection in a braided pipe mixer. Phys. Fluids 15, L77-L80. (doi:10.1063/1.1616555)
    • (2003) Phys. Fluids , vol.15
    • Finn, M.D.1    Cox, S.M.2    Byrne, H.M.3
  • 18
    • 1342328975 scopus 로고    scopus 로고
    • Mixing measures for a two-dimensional chaotic Stokes flow
    • (doi:10.1023/B:ENGI.0000011930.55539.69)
    • Finn, M. D., Cox, S. M. & Byrne, H. M. 2004 Mixing measures for a two-dimensional chaotic Stokes flow. J. Eng. Math. 48, 129-155. (doi:10.1023/B:ENGI.0000011930.55539.69)
    • (2004) J. Eng. Math. , vol.48 , pp. 129-155
    • Finn, M.D.1    Cox, S.M.2    Byrne, H.M.3
  • 19
    • 33747769246 scopus 로고    scopus 로고
    • Topological chaos in spatially periodic mixers
    • (doi:10.1016/j.physd.2006.07.018)
    • Finn, M. D., Thiffeault, J.-L. & Gouillart, E. 2005 Topological chaos in spatially periodic mixers. Physica D 221, 92-100. (doi:10.1016/j.physd.2006. 07.018)
    • (2005) Physica D , vol.221 , pp. 92-100
    • Finn, M.D.1    Thiffeault, J.-L.2    Gouillart, E.3
  • 21
    • 0041035489 scopus 로고    scopus 로고
    • Dynamical cocycles with values in the Artin braid group
    • (doi:10.1017/S0143385799130207)
    • Gambaudo, J.-M. & Pécou, E. E. 1999 Dynamical cocycles with values in the Artin braid group. Ergod. Theory Dyn. Syst. 19, 627-641. (doi:10.1017/S0143385799130207)
    • (1999) Ergod. Theory Dyn. Syst. , vol.19 , pp. 627-641
    • Gambaudo, J.-M.1    Pécou, E.E.2
  • 22
    • 85020772615 scopus 로고    scopus 로고
    • Knots and links
    • Lecture Notes in Mathematics, no. 1654. Berlin, Germany: Springer
    • Ghrist, R. W., Holmes, P. J., Sullivan, M. C.1997 Knots and links. In Three-dimensional flows. Lecture Notes in Mathematics, no. 1654. Berlin, Germany: Springer.
    • (1997) Three-dimensional Flows
    • Ghrist, R.W.1    Holmes, P.J.2    Sullivan, M.C.3
  • 23
    • 33645152009 scopus 로고    scopus 로고
    • Topological mixing with ghost rods
    • (doi:10.1103/PhysRevE.73.036311)
    • Gouillart, E., Finn, M. D. & Thiffeault, J.-L. 2006 Topological mixing with ghost rods. Phys. Rev. E 73, 036311. (doi:10.1103/PhysRevE.73. 036311)
    • (2006) Phys. Rev. E , vol.73 , pp. 036311
    • Gouillart, E.1    Finn, M.D.2    Thiffeault, J.-L.3
  • 25
    • 0001173010 scopus 로고
    • Global shadowing of pseudo-Anosov homeomorphisms
    • Handel, M. 1985 Global shadowing of pseudo-Anosov homeomorphisms. Ergod. Theory Dyn. Syst. 5, 373-377.
    • (1985) Ergod. Theory Dyn. Syst. , vol.5 , pp. 373-377
    • Handel, M.1
  • 26
    • 0000088090 scopus 로고
    • Sur la topologie des lignes de courant dans un cas particulier
    • Hénon, M. 1966 Sur la topologie des lignes de courant dans un cas particulier. C.R. Acad. Sci. Paris 262, 312-314.
    • (1966) C.R. Acad. Sci. Paris , vol.262 , pp. 312-314
    • Hénon, M.1
  • 27
    • 0001742803 scopus 로고
    • Entropie topologique et représentation de Burau
    • Kolev, B. 1989 Entropie topologique et représentation de Burau. C.R. Acad. Sci. Sér. I 309, 835-838.
    • (1989) C.R. Acad. Sci. Sér. I , vol.309 , pp. 835-838
    • Kolev, B.1
  • 29
    • 21144481878 scopus 로고
    • On the estimation of topological entropy
    • (doi:10.1007/BF01048189)
    • Newhouse, S. & Pignataro, T. 1993 On the estimation of topological entropy. J. Stat. Phys. 72, 1331-1351. (doi:10.1007/BF01048189)
    • (1993) J. Stat. Phys. , vol.72 , pp. 1331-1351
    • Newhouse, S.1    Pignataro, T.2
  • 30
    • 0000032056 scopus 로고    scopus 로고
    • Microfluidics: Basic issues, applications, and challenges
    • (doi:10.1002/aic.690470602)
    • Stone, H. A. & Kim, S. 2001 Microfluidics: basic issues, applications, and challenges. AIChE J. 47, 1250-1254. (doi:10.1002/aic. 690470602)
    • (2001) AIChE J. , vol.47 , pp. 1250-1254
    • Stone, H.A.1    Kim, S.2
  • 31
    • 18144365857 scopus 로고    scopus 로고
    • Measuring topological chaos
    • (doi:10.1103/PhysRevLett.94.084502)
    • Thiffeault, J.-L. 2005 Measuring topological chaos. Phys. Rev. Lett. 94, 084502. (doi:10.1103/PhysRevLett.94.084502)
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 084502
    • Thiffeault, J.-L.1
  • 33
    • 84968476184 scopus 로고
    • On the geometry and dynamics of diffeomorphisms of surfaces
    • Thurston, W. 1988 On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Am. Math. Soc. 19, 417-431.
    • (1988) Bull. Am. Math. Soc. , vol.19 , pp. 417-431
    • Thurston, W.1
  • 34
    • 1842587988 scopus 로고    scopus 로고
    • Simulation of topological chaos in laminar flows
    • (doi:10.1063/1.1621092)
    • Vikhansky, A. 2004 Simulation of topological chaos in laminar flows. Chaos 14, 14-22. (doi:10.1063/1.1621092)
    • (2004) Chaos , vol.14 , pp. 14-22
    • Vikhansky, A.1
  • 35
    • 0035369682 scopus 로고    scopus 로고
    • Flexible methods for microfluidics
    • Whitesides, G. M. & Stroock, A. D. 2001 Flexible methods for microfluidics. Phys. Today 54, 42-48.
    • (2001) Phys. Today , vol.54 , pp. 42-48
    • Whitesides, G.M.1    Stroock, A.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.