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Volumn 469, Issue 2156, 2013, Pages

Collective behaviour of large number of vortices in the plane

Author keywords

Dynamical systems; Swarming; Vortex dynamics

Indexed keywords

DYNAMICAL SYSTEMS; EXPERIMENTS;

EID: 84880223127     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2013.0085     Document Type: Article
Times cited : (25)

References (40)
  • 1
    • 0001882383 scopus 로고
    • About integrals of hydrodynamic equations related with vortical motions
    • doi:10.1515/crll.1858.55.25
    • Helmholtz H. 1858 About integrals of hydrodynamic equations related with vortical motions. J. für die reine Angewandte Mathematik 55, 25 pages. (doi:10.1515/crll.1858.55.25)
    • (1858) J. für Die Reine Angewandte Mathematik , vol.55 , pp. 25
    • Helmholtz, H.1
  • 3
    • 0001402296 scopus 로고
    • Observation of stationary vortex arrays in rotating superfluid helium
    • doi:10.1103/PhysRevLett.43.214
    • Yarmchuk E, Gordon M, Packard R. 1979 Observation of stationary vortex arrays in rotating superfluid helium. Phys. Rev. Lett. 43, 214-217. (doi:10.1103/PhysRevLett.43.214)
    • (1979) Phys. Rev. Lett. , vol.43 , pp. 214-217
    • Yarmchuk, E.1    Gordon, M.2    Packard, R.3
  • 4
    • 0035917810 scopus 로고    scopus 로고
    • Observation of vortex lattices in Bose- Einstein condensates
    • doi:10.1126/science.1060182
    • Abo-Shaeer J, Raman C, Vogels J, Ketterle W. 2001 Observation of vortex lattices in Bose- Einstein condensates. Science 292 476-479. (doi:10.1126/science.1060182)
    • (2001) Science , vol.292 , pp. 476-479
    • Abo-Shaeer, J.1    Raman, C.2    Vogels, J.3    Ketterle, W.4
  • 5
    • 77951109519 scopus 로고    scopus 로고
    • Observation of vortex dipoles in an oblate Bose-Einstein condensate
    • doi:10.1103/ PhysRevLett.104.160401
    • Neely T, Samson E, Bradley A, Davis M, Anderson B. 2010 Observation of vortex dipoles in an oblate Bose-Einstein condensate. Phys. Rev. Lett. 104, 160401. (doi:10.1103/ PhysRevLett.104.160401)
    • (2010) Phys. Rev. Lett. , vol.104 , pp. 160401
    • Neely, T.1    Samson, E.2    Bradley, A.3    Davis, M.4    Anderson, B.5
  • 7
    • 0039651826 scopus 로고
    • Relaxation of 2D turbulence to vortex crystals
    • doi:10.1103/PhysRevLett.75.3277
    • Fine K, Cass A, FlynnW, Driscoll C. 1995 Relaxation of 2D turbulence to vortex crystals. Phys. Rev. Lett. 75, 3277-3280. (doi:10.1103/PhysRevLett.75. 3277)
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 3277-3280
    • Fine, K.1    Cass, A.2    Flynn, W.3    Driscoll, C.4
  • 8
    • 0034118640 scopus 로고    scopus 로고
    • Experiments on two-dimensional vortex patterns
    • doi:10.1063/1.870307
    • Durkin D, Fajans J. 2000 Experiments on two-dimensional vortex patterns. Physics Fluids 12, 289-293. (doi:10.1063/1.870307)
    • (2000) Physics Fluids , vol.12 , pp. 289-293
    • Durkin, D.1    Fajans, J.2
  • 9
    • 0035395886 scopus 로고    scopus 로고
    • Dynamic, self-assembled aggregates of magnetized, millimeter-sized objects rotating at the liquid-air interface: Macroscopic, twodimensional classical artificial atoms and molecules
    • doi:10.1103/ PhysRevE.64.011603
    • Grzybowski B, Jiang X, Stone H, Whitesides G. 2001 Dynamic, self-assembled aggregates of magnetized, millimeter-sized objects rotating at the liquid-air interface: macroscopic, twodimensional classical artificial atoms and molecules. Phys. Rev. E 64, 011603. (doi:10.1103/ PhysRevE.64.011603)
    • (2001) Phys. Rev. e , vol.64 , pp. 011603
    • Grzybowski, B.1    Jiang, X.2    Stone, H.3    Whitesides, G.4
  • 10
    • 0037007111 scopus 로고    scopus 로고
    • Dynamics of self assembly of magnetized disks rotating at the liquid-air interface
    • doi:10.1073/ pnas.062036699
    • Grzybowski B, Stone H, Whitesides G. 2002 Dynamics of self assembly of magnetized disks rotating at the liquid-air interface. Proc. Natl Acad. Sci. USA 99, 4147-4151. (doi:10.1073/ pnas.062036699)
    • (2002) Proc. Natl Acad. Sci. USA , vol.99 , pp. 4147-4151
    • Grzybowski, B.1    Stone, H.2    Whitesides, G.3
  • 11
    • 0034729748 scopus 로고    scopus 로고
    • Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid-air interface
    • doi:10.1038/35016528
    • Grzybowski B, Stone H, Whitesides G. 2000 Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid-air interface. Nature 405, 1033-1036. (doi:10.1038/ 35016528)
    • (2000) Nature , vol.405 , pp. 1033-1036
    • Grzybowski, B.1    Stone, H.2    Whitesides, G.3
  • 13
    • 0023208192 scopus 로고
    • Isolated eddy models in geophysics
    • doi:10.1146/annurev.fl.19.010187.002425
    • Flierl G. 1987 Isolated eddy models in geophysics. Annu. Rev. Fluid Mech. 19, 493-530. (doi:10.1146/annurev.fl.19.010187.002425)
    • (1987) Annu. Rev. Fluid Mech. , vol.19 , pp. 493-530
    • Flierl, G.1
  • 14
    • 35949004902 scopus 로고
    • Statistical mechanics, Euler's equation, and Jupiter's red spot
    • doi:10.1103/PhysRevA.45.2328
    • Miller J, Weichman P, Cross M. 1992 Statistical mechanics, Euler's equation, and Jupiter's red spot. Phys. Rev. A 45, 2328-2359. (doi:10.1103/PhysRevA.45.2328)
    • (1992) Phys. Rev. A , vol.45 , pp. 2328-2359
    • Miller, J.1    Weichman, P.2    Cross, M.3
  • 15
    • 0035418486 scopus 로고    scopus 로고
    • Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-like vortices
    • doi:10.1175/1520-0469(2001)058<2196:MPFPAR>2.0.CO;2
    • Kossin J, Schubert W. 2001 Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-like vortices. J. Atmos. Sci. 58, 2196-2209. (doi:10.1175/1520-0469(2001)058<2196:MPFPAR>2.0.CO;2)
    • (2001) J. Atmos. Sci. , vol.58 , pp. 2196-2209
    • Kossin, J.1    Schubert, W.2
  • 16
    • 0033248412 scopus 로고    scopus 로고
    • Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states)
    • doi:10.1103/RevModPhys.71.87
    • Dubin D, OŠneil T. 1999 Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states). Rev. Mod. Phys. 71, 87-172. (doi:10.1103/RevModPhys.71.87)
    • (1999) Rev. Mod. Phys. , vol.71 , pp. 87-172
    • Dubin, D.1    Ošneil, T.2
  • 18
    • 85041150744 scopus 로고
    • Cambridge, UK: Cambridge University Press
    • Saffman P. 1993 Vortex dynamics. Cambridge, UK: Cambridge University Press.
    • (1993) Vortex Dynamics
    • Saffman, P.1
  • 20
    • 84856555535 scopus 로고    scopus 로고
    • Relative equilibria of the (1 + n)-vortex problem
    • doi:10.1007/s00332-011-9108-z
    • Barry A, Hall G, Wayne C. 2012 Relative equilibria of the (1 + n)-vortex problem. J. Nonlinear Sci. 22, 63-83. (doi:10.1007/s00332-011-9108-z)
    • (2012) J. Nonlinear Sci. , vol.22 , pp. 63-83
    • Barry, A.1    Hall, G.2    Wayne, C.3
  • 21
    • 0040773104 scopus 로고
    • Relative equilibria of vortices in two dimensions
    • doi:10.1073/pnas.79.2.716
    • Palmore J. 1982 Relative equilibria of vortices in two dimensions. Proc. Natl Acad. Sci. USA 79, 716-718. (doi:10.1073/pnas.79.2.716)
    • (1982) Proc. Natl Acad. Sci. USA , vol.79 , pp. 716-718
    • Palmore, J.1
  • 22
    • 0011073785 scopus 로고
    • Catalog of two-dimensional vortex patterns
    • Campbell L, Ziff R. 1978 Catalog of two-dimensional vortex patterns. NASA STI/Recon Tech. Rep. 80, 16309.
    • (1978) NASA STI/Recon Tech. Rep. , vol.80 , pp. 16309
    • Campbell, L.1    Ziff, R.2
  • 23
    • 0032560203 scopus 로고    scopus 로고
    • Point vortices exhibit asymmetric equilibria
    • doi:10.1038/33827
    • Aref H, Vainchtein D. 1998 Point vortices exhibit asymmetric equilibria. Nature 392, 769-770. (doi:10.1038/33827)
    • (1998) Nature , vol.392 , pp. 769-770
    • Aref, H.1    Vainchtein, D.2
  • 25
    • 0001005903 scopus 로고
    • Lii. The stability of motion of rectilinear vortices in ring formation
    • Havelock T. 1931 Lii. the stability of motion of rectilinear vortices in ring formation. London, Edinburgh, Dublin Philos. Mag. J. Sci. 11, 617-633.
    • (1931) London, Edinburgh, Dublin Philos. Mag. J. Sci. , vol.11 , pp. 617-633
    • Havelock, T.1
  • 26
    • 0033474942 scopus 로고    scopus 로고
    • Stability of relative equilibria in the problem of n + 1 vortices
    • doi:10.1137/S0036141098302124
    • Cabral H, Schmidt D. 2000 Stability of relative equilibria in the problem of n + 1 vortices. SIAM J. Math. Anal. 31, 231-250. (doi:10.1137/ S0036141098302124)
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 231-250
    • Cabral, H.1    Schmidt, D.2
  • 27
    • 0001431536 scopus 로고    scopus 로고
    • Vortex crystals from 2D Euler flow: Experiment and simulation
    • doi:10.1063/1.869961
    • Schecter D, Dubin D, Fine K, Driscoll C. 1999 Vortex crystals from 2D Euler flow: experiment and simulation. Phys. Fluids 11, 905. (doi:10.1063/1.869961)
    • (1999) Phys. Fluids , vol.11 , pp. 905
    • Schecter, D.1    Dubin, D.2    Fine, K.3    Driscoll, C.4
  • 28
    • 80053259548 scopus 로고    scopus 로고
    • Swarm dynamics and equilibria for a nonlocal aggregation model
    • doi:10.1088/0951-7715/24/10/002
    • Fetecau R, Huang Y, Kolokolnikov T. 2011 Swarm dynamics and equilibria for a nonlocal aggregation model. Nonlinearity 24, 2681. (doi:10.1088/0951-7715/ 24/10/002)
    • (2011) Nonlinearity , vol.24 , pp. 2681
    • Fetecau, R.1    Huang, Y.2    Kolokolnikov, T.3
  • 29
    • 84857862616 scopus 로고    scopus 로고
    • Aggregation via the Newtonian potential and aggregation patches
    • doi:10.1142/S0218202511400057
    • Bertozzi A, Laurent T, Leger F. 2011 Aggregation via the Newtonian potential and aggregation patches. Math. Models Methods Appl. Sci. 22, 114005. (doi:10.1142/S0218202511400057)
    • (2011) Math. Models Methods Appl. Sci. , vol.22 , pp. 114005
    • Bertozzi, A.1    Laurent, T.2    Leger, F.3
  • 30
    • 79955651996 scopus 로고    scopus 로고
    • A primer of swarm equilibria
    • doi:10.1137/100804504
    • Bernoff A, Topaz C. 2011 A primer of swarm equilibria. SIAM J. Appl. Dyn. Syst. 10, 212-250. (doi:10.1137/100804504)
    • (2011) SIAM J. Appl. Dyn. Syst. , vol.10 , pp. 212-250
    • Bernoff, A.1    Topaz, C.2
  • 31
    • 0000006313 scopus 로고    scopus 로고
    • Holtsmark distributions in point-vortex systems
    • doi:10.1103/PhysRevLett.84.650
    • Kuvshinov B, Schep T. 2000 Holtsmark distributions in point-vortex systems. Phys. Rev. Lett. 84, 650-653. (doi:10.1103/PhysRevLett.84.650)
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 650-653
    • Kuvshinov, B.1    Schep, T.2
  • 32
    • 0031122926 scopus 로고    scopus 로고
    • Intrinsic and extrinsic mechanisms of vortex formation in superfluid 3 HE-b
    • doi:10.1007/BF02396838
    • Ruutu V, Parts Ü, Koivuniemi J, Kopnin N, Krusius M. 1997 Intrinsic and extrinsic mechanisms of vortex formation in superfluid 3 HE-b. J. Low Temp. Phys. 107, 93-164. (doi:10.1007/BF02396838)
    • (1997) J. Low Temp. Phys. , vol.107 , pp. 93-164
    • Ruutu, V.1    Parts, Ü.2    Koivuniemi, J.3    Kopnin, N.4    Krusius, M.5
  • 33
    • 0004749149 scopus 로고
    • On the stability of the motion of Saturn's rings (1859)
    • Cambridge, UK: Cambridge University Press
    • Maxwell J. 1890 On the stability of the motion of Saturn's rings (1859). In The scientific papers of James Clerk Maxwell (ed. WD Niven). Cambridge, UK: Cambridge University Press.
    • (1890) The Scientific Papers of James Clerk Maxwell (Ed. WD Niven)
    • Maxwell, J.1
  • 35
    • 0001118153 scopus 로고    scopus 로고
    • Coherent disintegration and stability of vortices in trapped Bose condensates
    • doi:10.1103/PhysRevA.59.1533
    • Pu H, Law C, Eberly J, Bigelow, N. 1999 Coherent disintegration and stability of vortices in trapped Bose condensates. Phys. Rev. A 59, 1533-1537. (doi:10.1103/PhysRevA.59.1533)
    • (1999) Phys. Rev. A , vol.59 , pp. 1533-1537
    • Pu, H.1    Law, C.2    Eberly, J.3    Bigelow, N.4
  • 36
    • 84858171800 scopus 로고    scopus 로고
    • Spectral stability of vortices in two-dimensional Bose-Einstein condensates via the Evans function and Krein signature
    • doi:10.1093/amrx/abr007
    • Kollár R, Pego RL. 2012 Spectral stability of vortices in two-dimensional Bose-Einstein condensates via the Evans function and Krein signature. Appl. Math. Res. Express. 2012, 1-46. (doi:10.1093/amrx/abr007)
    • (2012) Appl. Math. Res. Express. , vol.2012 , pp. 1-46
    • Kollár, R.1    Pego, R.L.2
  • 39
    • 71049182639 scopus 로고    scopus 로고
    • Stability of relative equilibria of three vortices
    • doi:10.1063/1.3216063
    • Aref H. 2009 Stability of relative equilibria of three vortices. Phys. Fluids 21, 094101. (doi:10.1063/1.3216063)
    • (2009) Phys. Fluids , vol.21 , pp. 094101
    • Aref, H.1
  • 40
    • 77949858883 scopus 로고    scopus 로고
    • Dynamics for Ginzburg-Landau vortices under a mixed flow
    • doi:10.1512/iumj.2009.58.3842
    • Kurzke M, Melcher C,Moser R, Spirn D. 2009 Dynamics for Ginzburg-Landau vortices under a mixed flow. Indiana Univ. Math. J. 58, 2597-2622. (doi:10.1512/iumj.2009.58.3842)
    • (2009) Indiana Univ. Math. J. , vol.58 , pp. 2597-2622
    • Kurzke, M.1    Melcher, C.2    Moser, R.3    Spirn, D.4


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