메뉴 건너뛰기




Volumn 15, Issue 1, 2014, Pages 1-45

Numerical bifurcation methods and their application to fluid dynamics: Analysis beyond simulation

(15)  Dijkstra, Henk A a   Wubs, Fred W b   Cliffe, Andrew K c   Doedel, Eusebius d   Dragomirescu, Ioana F e   Eckhardt, Bruno f   Gelfgat, Alexander Yu g   Hazel, Andrew L h   Lucarini, Valerio i,j   Salinger, Andy G k   Phipps, Erik T k   Juan, Sanchez Umbria l   Schuttelaars, Henk m   Tuckerman, Laurette S n   Thiele, Uwe o  


Author keywords

High dimensional dynamical systems; Numerical bifurcation analysis; Transitions in fluid flows

Indexed keywords


EID: 84887674187     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.240912.180613a     Document Type: Review
Times cited : (188)

References (141)
  • 1
    • 43049149575 scopus 로고    scopus 로고
    • Spatially localized states in Marangoni convection in binary mixtures
    • Assemat, P., A. Bergeon, and E. Knobloch, 2008: Spatially localized states in Marangoni convection in binary mixtures. FluidDyn. Res., 40, 852-876.
    • (2008) FluidDyn. Res. , vol.40 , pp. 852-876
    • Assemat, P.1    Bergeon, A.2    Knobloch, E.3
  • 2
    • 0030239356 scopus 로고    scopus 로고
    • Floquet stability analysis of the periodic wake of a circular cylinder
    • Barkley, D. and R. D. Henderson, 1996: Floquet stability analysis of the periodic wake of a circular cylinder. J. Fluid Mech., 322, 215-241.
    • (1996) J. Fluid Mech , vol.322 , pp. 215-241
    • Barkley, D.1    Henderson, R.D.2
  • 3
    • 33748286006 scopus 로고    scopus 로고
    • Spatially localized binary-fluid convection
    • DOI 10.1017/S0022112006000759, PII S0022112006000759
    • Batiste, O., E. Knobloch, A. Alonso, and I. Mercader, 2006: Spatially localized binary fluid convection. J. Fluid Mech., 560, 149-158. (Pubitemid 44316965)
    • (2006) Journal of Fluid Mechanics , vol.560 , pp. 149-158
    • Batiste, O.1    Knobloch, E.2    Alonso, A.3    Mercader, I.4
  • 4
    • 79051470181 scopus 로고    scopus 로고
    • Depinning of three-dimensional drops from wettability defects
    • doi:10.1209/0295-5075/86/24006
    • Beltrame, P., P. Hänggi, and U. Thiele, 2009: Depinning of three-dimensional drops from wettability defects. Europhys. Lett., 86, 24 006, doi:10.1209/0295-5075/86/24006.
    • (2009) Europhys. Lett. , vol.86 , pp. 24006
    • Beltrame, P.1    Hänggi, P.2    Thiele, U.3
  • 5
    • 78751496850 scopus 로고    scopus 로고
    • Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates
    • doi:10.1103/PhysRevE.83.016305
    • Beltrame, P., E. Knobloch, P. Hänggi, and U. Thiele, 2011: Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates. Phys. Rev. E, 83, 016 305, doi:10.1103/PhysRevE.83.016305.
    • (2011) Phys. Rev. e , vol.83 , pp. 016305
    • Beltrame, P.1    Knobloch, E.2    Hänggi, P.3    Thiele, U.4
  • 6
    • 77953278361 scopus 로고    scopus 로고
    • Time integration and steady-state continuation method for lubrication equations
    • doi:10.1137/080718619
    • Beltrame, P. and U. Thiele, 2010: Time integration and steady-state continuation method for lubrication equations. SIAM J. Appl. Dyn. Syst., 9, 484-518, doi:10.1137/080718619.
    • (2010) SIAM J. Appl. Dyn. Syst. , vol.9 , pp. 484-518
    • Beltrame, P.1    Thiele, U.2
  • 7
    • 77955918980 scopus 로고    scopus 로고
    • The application of Jacobian-free Newton-Krylov methods to reduce the spin-up time of ocean general circulation models
    • Bernsen, E., H. A. Dijkstra, J. Thies, and F. W. Wubs, 2010: The application of Jacobian-free Newton-Krylov methods to reduce the spin-up time of ocean general circulation models. Journal of Computational Physics, 229 (21), 8167-8179.
    • (2010) Journal of Computational Physics , vol.229 , Issue.21 , pp. 8167-8179
    • Bernsen, E.1    Dijkstra, H.A.2    Thies, J.3    Wubs, F.W.4
  • 8
    • 37849018804 scopus 로고    scopus 로고
    • A method to reduce the spin-up time of ocean models
    • Bernsen, E., H. A. Dijkstra, and F. W. Wubs, 2008: A method to reduce the spin-up time of ocean models. Ocean Modelling, 20 (4), 380-392.
    • (2008) Ocean Modelling , vol.20 , Issue.4 , pp. 380-392
    • Bernsen, E.1    Dijkstra, H.A.2    Wubs, F.W.3
  • 9
    • 68749119345 scopus 로고    scopus 로고
    • Bifurcation analysis of wind-driven flows with MOM4
    • Bernsen, E.,H. A. Dijkstra, and F.W.Wubs, 2009: Bifurcation analysis of wind-driven flows with MOM4. Ocean Modelling, 30 (2-3), 95-105.
    • (2009) Ocean Modelling , vol.30 , Issue.2-3 , pp. 95-105
    • Dijkstra, A.H.B.E.1    Wubs, F.W.2
  • 10
    • 0035939256 scopus 로고    scopus 로고
    • Surface patterns of laterally extended thin liquid films in three dimensions
    • doi:10.1103/PhysRevLett.87.046101
    • Bestehorn, M. and K. Neuffer, 2001: Surface patterns of laterally extended thin liquid films in three dimensions. Phys. Rev. Lett., 87, 046 101, doi:10.1103/PhysRevLett.87.046101.
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 046101
    • Bestehorn, M.1    Neuffer, K.2
  • 11
    • 1142272619 scopus 로고    scopus 로고
    • 3D large scale Marangoni convection in liquid films
    • DOI 10.1140/epjb/e2003-00186-3
    • Bestehorn, M., A. Pototsky, and U. Thiele, 2003: 3D large scale Marangoni convection in liquid films. Eur. Phys. J. B, 33, 457-467. (Pubitemid 41201059)
    • (2003) European Physical Journal B , vol.33 , Issue.4 , pp. 457-467
    • Bestehorn, M.1    Pototsky, A.2    Thiele, U.3
  • 12
    • 0034592313 scopus 로고    scopus 로고
    • Recent developments in Rayleigh-Bénard convection
    • Bodenschatz, E., W. Pesch, and G. Ahlers, 2000: Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech., 32, 709-778.
    • (2000) Annu. Rev. Fluid Mech. , vol.32 , pp. 709-778
    • Bodenschatz, E.1    Pesch, W.2    Ahlers, G.3
  • 14
    • 77950173439 scopus 로고    scopus 로고
    • Extreme multiplicity in cylindrical Rayleigh-Bénard convection. II. Bifurcation diagram and symmetry classification
    • Boronska, K. and L. Tuckerman, 2010: Extreme multiplicity in cylindrical Rayleigh-Bénard convection. II. Bifurcation diagram and symmetry classification. Phys. Rev., E81, 036 321.
    • (2010) Phys. Rev , vol.E81 , pp. 036321
    • Boronska, K.1    Tuckerman, L.2
  • 15
    • 0000977352 scopus 로고
    • Hybrid Krylovmethods for nonlinear systems of equations
    • Brown, P.N. and Y. Saad, 1990: Hybrid Krylovmethods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput., 11 (3), 450-481.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , Issue.3 , pp. 450-481
    • Brown, P.N.1    Saad, Y.2
  • 16
    • 0002741587 scopus 로고
    • Transition to turbulence in thermal convection
    • (eds. H.L. Swinney and J.P. Gollub)
    • Busse, F., 1981: Transition to turbulence in thermal convection. Topics in Applied Physics (eds. H.L. Swinney and J.P. Gollub), 45, 81-137.
    • (1981) Topics in Applied Physics , vol.45 , pp. 81-137
    • Busse, F.1
  • 19
    • 0024610290 scopus 로고
    • Performance of iterative methods for Newtonian and generalized Newtonian flows
    • Carey, G. F., K. Wang, and W. Joubert, 1989: Performance of iterative methods for Newtonian and generalized Newtonian flows. Int. J.Num. Meth. Fluids, 9, 127-150.
    • (1989) Int. J.Num. Meth. Fluids , vol.9 , pp. 127-150
    • Carey, G.F.1    Wang, K.2    Joubert, W.3
  • 21
    • 0000187409 scopus 로고
    • The effect of insulating vertical walls on the onset of motion in a fluid heated from below
    • Catton, I., 1972: The effect of insulating vertical walls on the onset of motion in a fluid heated from below. Int. J. Heat Mass Transfer, 15, 665-672.
    • (1972) Int. J. Heat Mass Transfer , vol.15 , pp. 665-672
    • Catton, I.1
  • 23
    • 0004185917 scopus 로고
    • Wave evolution on a falling film
    • Chang, H.-C., 1994: Wave evolution on a falling film. Ann. Rev. Fluid Mech., 26, 103-136. (Pubitemid 24987419)
    • (1994) Annual Review of Fluid Mechanics , vol.26 , Issue.1 , pp. 103-136
    • Chang, H.-C.1
  • 24
    • 0027473084 scopus 로고
    • Nonlinear evolution of waves on a vertically falling film
    • Chang, H. C., E. A. Demekhin, and D. I. Kopelevich, 1993: Nonlinear evolution of waves on a vertically falling film. J. Fluid Mech., 250, 433-480.
    • (1993) J. Fluid Mech. , vol.250 , pp. 433-480
    • Chang, H.C.1    Demekhin, E.A.2    Kopelevich, D.I.3
  • 26
    • 0031205838 scopus 로고    scopus 로고
    • Tertiary and quaternary solutions for plane Couette flow
    • Clever, R. M. and F. H. Busse, 1997: Tertiary and quaternary solutions for plane Couette flow. J. Fluid Mech., 344, 137-153.
    • (1997) J. Fluid Mech. , vol.344 , pp. 137-153
    • Clever, R.M.1    Busse, F.H.2
  • 29
    • 8744230577 scopus 로고    scopus 로고
    • MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
    • DOI 10.1145/779359.779362
    • Dhooge, A., W. J. F. Govaerts, and Y. A. Kuznetsov, 2003: MatCont: A MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Soft., 29, 141-164. (Pubitemid 40001448)
    • (2003) ACM Transactions on Mathematical Software , vol.29 , Issue.2 , pp. 141-164
    • Dhooge, A.1    Govaerts, W.2    Kuznetsov, Yu.A.3
  • 31
    • 0031428871 scopus 로고    scopus 로고
    • Temporal variability of the wind-driven quasigeostrophic double gyre ocean circulation: Basic bifurcation diagrams
    • Dijkstra, H. A. and C. A. Katsman, 1997: Temporal variability of the wind-driven quasigeostrophic double gyre ocean circulation: Basic bifurcation diagrams. Geophys. Astrophys. Fluid Dyn., 85, 195-232.
    • (1997) Geophys. Astrophys. Fluid Dyn. , vol.85 , pp. 195-232
    • Dijkstra, H.A.1    Katsman, C.A.2
  • 32
    • 2442447496 scopus 로고    scopus 로고
    • Stability of the global ocean circulation: The connection of equilibria within a hierarchy of models
    • DOI 10.1357/002224003322981129
    • Dijkstra, H. A. andW.Weijer, 2003: Stability of the global ocean circulation: The connection of equilibria in a hierarchy of models. J. Mar. Res., 61, 725-743. (Pubitemid 38616838)
    • (2003) Journal of Marine Research , vol.61 , Issue.6 , pp. 725-743
    • Dijkstra, H.A.1    Weijer, W.2
  • 34
    • 0001755071 scopus 로고
    • AUTO:Aprogramfor the automatic bifurcation analysis of autonomous systems
    • Doedel, E. J., 1980: AUTO:Aprogramfor the automatic bifurcation analysis of autonomous systems. Proc. 10th Manitoba Conf. on Numerical Math. and Comp., Vol. 30, 265-274.
    • (1980) Proc. 10th Manitoba Conf. on Numerical Math. and Comp. , vol.30 , pp. 265-274
    • Doedel, E.J.1
  • 35
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems, Part i: Bifurcation in finite dimensions
    • Doedel, E. J., H. B. Keller, and J. P. Kernévez, 1991): Numerical analysis and control of bifurcation problems, Part I: Bifurcation in finite dimensions. Int. J. Bifurcation and Chaos, 1 (3), 493-520.
    • (1991) Int. J. Bifurcation and Chaos , vol.1 , Issue.3 , pp. 493-520
    • Doedel, E.J.1    Keller, H.B.2    Kernévez, J.P.3
  • 37
    • 57149115946 scopus 로고    scopus 로고
    • Relative periodic orbits in transitional pipe flow
    • Duguet, Y., C. C. T. Pringle, and R. R. Kerswell, 2008a: Relative periodic orbits in transitional pipe flow. Phys. Fluids, 20 (11), 114102.
    • (2008) Phys. Fluids , vol.20 , Issue.11 , pp. 114102
    • Duguet, Y.1    Pringle, C.C.T.2    Kerswell, R.R.3
  • 38
    • 84856155800 scopus 로고    scopus 로고
    • Self-sustained localized structures in a boundary layer-flow
    • Duguet, Y., P. Schlatter, D. Henningson, and B. Eckhardt, 2012: Self-sustained localized structures in a boundary layer-flow. Phys. Rev. Lett., 108, 044 501.
    • (2012) Phys. Rev. Lett , vol.108 , pp. 044501
    • Duguet, Y.1    Schlatter, P.2    Henningson, D.3    Eckhardt, B.4
  • 39
    • 54049091638 scopus 로고    scopus 로고
    • Transition in pipe flow: The saddle structure on the boundary of turbulence
    • Duguet, Y., A. P. Willis, and R. R. Kerswell, 2008b: Transition in pipe flow: the saddle structure on the boundary of turbulence. Journal Of Fluid Mechanics, 613, 255-274.
    • (2008) Journal of Fluid Mechanics , vol.613 , pp. 255-274
    • Duguet, Y.1    Willis, A.P.2    Kerswell, R.R.3
  • 43
    • 0347319490 scopus 로고    scopus 로고
    • Traveling waves in pipe flow
    • Faisst, H. and B. Eckhardt, 2003: Traveling waves in pipe flow. Physical Review Letters, 91 (22), 224 502.
    • (2003) Physical Review Letters , vol.91 , Issue.22 , pp. 224502
    • Faisst, H.1    Eckhardt, B.2
  • 44
    • 0005751090 scopus 로고
    • Calculation of thermal explosion limits
    • Frank-Kamenetskii, D. A., 1939: Calculation of thermal explosion limits. Acta. Phys.-Chim USSR, 10, 365.
    • (1939) Acta. Phys.-Chim USSR , vol.10 , pp. 365
    • Frank-Kamenetskii, D.A.1
  • 45
    • 0000808258 scopus 로고    scopus 로고
    • Different modes of Rayleigh-Bénard instability in two- and three dimensional rectangular enclosures
    • Gelfgat, A. Y., 1999: Different modes of Rayleigh-Bénard instability in two- and three dimensional rectangular enclosures. J. Comp. Physics, 156, 300-324.
    • (1999) J. Comp. Physics , vol.156 , pp. 300-324
    • Gelfgat, A.Y.1
  • 47
    • 71049195105 scopus 로고    scopus 로고
    • Equilibrium and traveling-wave solutions of plane Couette flow
    • Gibson, J. F., J.Halcrow, and P. Cvitanovic, 2009: Equilibrium and traveling-wave solutions of plane Couette flow. J. Fluid Mech., 638, 243-266.
    • (2009) J. Fluid Mech. , vol.638 , pp. 243-266
    • Gibson, J.F.1    Halcrow, J.2    Cvitanovic, P.3
  • 49
    • 0004236492 scopus 로고
    • The Johns Hopkins University Press, Baltimore, U.S.A.
    • Golub, G. H. and C. F. Van Loan, 1983: Matrix Computations. The Johns Hopkins University Press, Baltimore, U.S.A.
    • (1983) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 51
    • 0034341944 scopus 로고    scopus 로고
    • The onset of shear flow turbulence
    • Grossmann, S., 2000: The onset of shear flow turbulence. Reviews Of Modern Physics, 72 (2), 603.
    • (2000) Reviews of Modern Physics , vol.72 , Issue.2 , pp. 603
    • Grossmann, S.1
  • 52
    • 0035618412 scopus 로고    scopus 로고
    • Simulation of singularities and instabilities arising in thin film flow
    • Grün, G. and M. Rumpf, 2001: Simulation of singularities and instabilities arising in thin film flow. Euro. Jnl of Applied Mathematics, 12, 293-320.
    • (2001) Euro. Jnl of Applied Mathematics , vol.12 , pp. 293-320
    • Grün, G.1    Rumpf, M.2
  • 54
    • 84855512808 scopus 로고    scopus 로고
    • The Jeffery-Hamel similarity solution and its relation to flow in a diverging channel
    • Haines, P. E., R. E. Hewitt, and A. L.Hazel, 2011: The Jeffery-Hamel similarity solution and its relation to flow in a diverging channel. Journal of Fluid Mechanics, 687, 404-430.
    • (2011) Journal of Fluid Mechanics , vol.687 , pp. 404-430
    • Haines, P.E.1    Hewitt, R.E.2    Hazel, A.L.3
  • 55
    • 80052173365 scopus 로고    scopus 로고
    • Fluid-Structure Interaction, Lecture Notes on Computational Science and Engineering, Editors: M. Schafer und H.-J. Bungartz
    • Heil,M. and A.Hazel, 2006: oomph-lib - An Object-OrientedMulti-Physics Finite-Element Library. Fluid-Structure Interaction, Lecture Notes on Computational Science and Engineering, Editors: M. Schafer und H.-J. Bungartz.
    • (2006) Oomph-lib - An Object-OrientedMulti-Physics Finite-Element Library
    • Heil, M.1    Hazel, A.2
  • 57
    • 13444275919 scopus 로고    scopus 로고
    • Stability and decay rates of non-isotropic attractive bose-einstein condensates
    • Huepe, C., L. S. Tuckerman, S. Métens, and M. E. Brachet, 2003: Stability and Decay Rates of Non-Isotropic Attractive Bose-Einstein Condensates. Phys. Rev.A, 68, 023 609.
    • (2003) Phys. Rev.A , vol.68 , pp. 023609
    • Huepe, C.1    Tuckerman, L.S.2    Métens, S.3    Brachet, M.E.4
  • 59
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and nonlinear eigenvalue problems
    • P. H. Rabinowitz, Ed., Academic Press, New York, U.S.A.
    • Keller, H. B., 1977: Numerical solution of bifurcation and nonlinear eigenvalue problems. Applications of Bifurcation Theory, P. H. Rabinowitz, Ed., Academic Press, New York, U.S.A.
    • (1977) Applications of Bifurcation Theory
    • Keller, H.B.1
  • 60
    • 1842481128 scopus 로고    scopus 로고
    • Steady nonlinear waves in diverging channel flow
    • DOI 10.1017/S0022112003007572
    • Kerswell, R., O. Tutty, and P. Drazin, 2004: Steady nonlinear waves in diverging channel flow. Journal of Fluid Mechanics, 501, 231-250. (Pubitemid 38431417)
    • (2004) Journal of Fluid Mechanics , vol.501 , pp. 231-250
    • Kerswell, R.R.1    Tutty, O.R.2    Drazin, P.G.3
  • 61
    • 0025448183 scopus 로고
    • Back in the saddle again. A computer assisted study of the Kuramoto-Sivashinsky equation
    • Kevrekidis, I. G., B. Nicolaenko, and J. C. Scovel, 1990: Back in the saddle again - a computer-assisted study of the Kuramoto-Sivashinsky equation. SIAM J. Appl. Math., 50, 760-790. (Pubitemid 20696104)
    • (1990) SIAM Journal on Applied Mathematics , vol.50 , Issue.3 , pp. 760-790
    • Kevrekidis, I.G.1    Nicolaenko Basil2    Scovel James, C.3
  • 63
    • 84892220342 scopus 로고    scopus 로고
    • Computing invariant manifolds via the continuation of orbit segments
    • O. H. Krauskopf B. and G.-V. J., Eds., Springer-Verlag, Understanding Complex Systems
    • Krauskopf, B. and H. Osinga, 2007: Computing invariant manifolds via the continuation of orbit segments. Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems, O. H. Krauskopf B. and G.-V. J., Eds., Springer-Verlag, Understanding Complex Systems, 117-154.
    • (2007) Numerical Continuation Methods for Dynamical Systems: Path Following and Boundary Value Problems , pp. 117-154
    • Krauskopf, B.1    Osinga, H.2
  • 68
    • 34250344081 scopus 로고    scopus 로고
    • On the nature and structure of possible three-dimensional steady flows in closed and open paralellepipedic and cubical containers under different heating conditions and driving forces
    • Lappa,M., 2005: On the nature and structure of possible three-dimensional steady flows in closed and open paralellepipedic and cubical containers under different heating conditions and driving forces. Fluid Mechanics and Material Processing, 1, 1-19.
    • (2005) Fluid Mechanics and Material Processing , vol.1 , pp. 1-19
    • Lappa, M.1
  • 69
    • 34447134840 scopus 로고    scopus 로고
    • Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 1: Rayleigh-Bénard systems
    • DOI 10.1016/j.crme.2007.05.003, PII S1631072107000745
    • Lappa, M., 2007: Secondary and oscillatory gravitational instabilities in canonical threedimensional models of crystal growth from the melt. Part 1: Rayleigh-Bénard systems. C.R. Mecanique, 335, 253-260. (Pubitemid 47033990)
    • (2007) Comptes Rendus - Mecanique , vol.335 , Issue.5-6 , pp. 253-260
    • Lappa, M.1
  • 71
  • 72
    • 0001639797 scopus 로고    scopus 로고
    • An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions
    • PII S1064827594277673
    • Lust, K., D. Roose, A. Spence, and A. Champneys, 1998: An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions. SIAM J. Sci. Comput., 19 (4), 1188-1209. (Pubitemid 128616137)
    • (1998) SIAM Journal of Scientific Computing , vol.19 , Issue.4 , pp. 1188-1209
    • Lust, K.1    Roose, D.2    Spence, A.3    Champneys, A.R.4
  • 73
    • 0029151986 scopus 로고
    • Asymmetry and Hopf bifurcation in spherical Couette flow
    • Mamun, C. K. and L. S. Tuckerman, 1995: Asymmetry and Hopf bifurcation in spherical Couette flow. Phys. Fluids, 7, 80-91.
    • (1995) Phys. Fluids , vol.7 , pp. 80-91
    • Mamun, C.K.1    Tuckerman, L.S.2
  • 74
    • 34250644219 scopus 로고    scopus 로고
    • Rayleigh-Bénard convection, thirty years of experimental, theoretical, and modeling work
    • (eds. I. Mutabazi, J.E. Guyin, and J.E.Wesfreid), Springer
    • Manneville, P., 2005: Rayleigh-Bénard convection, thirty years of experimental, theoretical, and modeling work. In: Damics of Spatio-Temporal Cellular Structures. Henri Bénard Centenary Review (eds. I. Mutabazi, J.E. Guyin, and J.E.Wesfreid), Springer.
    • (2005) Damics of Spatio-Temporal Cellular Structures. Henri Bénard Centenary Review
    • Manneville, P.1
  • 75
    • 0030500518 scopus 로고    scopus 로고
    • Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems
    • Meerbergen, K. and D. Roose, 1996: Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems. IMA J. Numer. Anal., 16, 297-346.
    • (1996) IMA J. Numer. Anal. , vol.16 , pp. 297-346
    • Meerbergen, K.1    Roose, D.2
  • 76
    • 11744299855 scopus 로고
    • Shift-invert and Cayley transforms for the detection of rightmost eigenvalues of nonsymmetric matrices
    • Meerbergen, K., A. Spence, and D. Roose, 1994: Shift-invert and Cayley transforms for the detection of rightmost eigenvalues of nonsymmetric matrices. BIT, 34, 409-423.
    • (1994) BIT , vol.34 , pp. 409-423
    • Meerbergen, K.1    Spence, A.2    Roose, D.3
  • 78
    • 0015638564 scopus 로고
    • Free convection and thermal explosion in reactive systems
    • Merzhanov, A. G. and E. A. Shtessel, 1973: Free convection and thermal explosion in reactive systems. Acta Astronautica, 18, 191.
    • (1973) Acta Astronautica , vol.18 , pp. 191
    • Merzhanov, A.G.1    Shtessel, E.A.2
  • 79
    • 13844257436 scopus 로고    scopus 로고
    • Multiple equilibria and stability of the North- Atlantic wind-driven ocean circulation
    • E. Doedel and L. S. Tuckerman, Eds., Springer, The IMA volumes in Mathematics and its applications
    • Molemaker, M. J. and H. A. Dijkstra, 2000: Multiple equilibria and stability of the North- Atlantic wind-driven ocean circulation. Numerical methods for bifurcation problems and large-scale dynamical systems, E. Doedel and L. S. Tuckerman, Eds., Springer, The IMA volumes in Mathematics and its applications, Vol. 119, 35-65.
    • (2000) Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems , vol.119 , pp. 35-65
    • Molemaker, M.J.1    Dijkstra, H.A.2
  • 81
    • 0037930671 scopus 로고    scopus 로고
    • From stationary to complex time-dependent flows at moderate Rayleigh numbers in two-dimensional annular thermal convection
    • DOI 10.1063/1.1565335
    • Net,M., A. Alonso, and J. Sánchez, 2003: Fromstationary to complex time-dependent flows in two-dimensional annular thermal convection atmoderate Rayleigh numbers. Phys. Fluids, 15 (5), 1314-1326. (Pubitemid 36751508)
    • (2003) Physics of Fluids , vol.15 , Issue.5 , pp. 1314-1326
    • Net, M.1    Alonso, A.2    Sanchez, J.3
  • 82
    • 42349111521 scopus 로고    scopus 로고
    • On the onset of low-Prandtl-number convection in rotating spherical shells: Non-slip boundary conditions
    • DOI 10.1017/S002211200800061X, PII S002211200800061X
    • Net, M., F. Garcia, and J. Sánchez, 2008: On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions. J. Fluid Mech., 601, 317-337. (Pubitemid 351552437)
    • (2008) Journal of Fluid Mechanics , vol.601 , pp. 317-337
    • Net, M.1    Garcia, F.2    Sanchez, J.3
  • 83
    • 0037172626 scopus 로고    scopus 로고
    • Absolute-convective instabilities of the Batchelor vortex in the viscous case
    • Olendraru, C. and A. Sellier, 2002: Absolute-convective instabilities of the Batchelor vortex in the viscous case. J. Fluid Mech., 459, 371-396.
    • (2002) J. Fluid Mech. , vol.459 , pp. 371-396
    • Olendraru, C.1    Sellier, A.2
  • 84
    • 0033924131 scopus 로고    scopus 로고
    • Nonlinear dynamics of three-dimensional long-wave Marangoni instability in thin liquid films
    • DOI 10.1063/1.870415
    • Oron, A., 2000a: Nonlinear dynamics of three-dimensional long-wave Marangoni instability in thin liquid films. Phys. Fluids, 12, 1633-1645. (Pubitemid 30454292)
    • (2000) Physics of Fluids , vol.12 , Issue.7 , pp. 1633-1645
    • Oron, A.1
  • 85
    • 0034274342 scopus 로고    scopus 로고
    • Three-dimensional nonlinear dynamics of thin liquid films
    • doi:10.1103/PhysRevLett.85.2108
    • Oron, A., 2000b: Three-dimensional nonlinear dynamics of thin liquid films. Phys. Rev. Lett., 85, 2108-2111, doi:10.1103/PhysRevLett.85.2108.
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 2108-2111
    • Oron, A.1
  • 86
    • 0031480080 scopus 로고    scopus 로고
    • Long-scale evolution of thin liquid films
    • DOI 10.1103/RevModPhys.69.931
    • Oron, A., S. H. Davis, and S. G. Bankoff, 1997: Long-scale evolution of thin liquid films. Rev. Mod. Phys., 69, 931-980, doi:10.1103/RevModPhys.69.931. (Pubitemid 127098261)
    • (1997) Reviews of Modern Physics , vol.69 , Issue.3 , pp. 931-980
    • Oron, A.1    Davis, S.H.2    Bankoff, S.G.3
  • 87
    • 33751428224 scopus 로고    scopus 로고
    • Globalization techniques for Newton-Krylov methods and applications to the fully coupled solution of the Navier-Stokes equations
    • DOI 10.1137/S0036144504443511
    • Pawlowski, R. P., J. N. Shadid, J. P. Simonis, and H. F. Walker, 2006: Globalization techniques for Newton-Krylov methods and applications to the fully coupled solution of the Navier-Stokes equations. SIAMRev., 48, 700-721. (Pubitemid 44817175)
    • (2006) SIAM Review , vol.48 , Issue.4 , pp. 700-721
    • Pawlowski, R.P.1    Shadid, J.N.2    Simonis, J.P.3    Walker, H.F.4
  • 88
    • 7244224903 scopus 로고    scopus 로고
    • Stability analysis of the flow in a cubical cavity heated from below
    • DOI 10.1063/1.1778031
    • Puigjaner, D., J. Herrero, F. Giralt, and C. Simó, 2004: Stability analysis of the flow in a cubical cavity heated from below. Phys. Fluids., 16, 3639-3655. (Pubitemid 39437596)
    • (2004) Physics of Fluids , vol.16 , Issue.10 , pp. 3639-3655
    • Puigjaner, D.1    Herrero, J.2    Giralt, F.3    Simo, C.4
  • 89
    • 79953749683 scopus 로고    scopus 로고
    • Fromsteady solutions to chaotic flows in a Rayleigh-Bénard problem at moderate Rayleigh numbers
    • Puigjaner, D., J.Herrero, C. Simó, and F. Giralt, 2011: Fromsteady solutions to chaotic flows in a Rayleigh-Bénard problem at moderate Rayleigh numbers. Physica D., 240, 920-934.
    • (2011) Physica D. , vol.240 , pp. 920-934
    • Puigjaner, D.1    Herrero, J.2    Simó, C.3    Giralt, F.4
  • 90
    • 0027084284 scopus 로고
    • Multiple equilibria in thermosolutal convection due to saltflux boundary conditions
    • Quon, C. and M. Ghil, 1992: Multiple equilibria in thermosolutal convection due to saltflux boundary conditions. J. Fluid Mech., 245, 449-484.
    • (1992) J. Fluid Mech. , vol.245 , pp. 449-484
    • Quon, C.1    Ghil, M.2
  • 91
    • 0028873610 scopus 로고
    • Multiple equilibria and stable oscillations in thermosolutal convection at small aspect ratio
    • Quon, C. and M. Ghil, 1995: Multiple equilibria and stable oscillations in thermosolutal convection at small aspect ratio. J. Fluid Mech., 291, 33-56.
    • (1995) J. Fluid Mech. , vol.291 , pp. 33-56
    • Quon, C.1    Ghil, M.2
  • 92
    • 49149143501 scopus 로고
    • Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
    • Saad, Y., 1980: Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices. Lin. Alg. & Appl., 34, 269-295.
    • (1980) Lin. Alg. & Appl. , vol.34 , pp. 269-295
    • Saad, Y.1
  • 93
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to thematrix exponential operator
    • Saad, Y., 1992: Analysis of some Krylov subspace approximations to thematrix exponential operator. SIAM J. Numer. Anal., 29 (1), 209-228.
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.1 , pp. 209-228
    • Saad, Y.1
  • 95
    • 0037142933 scopus 로고    scopus 로고
    • A continuation and bifurcation technique for Navier-Stokes flows
    • Sánchez, J., F. Marqués, and J. M. López, 2002: A continuation and bifurcation technique for Navier-Stokes flows. J.Comput. Phys., 180, 78-98.
    • (2002) J.Comput. Phys. , vol.180 , pp. 78-98
    • Sánchez, J.1    Marqués, F.2    López, J.M.3
  • 96
    • 77951605757 scopus 로고    scopus 로고
    • On the multiple shooting continuation of periodic orbits by Newton-Krylov methods
    • Sánchez, J. and M. Net, 2010: On the multiple shooting continuation of periodic orbits by Newton-Krylov methods. Int. J. Bifurcation and Chaos, 20 (1), 1-19.
    • (2010) Int. J. Bifurcation and Chaos , vol.20 , Issue.1 , pp. 1-19
    • Sánchez, J.1    Net, M.2
  • 97
    • 84875852589 scopus 로고    scopus 로고
    • A parallel algorithm for the computation of invariant tori in large-scale dissipative systems
    • Sánchez, J. and M. Net, 2013: A parallel algorithm for the computation of invariant tori in large-scale dissipative systems. Physica D, 252, 22-33.
    • (2013) Physica D , vol.252 , pp. 22-33
    • Sánchez, J.1    Net, M.2
  • 98
    • 13844253435 scopus 로고    scopus 로고
    • Newton-Krylov continuation of periodic orbits for Navier-Stokes flows
    • DOI 10.1016/j.jcp.2004.04.018, PII S0021999104001895
    • Sánchez, J., M. Net, B. García-Archilla, and C. Simó, 2004: Newton-Krylov continuation of periodic orbits for Navier-Stokes flows. J.Comput. Phys., 201 (1), 13-33. (Pubitemid 40256582)
    • (2004) Journal of Computational Physics , vol.201 , Issue.1 , pp. 13-33
    • Sanchez, J.1    Net, M.2    Garcia-Archilla, B.3    Simo, C.4
  • 99
    • 71649115988 scopus 로고    scopus 로고
    • Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems
    • Sánchez, J., M. Net, and C. Simó, 2010: Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems. Physica D, 239, 123-133.
    • (2010) Physica D , vol.239 , pp. 123-133
    • Sánchez, J.1    Net, M.2    Simó, C.3
  • 100
    • 33750572430 scopus 로고    scopus 로고
    • Amplitude equations close to a triple-(+1) bifurcation point of double-struck D sign-symmetric periodic orbits in double-struck O sign(2)-equivariant systems
    • Sánchez, J.,M.Net, and J. Vega, 2006: Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2)-equivariant systems. Discrete and Continuous Dynamical Systems-Series B, 6 (6), 1357-1380. (Pubitemid 44668665)
    • (2006) Discrete and Continuous Dynamical Systems - Series B , vol.6 , Issue.6 , pp. 1357-1380
    • Sanchez, J.1    Net, M.2    Vega, J.M.3
  • 101
    • 0036953286 scopus 로고    scopus 로고
    • Nonlinear evolution of nonuniformly heated falling liquid films
    • DOI 10.1063/1.1515270
    • Scheid, B., A. Oron, P. Colinet, U. Thiele, and J. C. Legros, 2002: Nonlinear evolution of nonuniformly heated falling liquid films. Phys. Fluids, 14, 4130-4151. (Pubitemid 36111362)
    • (2002) Physics of Fluids , vol.14 , Issue.12 , pp. 4130-4151
    • Scheid, B.1    Oron, A.2    Colinet, P.3    Thiele, U.4    Legros, J.C.5
  • 102
    • 33749027789 scopus 로고    scopus 로고
    • Wave patterns in film flows: Modelling and three-dimensional waves
    • DOI 10.1017/S0022112006000978, PII S0022112006000978
    • Scheid, B., C. Ruyer-Quil, and P. Manneville, 2006: Wave patterns in film flows: modelling and three-dimensional waves. J. Fluid Mech., 562, 183-222, doi:10.1017/S0022112006000978. (Pubitemid 44445193)
    • (2006) Journal of Fluid Mechanics , vol.562 , pp. 183-222
    • Scheid, B.1    Ruyer-Quil, C.2    Manneville, P.3
  • 103
    • 17044435482 scopus 로고    scopus 로고
    • Validity domain of the Benney equation including Marangoni effect for closed and open flows
    • doi:10.1017/S0022112004003179
    • Scheid, B., C. Ruyer-Quil, U. Thiele, O. A. Kabov, J. C. Legros, and P. Colinet, 2005: Validity domain of the Benney equation including Marangoni effect for closed and open flows. J. Fluid Mech., 527, 303-335, doi:10.1017/ S0022112004003179.
    • (2005) J. Fluid Mech. , vol.527 , pp. 303-335
    • Scheid, B.1    Ruyer-Quil, C.2    Thiele, U.3    Kabov, O.A.4    Legros, J.C.5    Colinet, P.6
  • 105
    • 34547258707 scopus 로고    scopus 로고
    • Statistical analysis of coherent structures in transitional pipe flow
    • Schneider, T. M., B. Eckhardt, and J. Vollmer, 2007a: Statistical analysis of coherent structures in transitional pipe flow. Physical Review E, 75 (6), 066 313.
    • (2007) Physical Review e , vol.75 , Issue.6 , pp. 066313
    • Schneider, T.M.1    Eckhardt, B.2    Vollmer, J.3
  • 106
    • 34547414467 scopus 로고    scopus 로고
    • Turbulence transition and the edge of chaos in pipe flow
    • Schneider, T.M., B. Eckhardt, and J. A. Yorke, 2007b: Turbulence transition and the edge of chaos in pipe flow. Physical Review Letters, 99 (3), 034 502.
    • (2007) Physical Review Letters , vol.99 , Issue.3 , pp. 034502
    • Schneider, T.M.1    Eckhardt, B.2    Yorke, J.A.3
  • 108
    • 0029735927 scopus 로고    scopus 로고
    • An idealized long-term morphodynamic model of a tidal embayment
    • Schuttelaars, H. and H. De Swart, 1996: An idealized long-term morphodynamic model of a tidal embayment. Eur. J. Mech., B/Fluids, 15 (1), 55-80.
    • (1996) Eur. J. Mech., B/Fluids , vol.15 , Issue.1 , pp. 55-80
    • Schuttelaars, H.1    De Swart, H.2
  • 110
    • 0000104024 scopus 로고    scopus 로고
    • Pattern formation in unstable thin liquid films
    • Sharma, A. and R. Khanna, 1998: Pattern formation in unstable thin liquid films. Phys. Rev. Lett., 81, 3463-3466, doi:10.1103/PhysRevLett.81.3463. (Pubitemid 128631897)
    • (1998) Physical Review Letters , vol.81 , Issue.16 , pp. 3463-3466
    • Sharma, A.1    Khanna, R.2
  • 111
    • 0027641824 scopus 로고
    • Stabilization of unstable procedures: The recursive projection method
    • Shroff, G. M. and H. B. Keller, 1993: Stabilization of unstable procedures: the recursive projection method. SIAM J.Numer. Anal., 30 (4), 1099-1120.
    • (1993) SIAM J.Numer. Anal. , vol.30 , Issue.4 , pp. 1099-1120
    • Shroff, G.M.1    Keller, H.B.2
  • 112
    • 0003053628 scopus 로고
    • Analytical and numerical computation of invariant manifolds
    • C. Benest and C. Froeschlé, Eds., Editions Frontiéres
    • Simó, C., 1990: Analytical and numerical computation of invariant manifolds. Modern methods in celestial mechanics, C. Benest and C. Froeschlé, Eds., Editions Frontiéres, 285-330. Also at http://www.maia.ub.es/dsg/2004/.
    • (1990) Modern Methods in Celestial Mechanics , pp. 285-330
    • Simó, C.1
  • 113
    • 27744566830 scopus 로고    scopus 로고
    • Homoclinic bifurcations in the quasi-geostrophic double-gyre circulation
    • DOI 10.1357/002224005774464210
    • Simonnet, E., M. Ghil, and H. A. Dijkstra, 2005: Homoclinic bifurcations of barotropic QG double-gyre circulation. J. Mar. Res., 63, 931-956. (Pubitemid 41630355)
    • (2005) Journal of Marine Research , vol.63 , Issue.5 , pp. 931-956
    • Simonnet, E.1    Ghil, M.2    Dijkstra, H.3
  • 114
    • 0141637397 scopus 로고    scopus 로고
    • Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part I: Steady solution1
    • DOI 10.1175/1520-0485(2003)33<712:LVISMO>2.0.CO;2
    • Simonnet, E., M. Ghil, K. Ide, R. Temam, and S. Wang, 2003: Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part I: Steady-state solutions. J. Phys. Oceanogr., 33, 712-728. (Pubitemid 37190153)
    • (2003) Journal of Physical Oceanography , vol.33 , Issue.4 , pp. 712-728
    • Simonnet, E.1    Ghil, M.2    Ide, K.3    Temam, R.4    Wang, S.5
  • 115
    • 33646430044 scopus 로고    scopus 로고
    • The edge of chaos in a model for a parallel shear flow
    • Skufca, J., J. A. Yorke, and B. Eckhardt, 2006: The edge of chaos in a model for a parallel shear flow. Phys. Rev. Lett., 96, 174 101.
    • (2006) Phys. Rev. Lett. , vol.96 , Issue.174 , pp. 101
    • Skufca, J.1    Yorke, J.A.2    Eckhardt, B.3
  • 116
    • 0030560293 scopus 로고    scopus 로고
    • A Jacobi-Davidson iteration method for linear eigenvalue problems
    • Sleijpen, G. and H. van der Vorst, 1996: A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAMJ. Matrix Anal. Appl., 17, 401-425.
    • (1996) SIAMJ. Matrix Anal. Appl. , vol.17 , pp. 401-425
    • Sleijpen, G.1    Vorst Der H.Van2
  • 118
    • 0022925935 scopus 로고
    • Bifurcations of two-dimensional channel flows
    • Sobey, I. and P. Drazin, 1986: Bifurcations of two-dimensional channel flows. Journal of Fluid Mechanics, 171, 263-287.
    • (1986) Journal of Fluid Mechanics , vol.171 , pp. 263-287
    • Sobey, I.1    Drazin, P.2
  • 119
    • 84887799568 scopus 로고    scopus 로고
    • Numerical simulation and analysis of swirling flow in the draft tube cone of a Francis turbine
    • Susan-Resiga, R., G. Ciocan, S. Muntean, I. Anton, and F. Avellan, 2006: Numerical simulation and analysis of swirling flow in the draft tube cone of a Francis turbine: 23rdIAHR Symposium-Yokohama., Vol. 15. 1-15 pp.
    • (2006) 23rdIAHR Symposium-Yokohama. , vol.15
    • Susan-Resiga, R.1    Ciocan, G.2    Muntean, S.3    Anton, I.4    Avellan, F.5
  • 121
    • 77954760764 scopus 로고    scopus 로고
    • Modeling equilibrium bed profiles of short tidal embayments. on the effect of the vertical distribution of suspended sediment and the influence of the boundary conditions
    • ter Brake, M. and H. Schuttelaars, 2010: Modeling equilibrium bed profiles of short tidal embayments. on the effect of the vertical distribution of suspended sediment and the influence of the boundary conditions. Ocean Dynamics, 60, 183-204.
    • (2010) Ocean Dynamics , vol.60 , pp. 183-204
    • Ter Brake, M.1    Schuttelaars, H.2
  • 122
    • 77953280282 scopus 로고    scopus 로고
    • Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
    • doi:10.1088/0953- 8984/22/8/084019
    • Thiele, U., 2010: Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth. J. Phys.: Condens. Matter, 22, 084 019, doi:10.1088/0953- 8984/22/8/084019.
    • (2010) J. Phys.: Condens. Matter , vol.22 , pp. 084019
    • Thiele, U.1
  • 123
    • 1142303895 scopus 로고    scopus 로고
    • Thin liquid films on a slightly inclined heated plate
    • Thiele, U. and E. Knobloch, 2004: Thin liquid films on a slightly inclined heated plate. Physica D, 190, 213-248.
    • (2004) Physica D , vol.190 , pp. 213-248
    • Thiele, U.1    Knobloch, E.2
  • 124
    • 33751092571 scopus 로고    scopus 로고
    • Driven drops on heterogeneous substrates: Onset of sliding motion
    • DOI 10.1103/PhysRevLett.97.204501
    • Thiele, U. and E. Knobloch, 2006: Driven drops on heterogeneous substrates: Onset of sliding motion. Phys. Rev. Lett., 97, 204 501, doi:10.1103/PhysRevLett.97.204501. (Pubitemid 44771658)
    • (2006) Physical Review Letters , vol.97 , Issue.20 , pp. 204501
    • Thiele, U.1    Knobloch, E.2
  • 125
    • 84983699905 scopus 로고    scopus 로고
    • Sliding drops in the diffuse interface model coupled to hydrodynamics
    • doi: 10.1103/PhysRevE.64.061601
    • Thiele, U., M. G. Velarde, K. Neuffer, M. Bestehorn, and Y. Pomeau, 2001: Sliding drops in the diffuse interface model coupled to hydrodynamics. Phys. Rev. E, 64, 061 601, doi: 10.1103/PhysRevE.64.061601.
    • (2001) Phys. Rev. e , vol.64 , pp. 61-601
    • Thiele, U.1    Velarde, M.G.2    Neuffer, K.3    Bestehorn, M.4    Pomeau, Y.5
  • 126
    • 70349270560 scopus 로고    scopus 로고
    • Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model
    • Thies, J., F. Wubs, and H. A. Dijkstra, 2009: Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model. Ocean Modelling, 30 (4), 287-297.
    • (2009) Ocean Modelling , vol.30 , Issue.4 , pp. 287-297
    • Thies, J.1    Wubs, F.2    Dijkstra, H.A.3
  • 127
    • 0002699194 scopus 로고
    • The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models
    • Thual, O. and J. C.McWilliams, 1992: The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models. Geophys. Astrophys. Fluid Dyn., 64, 67-95.
    • (1992) Geophys. Astrophys. Fluid Dyn. , vol.64 , pp. 67-95
    • Thual, O.1    Mcwilliams, J.C.2
  • 128
    • 0036502984 scopus 로고    scopus 로고
    • Bifurcation analysis of incompressible flow in a driven cavity by the Newton-Picard method
    • DOI 10.1016/S0377-0427(01)00515-5, PII S0377042701005155, Proceedings of the 9th International Congress on Computational and Applied Mathematics (ICCAM-2000) Leuven, Belgium 17-21 July 2000
    • Tiesinga, G., F.Wubs, and A. Veldman, 2002: Bifurcation analysis of incompressible flow in a driven cavity by the Newton-Picard method. J. Comput. Appl. Math., 140 (1-2), 751-772. (Pubitemid 34299999)
    • (2002) Journal of Computational and Applied Mathematics , vol.140 , Issue.1-2 , pp. 751-772
    • Tiesinga, G.1    Wubs, F.W.2    Veldman, A.E.P.3
  • 129
    • 0038814126 scopus 로고    scopus 로고
    • A periodic-like solution in channel flow
    • DOI 10.1017/S0022112003003768
    • Toh, S. and T. Itano, 2003: A periodic-like solution in channel flow. J. Fluid Mech., 481, 67-76. (Pubitemid 36632351)
    • (2003) Journal of Fluid Mechanics , vol.481 , pp. 67-76
    • Toh, S.1    Itano, T.2
  • 132
    • 84880569410 scopus 로고    scopus 로고
    • A homotopy continuation approach for analysing finite-time singularities in thin liquid films
    • doi: 10.1093/imamat/hxt021, (online)
    • Tseluiko, D., J. Baxter, and U. Thiele, 2013: A homotopy continuation approach for analysing finite-time singularities in thin liquid films. IMA J. Appl. Math., doi: 10.1093/imamat/hxt021, (online).
    • (2013) IMA J. Appl. Math.
    • Tseluiko, D.1    Baxter, J.2    Thiele, U.3
  • 133
    • 0000962877 scopus 로고
    • Global bifurcation to travelling waves in axisymmetric convection
    • Tuckerman, L. and D. Barkley, 1988: Global bifurcation to travelling waves in axisymmetric convection. Phys. Rev. Lett., 61, 408-411.
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 408-411
    • Tuckerman, L.1    Barkley, D.2
  • 134
    • 0000894221 scopus 로고    scopus 로고
    • Bifurcation analysis for timesteppers
    • E. Doedel and L. S. Tuckerman, Eds., Springer-Verlag, IMA Volumes inMathematics and its Applications
    • Tuckerman, L. S. and D. Barkley, 2000: Bifurcation analysis for timesteppers. Numerical Methods for Bifurcation Problems and Large-ScaleDynamical Systems, E. Doedel and L. S. Tuckerman, Eds., Springer-Verlag, IMA Volumes inMathematics and its Applications, Vol. 119, 453-466.
    • (2000) Numerical Methods for Bifurcation Problems and Large-ScaleDynamical Systems , vol.119 , pp. 453-466
    • Tuckerman, L.S.1    Barkley, D.2
  • 136
    • 34547264698 scopus 로고    scopus 로고
    • Recurrent motions within plane Couette turbulence
    • DOI 10.1017/S0022112007005459, PII S0022112007005459
    • Viswanath, D., 2007: Recurrent motions within plane Couette turbulence. Journal Of Fluid Mechanics, 580, 339-358. (Pubitemid 47307547)
    • (2007) Journal of Fluid Mechanics , vol.580 , pp. 339-358
    • Viswanath, D.1
  • 138
    • 0037831083 scopus 로고    scopus 로고
    • Homotopy of exact coherent structures in plane shear flows
    • DOI 10.1063/1.1566753
    • Waleffe, F., 2003: Homotopy of exact coherent structures in plane shear flows. Phys. Fluids, 15, 1517-1534. (Pubitemid 36785200)
    • (2003) Physics of Fluids , vol.15 , Issue.6 , pp. 1517-1534
    • Waleffe, F.1
  • 139
    • 0033293111 scopus 로고    scopus 로고
    • An adaptation of Krylov subspacemethods to path following problems
    • Walker,H. F., 1999: An adaptation of Krylov subspacemethods to path following problems. SIAM J. Sci. Comput., 21, 1191-1198.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 1191-1198
    • Walkerh, F.1
  • 140
    • 2942685048 scopus 로고    scopus 로고
    • Exact coherent structures in pipe flow: Travelling wave solutions
    • Wedin, H. and R. R. Kerswell, 2004: Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech., 508, 333-371.
    • (2004) J. Fluid Mech. , vol.508 , pp. 333-371
    • Wedin, H.1    Kerswell, R.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.