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Volumn 18, Issue 12, 2013, Pages 3530-3557

Lagrangian descriptors: A method for revealing phase space structures of general time dependent dynamical systems

Author keywords

Aperiodically time dependent; Invariant manifolds; Nonautonomous systems; Transport barriers; Vector fields

Indexed keywords

BENCHMARKING; GEOMETRY; HEURISTIC METHODS; LAGRANGE MULTIPLIERS; LYAPUNOV METHODS; VECTOR SPACES; VECTORS;

EID: 84880042896     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2013.05.002     Document Type: Article
Times cited : (240)

References (61)
  • 2
    • 0021443337 scopus 로고
    • Stirring by chaotic advection
    • Aref H. Stirring by chaotic advection. J Fluid Mech 1984, 143:1-21.
    • (1984) J Fluid Mech , vol.143 , pp. 1-21
    • Aref, H.1
  • 4
    • 77953514016 scopus 로고    scopus 로고
    • Invariant-tori-like Lagrangian coherent structures in geophysical flows
    • Beron-Vera F.J., Olascoaga M.J., Brown M.G., Kocak H., Rypina I.I. Invariant-tori-like Lagrangian coherent structures in geophysical flows. Chaos 2010, 20:017514.
    • (2010) Chaos , vol.20 , pp. 017514
    • Beron-Vera, F.J.1    Olascoaga, M.J.2    Brown, M.G.3    Kocak, H.4    Rypina, I.I.5
  • 5
    • 67650093100 scopus 로고    scopus 로고
    • An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems
    • Branicki M., Wiggins S. An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems. Physica D 2009, 238(16):1625-1657.
    • (2009) Physica D , vol.238 , Issue.16 , pp. 1625-1657
    • Branicki, M.1    Wiggins, S.2
  • 6
    • 77953008084 scopus 로고    scopus 로고
    • Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents
    • Branicki M., Wiggins S. Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents. Nonlinear Processes Geophys 2010, 17:1-36.
    • (2010) Nonlinear Processes Geophys , vol.17 , pp. 1-36
    • Branicki, M.1    Wiggins, S.2
  • 7
    • 78650682551 scopus 로고    scopus 로고
    • A Lagrangian description of transport associated with a front-eddy interaction: application to data from the North-Western Mediterranean sea
    • Branicki M., Mancho A.M., Wiggins S. A Lagrangian description of transport associated with a front-eddy interaction: application to data from the North-Western Mediterranean sea. Physica D 2011, 240(3):282-304.
    • (2011) Physica D , vol.240 , Issue.3 , pp. 282-304
    • Branicki, M.1    Mancho, A.M.2    Wiggins, S.3
  • 8
    • 0027866956 scopus 로고
    • Imaging vector fields using line integral convolution
    • ACM Press
    • Cabral B., Leedom L. Imaging vector fields using line integral convolution. Proc. siggraph 1993, 263-270. ACM Press.
    • (1993) Proc. siggraph , pp. 263-270
    • Cabral, B.1    Leedom, L.2
  • 9
    • 0002709196 scopus 로고
    • Dichotomies in stability theory
    • Springer-Verlag, New York, Heidelberg, Berlin
    • Coppel W.A. Dichotomies in stability theory. Lecture notes in mathematics 1978, vol. 629. Springer-Verlag, New York, Heidelberg, Berlin.
    • (1978) Lecture notes in mathematics , vol.629
    • Coppel, W.A.1
  • 10
    • 0035088907 scopus 로고    scopus 로고
    • Intergyre transport in a wind-driven, quasigeostrophic double gyre: an application of lobe dynamics
    • Coulliette C., Wiggins S. Intergyre transport in a wind-driven, quasigeostrophic double gyre: an application of lobe dynamics. Nonlinear Processes Geophys 2001, 8:69-94.
    • (2001) Nonlinear Processes Geophys , vol.8 , pp. 69-94
    • Coulliette, C.1    Wiggins, S.2
  • 11
    • 84857204037 scopus 로고    scopus 로고
    • Routes of transport across the Antarctic polar vortex in the southern spring
    • de la Cámara A., Mancho A.M., Ide K., Serrano E., Mechoso C. Routes of transport across the Antarctic polar vortex in the southern spring. J Atmos Sci 2012, 69(2):753-767.
    • (2012) J Atmos Sci , vol.69 , Issue.2 , pp. 753-767
    • de la Cámara, A.1    Mancho, A.M.2    Ide, K.3    Serrano, E.4    Mechoso, C.5
  • 12
    • 0038693395 scopus 로고    scopus 로고
    • Lyapunov spectral intervals: theory and computation
    • Dieci L., Vleck E.S.V. Lyapunov spectral intervals: theory and computation. SIAM J Numer Anal 2002, 40(2):516-542.
    • (2002) SIAM J Numer Anal , vol.40 , Issue.2 , pp. 516-542
    • Dieci, L.1    Vleck, E.S.V.2
  • 13
    • 0000223905 scopus 로고    scopus 로고
    • On the computation of Lyapunov exponents for continuous dynamical systems
    • Dieci L., Russell R.D., Vleck E.S.V. On the computation of Lyapunov exponents for continuous dynamical systems. SIAM J Numer Anal 1997, 34(1):402-423.
    • (1997) SIAM J Numer Anal , vol.34 , Issue.1 , pp. 402-423
    • Dieci, L.1    Russell, R.D.2    Vleck, E.S.V.3
  • 14
    • 0033297391 scopus 로고    scopus 로고
    • Abundance of elliptic isles at conservative bifurcations
    • Duarte P. Abundance of elliptic isles at conservative bifurcations. Dyn Stab Sys 1999, 14(4):339-356.
    • (1999) Dyn Stab Sys , vol.14 , Issue.4 , pp. 339-356
    • Duarte, P.1
  • 15
    • 45149090989 scopus 로고    scopus 로고
    • Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals
    • Duc L.H., Siegmund S. Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals. Int J Bifurcation Chaos 2008, 18(3):641-674.
    • (2008) Int J Bifurcation Chaos , vol.18 , Issue.3 , pp. 641-674
    • Duc, L.H.1    Siegmund, S.2
  • 16
    • 0007091042 scopus 로고
    • Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method
    • Goldhirsch I., Sulem P.-L., Orszag S. Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method. Physica D 1987, 27:311-337.
    • (1987) Physica D , vol.27 , pp. 311-337
    • Goldhirsch, I.1    Sulem, P.-L.2    Orszag, S.3
  • 17
    • 0034287926 scopus 로고    scopus 로고
    • On two dimensional area preserving diffeomorphisms with infinitely many elliptic islands
    • Gonchenko S.V., Silnikov L.P. On two dimensional area preserving diffeomorphisms with infinitely many elliptic islands. J Stat Phys 2000, 101(1/2):321-356.
    • (2000) J Stat Phys , vol.101 , Issue.1-2 , pp. 321-356
    • Gonchenko, S.V.1    Silnikov, L.P.2
  • 18
    • 0034147430 scopus 로고    scopus 로고
    • Finding finite-time invariant manifolds in two-dimensional velocity fields
    • Haller G. Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos 2000, 10(1):99-108.
    • (2000) Chaos , vol.10 , Issue.1 , pp. 99-108
    • Haller, G.1
  • 19
    • 0035505014 scopus 로고    scopus 로고
    • Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence
    • Haller G. Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Phys Fluids 2001, 13(11):3365-3385.
    • (2001) Phys Fluids , vol.13 , Issue.11 , pp. 3365-3385
    • Haller, G.1
  • 20
    • 84859149177 scopus 로고    scopus 로고
    • The impact of advective transport by the South Indian ocean countercurrent on the Madagascar plankton bloom
    • Huhn F., von Kameke A., Perez-Munuzuri V., Olascoaga M.J., Beron-Vera F.J. The impact of advective transport by the South Indian ocean countercurrent on the Madagascar plankton bloom. Geophys Res Lett 2012, 39(6):L06602.
    • (2012) Geophys Res Lett , vol.39 , Issue.6
    • Huhn, F.1    von Kameke, A.2    Perez-Munuzuri, V.3    Olascoaga, M.J.4    Beron-Vera, F.J.5
  • 21
    • 0036315576 scopus 로고    scopus 로고
    • Distinguished hyperbolic trajectories in time dependent fluid flows: analytical and computational approach for velocity fields defined as data sets
    • Ide K., Small D., Wiggins S. Distinguished hyperbolic trajectories in time dependent fluid flows: analytical and computational approach for velocity fields defined as data sets. Nonlinear Processes Geophys 2002, 9:237-263.
    • (2002) Nonlinear Processes Geophys , vol.9 , pp. 237-263
    • Ide, K.1    Small, D.2    Wiggins, S.3
  • 22
    • 67649526108 scopus 로고    scopus 로고
    • Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere
    • North-Holland, Amsterdam
    • Jones C.K.R.T., Winkler S. Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere. Handbook of dynamical systems 2002, 55-92. North-Holland, Amsterdam.
    • (2002) Handbook of dynamical systems , pp. 55-92
    • Jones, C.K.R.T.1    Winkler, S.2
  • 24
    • 0036711474 scopus 로고    scopus 로고
    • Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence
    • Lapeyre G. Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. Chaos 2002, 12:688-698.
    • (2002) Chaos , vol.12 , pp. 688-698
    • Lapeyre, G.1
  • 25
    • 0000252343 scopus 로고    scopus 로고
    • A guide to Liapunov vectors
    • ECMWF, Reading, UK
    • Legras B., Vautard R. A guide to Liapunov vectors. Predictability 1996, vol. 1:135-146. ECMWF, Reading, UK.
    • (1996) Predictability , vol.1 , pp. 135-146
    • Legras, B.1    Vautard, R.2
  • 26
    • 34250616203 scopus 로고    scopus 로고
    • Lagrangian coherent structures in n-dimensional systems
    • Lekien F., Shadden S., Marsden J.E. Lagrangian coherent structures in n-dimensional systems. J Math Phys 2007, 48:065404.
    • (2007) J Math Phys , vol.48 , pp. 065404
    • Lekien, F.1    Shadden, S.2    Marsden, J.E.3
  • 27
    • 63849179138 scopus 로고    scopus 로고
    • Distinguished trajectories in time dependent vector fields
    • Madrid J.A.J., Mancho A.M. Distinguished trajectories in time dependent vector fields. Chaos 2009, 19:013111.
    • (2009) Chaos , vol.19 , pp. 013111
    • Madrid, J.A.J.1    Mancho, A.M.2
  • 28
    • 0032091264 scopus 로고    scopus 로고
    • Patchiness: a new diagnostic for Lagrangian trajectory analysis in time-dependent fluid flows
    • Malhotra N., Mezic I., Wiggins S. Patchiness: a new diagnostic for Lagrangian trajectory analysis in time-dependent fluid flows. Int J Bifurcation Chaos 1998, 8(6):1053-1093.
    • (1998) Int J Bifurcation Chaos , vol.8 , Issue.6 , pp. 1053-1093
    • Malhotra, N.1    Mezic, I.2    Wiggins, S.3
  • 29
    • 0041529987 scopus 로고    scopus 로고
    • Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vectors fields
    • Mancho A.M., Small D., Wiggins S., Ide K. Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vectors fields. Physica D 2003, 182:188-222.
    • (2003) Physica D , vol.182 , pp. 188-222
    • Mancho, A.M.1    Small, D.2    Wiggins, S.3    Ide, K.4
  • 30
    • 1842682569 scopus 로고    scopus 로고
    • Computation of hyperbolic and their stable and unstable manifolds for oceanographic flows represented as data sets
    • Mancho A.M., Small D., Wiggins S. Computation of hyperbolic and their stable and unstable manifolds for oceanographic flows represented as data sets. Nonlinear Processes Geophys 2004, 11:17-33.
    • (2004) Nonlinear Processes Geophys , vol.11 , pp. 17-33
    • Mancho, A.M.1    Small, D.2    Wiggins, S.3
  • 31
    • 29544431525 scopus 로고    scopus 로고
    • A comparison of methods for interpolating chaotic flows from discrete velocity data
    • Mancho A.M., Small D., Wiggins S. A comparison of methods for interpolating chaotic flows from discrete velocity data. Comput Fluids 2006, 35:416-428.
    • (2006) Comput Fluids , vol.35 , pp. 416-428
    • Mancho, A.M.1    Small, D.2    Wiggins, S.3
  • 32
    • 63849198805 scopus 로고    scopus 로고
    • Lagrangian transport through an ocean front in the North-Western Mediterranean sea
    • Mancho A.M., Hernández-García E., Small D., Wiggins S., Fernández V. Lagrangian transport through an ocean front in the North-Western Mediterranean sea. J Phys Oceanogr 2006, 38(6):1222-1237.
    • (2006) J Phys Oceanogr , vol.38 , Issue.6 , pp. 1222-1237
    • Mancho, A.M.1    Hernández-García, E.2    Small, D.3    Wiggins, S.4    Fernández, V.5
  • 33
    • 85196192509 scopus 로고    scopus 로고
    • A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: theoretical and computational issues
    • Mancho A.M., Small D., Wiggins S. A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: theoretical and computational issues. Phys Rep 2006, 237:3-4.
    • (2006) Phys Rep , vol.237 , pp. 3-4
    • Mancho, A.M.1    Small, D.2    Wiggins, S.3
  • 34
    • 77954793996 scopus 로고    scopus 로고
    • The hidden geometry of ocean flows
    • Mendoza C., Mancho A.M. The hidden geometry of ocean flows. Phys Rev Lett 2010, 105(3):038501.
    • (2010) Phys Rev Lett , vol.105 , Issue.3 , pp. 038501
    • Mendoza, C.1    Mancho, A.M.2
  • 35
    • 84867762649 scopus 로고    scopus 로고
    • The Lagrangian description of ocean flows: a case study of the Kuroshio current
    • Mendoza C., Mancho A.M. The Lagrangian description of ocean flows: a case study of the Kuroshio current. Nonlinear Processes Geophys 2012, 19(4):449-472.
    • (2012) Nonlinear Processes Geophys , vol.19 , Issue.4 , pp. 449-472
    • Mendoza, C.1    Mancho, A.M.2
  • 36
    • 77952983698 scopus 로고    scopus 로고
    • The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields
    • Mendoza C., Mancho A.M., Rio M.-H. The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields. Nonlinear Processes Geophys 2010, 17(2):103-111.
    • (2010) Nonlinear Processes Geophys , vol.17 , Issue.2 , pp. 103-111
    • Mendoza, C.1    Mancho, A.M.2    Rio, M.-H.3
  • 37
    • 0033098238 scopus 로고    scopus 로고
    • A method for visualization of invariant sets of dynamical systems based on the ergodic partition
    • Mezic I., Wiggins S. A method for visualization of invariant sets of dynamical systems based on the ergodic partition. Chaos 1999, 9(1):213-218.
    • (1999) Chaos , vol.9 , Issue.1 , pp. 213-218
    • Mezic, I.1    Wiggins, S.2
  • 38
    • 77958184134 scopus 로고    scopus 로고
    • A new mixing diagnostic and Gulf oil spill movement
    • Mezic I., Loire S., Fonoberov V.A., Hogan P.A. A new mixing diagnostic and Gulf oil spill movement. Science 2010, 330(6003):486-489.
    • (2010) Science , vol.330 , Issue.6003 , pp. 486-489
    • Mezic, I.1    Loire, S.2    Fonoberov, V.A.3    Hogan, P.A.4
  • 39
    • 0001128134 scopus 로고
    • Quasi-elliptic periodic points in conservative dynamical systems
    • Newhouse S.E. Quasi-elliptic periodic points in conservative dynamical systems. Am J Math 1977, 99(5):1061-1087.
    • (1977) Am J Math , vol.99 , Issue.5 , pp. 1061-1087
    • Newhouse, S.E.1
  • 40
    • 0001073291 scopus 로고
    • Horizontal dispersion of floatable trajectories in the vicinity of velocity singularities such as convergencies
    • Okubo A. Horizontal dispersion of floatable trajectories in the vicinity of velocity singularities such as convergencies. Deep Sea Res 1970, 17:445-454.
    • (1970) Deep Sea Res , vol.17 , pp. 445-454
    • Okubo, A.1
  • 41
    • 0000430490 scopus 로고
    • Evolution of the stratosphere during northern winter 1991-1992 as diagnosed by the UKMO analysis
    • O'Neill A., Grose W.L., Pope V.D., McLean H., Swinbank R. Evolution of the stratosphere during northern winter 1991-1992 as diagnosed by the UKMO analysis. J Atmos Sci 1994, 51:2800-2817.
    • (1994) J Atmos Sci , vol.51 , pp. 2800-2817
    • O'Neill, A.1    Grose, W.L.2    Pope, V.D.3    McLean, H.4    Swinbank, R.5
  • 42
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
    • Oseledets V.I. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans Mosc Math Soc 1968, 19:197-231.
    • (1968) Trans Mosc Math Soc , vol.19 , pp. 197-231
    • Oseledets, V.I.1
  • 44
    • 77951516344 scopus 로고
    • Sur le problème des trois corps et les équations de la dynamique
    • Poincaré H. Sur le problème des trois corps et les équations de la dynamique. Acta Math 1890, 13:1-270.
    • (1890) Acta Math , vol.13 , pp. 1-270
    • Poincaré, H.1
  • 45
    • 0001323204 scopus 로고    scopus 로고
    • The geometry and statistics of mixing in aperiodic flows
    • Poje A., Haller G., Mezic I. The geometry and statistics of mixing in aperiodic flows. Phys Fluids 1999, 11(10):2963-2968.
    • (1999) Phys Fluids , vol.11 , Issue.10 , pp. 2963-2968
    • Poje, A.1    Haller, G.2    Mezic, I.3
  • 46
    • 84874320368 scopus 로고    scopus 로고
    • Dynamical systems theory methods for studying mixing and transport in the ocean
    • Prants S.V. Dynamical systems theory methods for studying mixing and transport in the ocean. Phys Scr 2013, 87:0381115.
    • (2013) Phys Scr , vol.87 , pp. 0381115
    • Prants, S.V.1
  • 47
    • 79954419800 scopus 로고    scopus 로고
    • Lagrangian study of transport and mixing in a mesoscale eddy street
    • Prants S.V., Budyansky M., Ponomarev V.I., Uleysky M.Y. Lagrangian study of transport and mixing in a mesoscale eddy street. Ocean Model 2011, 38(1-2):114-125.
    • (2011) Ocean Model , vol.38 , Issue.1-2 , pp. 114-125
    • Prants, S.V.1    Budyansky, M.2    Ponomarev, V.I.3    Uleysky, M.Y.4
  • 48
    • 80053972942 scopus 로고    scopus 로고
    • Numerical simulation of propagation of radioactive pollution in the ocean from the Fukushima Dai-ichi nuclear power plant
    • Prants S.V., Uleysky M.Y., Budyansky M.V. Numerical simulation of propagation of radioactive pollution in the ocean from the Fukushima Dai-ichi nuclear power plant. Dokl Earth Sci 2011, 439(2):1179-1182.
    • (2011) Dokl Earth Sci , vol.439 , Issue.2 , pp. 1179-1182
    • Prants, S.V.1    Uleysky, M.Y.2    Budyansky, M.V.3
  • 51
    • 0001229472 scopus 로고
    • Selected topics from the metric theory of dynamical systems
    • Rokhlin V.A. Selected topics from the metric theory of dynamical systems. Am Math Soc Transl Ser 1966, 2(49):171-240.
    • (1966) Am Math Soc Transl Ser , vol.2 , Issue.49 , pp. 171-240
    • Rokhlin, V.A.1
  • 53
    • 84867792231 scopus 로고    scopus 로고
    • Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures
    • Rypina I.I., Scott S.E., Pratt L.J., Brown M.G. Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures. Nonlinear Processes Geophys 2011, 18:977-987.
    • (2011) Nonlinear Processes Geophys , vol.18 , pp. 977-987
    • Rypina, I.I.1    Scott, S.E.2    Pratt, L.J.3    Brown, M.G.4
  • 55
    • 85196160311 scopus 로고    scopus 로고
    • Analysis of time-dependent dynamical systems using finite-time Lyapunov exponents
    • Shadden S.C. Lagrangian coherent structures. Analysis of time-dependent dynamical systems using finite-time Lyapunov exponents; 2005. http://mmae.iit.edu/shadden/LCS-tutorial/overview.html/.
    • (2005) Lagrangian coherent structures.
    • Shadden, S.C.1
  • 56
    • 28244461621 scopus 로고    scopus 로고
    • Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
    • Shadden S.C., Lekien F., Marsden J.E. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 2005, 212:271-304.
    • (2005) Physica D , vol.212 , pp. 271-304
    • Shadden, S.C.1    Lekien, F.2    Marsden, J.E.3
  • 58
    • 0000267689 scopus 로고
    • High resolution stratospheric tracer fields estimated from satellite observations using Lagrangian trajectory calculations
    • Sutton R.T., McLean H., Swinbank R., O'Neill A., Taylor F.W. High resolution stratospheric tracer fields estimated from satellite observations using Lagrangian trajectory calculations. J Atmos Sci 1994, 51:2995-3005.
    • (1994) J Atmos Sci , vol.51 , pp. 2995-3005
    • Sutton, R.T.1    McLean, H.2    Swinbank, R.3    O'Neill, A.4    Taylor, F.W.5
  • 59
    • 0000811285 scopus 로고
    • The dynamics of enstrophy transfer in 2-dimensional hydrodynamics
    • Weiss J. The dynamics of enstrophy transfer in 2-dimensional hydrodynamics. Physica D 1991, 48:273-294.
    • (1991) Physica D , vol.48 , pp. 273-294
    • Weiss, J.1
  • 60
    • 14544294888 scopus 로고    scopus 로고
    • The dynamical systems approach to Lagrangian transport in oceanic flows
    • Wiggins S. The dynamical systems approach to Lagrangian transport in oceanic flows. Annu Rev Fluid Mech 2005, 37:295-328.
    • (2005) Annu Rev Fluid Mech , vol.37 , pp. 295-328
    • Wiggins, S.1
  • 61
    • 2442475063 scopus 로고    scopus 로고
    • Foundations of chaotic mixing
    • Wiggins S., Ottino J. Foundations of chaotic mixing. Philos Trans R Soc 2004, 362(1818):937-970.
    • (2004) Philos Trans R Soc , vol.362 , Issue.1818 , pp. 937-970
    • Wiggins, S.1    Ottino, J.2


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