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1

Haller, George. "Lagrangian Coherent Structures." Annual Review of Fluid Mechanics 47, no. 1 (2015): 137–62. http://dx.doi.org/10.1146/annurev-fluid-010313-141322.

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2

Balasuriya, Sanjeeva, Nicholas T. Ouellette, and Irina I. Rypina. "Generalized Lagrangian coherent structures." Physica D: Nonlinear Phenomena 372 (June 2018): 31–51. http://dx.doi.org/10.1016/j.physd.2018.01.011.

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3

Wilson, Z. D., M. Tutkun, and R. B. Cal. "Identification of Lagrangian coherent structures in a turbulent boundary layer." Journal of Fluid Mechanics 728 (July 11, 2013): 396–416. http://dx.doi.org/10.1017/jfm.2013.214.

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AbstractLagrangian coherent structures (LCS) of a turbulent boundary layer at${\mathit{Re}}_{\theta } $of 9800 are identified in a plane parallel to the wall at${y}^{+ } = 50$. Three-component high-speed stereo particle image velocimetry measurements on a two-dimensional rectangular plane are used for the analysis. The velocity field is extended in the streamwise direction, using Taylor’s frozen field hypothesis. A computational approach utilizing the variational theory of hyperbolic Lagrangian coherent structures is applied to the domain and trajectories are computed using the extended field.
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4

de Oliveira, Luis C., Caroline G. L. Martins, M. Roberto, I. L. Caldas, and R. Egydio de Carvalho. "Robust tori-like Lagrangian coherent structures." Physica A: Statistical Mechanics and its Applications 391, no. 24 (2012): 6611–16. http://dx.doi.org/10.1016/j.physa.2012.07.060.

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5

Garaboa-Paz, Daniel, Jorge Eiras-Barca, Florian Huhn, and Vicente Pérez-Muñuzuri. "Lagrangian coherent structures along atmospheric rivers." Chaos: An Interdisciplinary Journal of Nonlinear Science 25, no. 6 (2015): 063105. http://dx.doi.org/10.1063/1.4919768.

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6

Rempel, E. L., A. C. L. Chian, and A. Brandenburg. "LAGRANGIAN COHERENT STRUCTURES IN NONLINEAR DYNAMOS." Astrophysical Journal 735, no. 1 (2011): L9. http://dx.doi.org/10.1088/2041-8205/735/1/l9.

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7

Abernathey, Ryan, and George Haller. "Transport by Lagrangian Vortices in the Eastern Pacific." Journal of Physical Oceanography 48, no. 3 (2018): 667–85. http://dx.doi.org/10.1175/jpo-d-17-0102.1.

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AbstractRotationally coherent Lagrangian vortices (RCLVs) are identified from satellite-derived surface geostrophic velocities in the eastern Pacific (180°–130°W) using the objective (frame invariant) finite-time Lagrangian coherent structure detection method of Haller et al. based on the Lagrangian-averaged vorticity deviation. RCLVs are identified for 30-, 90-, and 270-day intervals over the entire satellite dataset, beginning in 1993. In contrast to structures identified using Eulerian eddy-tracking methods, the RCLVs maintain material coherence over the specified time intervals, making the
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8

Rutherford, B., G. Dangelmayr, and M. T. Montgomery. "Lagrangian coherent structures in tropical cyclone intensification." Atmospheric Chemistry and Physics Discussions 11, no. 10 (2011): 28125–68. http://dx.doi.org/10.5194/acpd-11-28125-2011.

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Abstract. Recent work has suggested that tropical cyclones intensify via a pathway of rotating deep moist convection in the presence of enhanced fluxes of moisture from the ocean. The rotating deep convective structures possessing enhanced cyclonic vorticity within their cores have been dubbed Vortical Hot Towers (VHTs). In general, the interaction between VHTs and the system-scale vortex, as well as the corresponding evolution of equivalent potential temperature θe that modulates the VHT activity, is a complex problem in moist helical turbulence. To better understand the structural aspects of
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9

Germer, T., M. Otto, R. Peikert, and H. Theisel. "Lagrangian Coherent Structures with Guaranteed Material Separation." Computer Graphics Forum 30, no. 3 (2011): 761–70. http://dx.doi.org/10.1111/j.1467-8659.2011.01925.x.

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10

Lekien, Francois, Shawn C. Shadden, and Jerrold E. Marsden. "Lagrangian coherent structures in n-dimensional systems." Journal of Mathematical Physics 48, no. 6 (2007): 065404. http://dx.doi.org/10.1063/1.2740025.

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11

Tang, Wenbo, and Thomas Peacock. "Lagrangian coherent structures and internal wave attractors." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 1 (2010): 017508. http://dx.doi.org/10.1063/1.3273054.

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12

Peacock, Thomas, and John Dabiri. "Introduction to Focus Issue: Lagrangian Coherent Structures." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 1 (2010): 017501. http://dx.doi.org/10.1063/1.3278173.

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13

Karrasch, Daniel. "Attracting Lagrangian coherent structures on Riemannian manifolds." Chaos: An Interdisciplinary Journal of Nonlinear Science 25, no. 8 (2015): 087411. http://dx.doi.org/10.1063/1.4928451.

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14

Lekien, Francois, Laurent Mortier, and Pierre Testor. "Glider Coordinated Control and Lagrangian Coherent Structures*." IFAC Proceedings Volumes 41, no. 1 (2008): 125–30. http://dx.doi.org/10.3182/20080408-3-ie-4914.00023.

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15

Tew Kai, E., V. Rossi, J. Sudre, et al. "Top marine predators track Lagrangian coherent structures." Proceedings of the National Academy of Sciences 106, no. 20 (2009): 8245–50. http://dx.doi.org/10.1073/pnas.0811034106.

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16

Haller, G. "Lagrangian coherent structures from approximate velocity data." Physics of Fluids 14, no. 6 (2002): 1851–61. http://dx.doi.org/10.1063/1.1477449.

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17

Miron, Philippe, Jérôme Vétel, André Garon, Michel Delfour, and Mouhammad El Hassan. "Anisotropic mesh adaptation on Lagrangian Coherent Structures." Journal of Computational Physics 231, no. 19 (2012): 6419–37. http://dx.doi.org/10.1016/j.jcp.2012.06.015.

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18

Rutherford, B., G. Dangelmayr, and M. T. Montgomery. "Lagrangian coherent structures in tropical cyclone intensification." Atmospheric Chemistry and Physics 12, no. 12 (2012): 5483–507. http://dx.doi.org/10.5194/acp-12-5483-2012.

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Abstract. Recent work has suggested that tropical cyclones intensify via a pathway of rotating deep moist convection in the presence of enhanced fluxes of moisture from the ocean. The rotating deep convective structures possessing enhanced cyclonic vorticity within their cores have been dubbed Vortical Hot Towers (VHTs). In general, the interaction between VHTs and the system-scale vortex, as well as the corresponding evolution of equivalent potential temperature (θe) that modulates the VHT activity, is a complex problem in moist helical turbulence. To better understand the structural aspects
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19

Ma, Tian, and Erik M. Bollt. "Shape Coherence and Finite-Time Curvature Evolution." International Journal of Bifurcation and Chaos 25, no. 05 (2015): 1550076. http://dx.doi.org/10.1142/s0218127415500765.

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We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the existence of shape coherent sets, and troughs in the field indicate the most significant shape coherence. Here, we will demonstrate these properties of the FTC, as well as contrast to the popular Finite-
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20

Chian, Abraham C.-L., Suzana S. A. Silva, Erico L. Rempel, et al. "Supergranular turbulence in the quiet Sun: Lagrangian coherent structures." Monthly Notices of the Royal Astronomical Society 488, no. 3 (2019): 3076–88. http://dx.doi.org/10.1093/mnras/stz1909.

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ABSTRACT The quiet Sun exhibits a wealth of magnetic activities that are fundamental for our understanding of solar magnetism. The magnetic fields in the quiet Sun are observed to evolve coherently, interacting with each other to form prominent structures as they are advected by photospheric flows. The aim of this paper is to study supergranular turbulence by detecting Lagrangian coherent structures (LCS) based on the horizontal velocity fields derived from Hinode intensity images at disc centre of the quiet Sun on 2010 November 2. LCS act as transport barriers and are responsible for attracti
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21

Nag, Preetom, Hiroshi Teramoto, Chun-Biu Li, and Tamiki Komatsuzaki. "3P313 Coherent dynamics in colloidal fluids in terms of Lagrangian coherent structures (LCS)(30.Miscellaneous topics,Poster,The 51st Annual Meeting of the Biophysical Society of Japan)." Seibutsu Butsuri 53, supplement1-2 (2013): S263. http://dx.doi.org/10.2142/biophys.53.s263_6.

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22

Schlueter-Kuck, Kristy L., and John O. Dabiri. "Coherent structure colouring: identification of coherent structures from sparse data using graph theory." Journal of Fluid Mechanics 811 (December 13, 2016): 468–86. http://dx.doi.org/10.1017/jfm.2016.755.

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We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph colouring and spectral graph drawing algorithms, examines a measure of the kinematic dissimilarity of all pairs of fluid trajectories, measured either experimentally, e.g. using particle tracking velocimetry, or numerically, by advecting fluid particles in the Eulerian velocity field. Coherence is assigned to groups of particles whose kinemati
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23

Chakraborty, Rishiraj, Aaron Coutino, and Marek Stastna. "Particle clustering and subclustering as a proxy for mixing in geophysical flows." Nonlinear Processes in Geophysics 26, no. 3 (2019): 307–24. http://dx.doi.org/10.5194/npg-26-307-2019.

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Abstract. The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating a Lagrangian description of the flow. The existence and persistence of Lagrangian coherent structures in fluid flow has been a topic of considerable study. Here we focus on the ability of Lagrangian methods to characterize mixing in geophysical flows. We study the instability of a strongly non-linear double-jet flow, initially in geostrophic balance, which forms qu
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24

Haller, George. "A variational theory of hyperbolic Lagrangian Coherent Structures." Physica D: Nonlinear Phenomena 240, no. 7 (2011): 574–98. http://dx.doi.org/10.1016/j.physd.2010.11.010.

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25

Gadde, Srinidhi Nagarada, and Sankaranarayanan Vengadesan. "Lagrangian coherent structures in tandem flapping wing hovering." Journal of Bionic Engineering 14, no. 2 (2017): 307–16. http://dx.doi.org/10.1016/s1672-6529(16)60399-2.

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26

Phillips, W. R. C. "Coherent Structures and the Generalized Lagrangian Mean Equation." Applied Mechanics Reviews 43, no. 5S (1990): S227—S231. http://dx.doi.org/10.1115/1.3120812.

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The Generalized Lagrangian mean equations are used to derive evolution equations for the perturbation flow about a turbulent mean base flow which is homogeneous in the streamwise and spanwise directions. The equations expose the mechanism which leads to the formation of streamwise vortices in the wall region of turbulent bounded flows and may be solved numerically. The advantage of this formulation is that the form of the coupling terms in the equations is known precisely; moreover, they can be expressed in terms of space time correlations, most of which have been measured. The result is a set
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27

Karrasch, Daniel, Mohammad Farazmand, and George Haller. "Attraction-based computation of hyperbolic Lagrangian coherent structures." Journal of Computational Dynamics 2, no. 1 (2015): 83–93. http://dx.doi.org/10.3934/jcd.2015.2.83.

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28

Wilson, Megan M., Jifeng Peng, John O. Dabiri, and Jeff D. Eldredge. "Lagrangian coherent structures in low Reynolds number swimming." Journal of Physics: Condensed Matter 21, no. 20 (2009): 204105. http://dx.doi.org/10.1088/0953-8984/21/20/204105.

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29

Reniers, A. J. H. M., J. H. MacMahan, F. J. Beron-Vera, and M. J. Olascoaga. "Rip-current pulses tied to Lagrangian coherent structures." Geophysical Research Letters 37, no. 5 (2010): n/a. http://dx.doi.org/10.1029/2009gl041443.

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30

Farazmand, Mohammad, and George Haller. "Computing Lagrangian coherent structures from their variational theory." Chaos: An Interdisciplinary Journal of Nonlinear Science 22, no. 1 (2012): 013128. http://dx.doi.org/10.1063/1.3690153.

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31

Tang, Wenbo, Manikandan Mathur, George Haller, Douglas C. Hahn, and Frank H. Ruggiero. "Lagrangian Coherent Structures near a Subtropical Jet Stream." Journal of the Atmospheric Sciences 67, no. 7 (2010): 2307–19. http://dx.doi.org/10.1175/2010jas3176.1.

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Abstract Direct Lyapunov exponents and stability results are used to extract and distinguish Lagrangian coherent structures (LCS) from a three-dimensional atmospheric dataset generated from the Weather Research and Forecasting (WRF) model. The numerical model is centered at 19.78°N, 155.55°W, initialized from the Global Forecast System for the case of a subtropical jet stream near Hawaii on 12 December 2002. The LCS are identified that appear to create optical and mechanical turbulence, as evidenced by balloon data collected during a measurement campaign near Hawaii.
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32

Gough, Matt K., Ad Reniers, M. Josefina Olascoaga, et al. "Lagrangian Coherent Structures in a coastal upwelling environment." Continental Shelf Research 128 (October 2016): 36–50. http://dx.doi.org/10.1016/j.csr.2016.09.007.

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33

MA, HONG-GUANG, QIN-BO JIANG, XIANG-YU KONG, ZHI-QIANG LIU, and ZHI-YUAN MA. "IDENTIFYING NONSTATIONARY JAMMING SIGNAL VIA LAGRANGIAN COHERENT STRUCTURES." International Journal of Bifurcation and Chaos 22, no. 03 (2012): 1250050. http://dx.doi.org/10.1142/s0218127412500502.

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The anti-jamming scheme is an important issue in the modern communication system, where the spread-spectrum signals are usually adopted. In a complex electromagnetic environment where the jamming sources may be close to the communication devices, a large jamming-to-signal ratio is possible. How to achieve the desired accuracy for the communication system in the presence of strong jamming is a crucial and outstanding problem. To solve this problem, we propose a method to identify the desired signal and the nonstationary jamming signal via Lagrangian Coherent Structures (LCS), and a new algorith
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34

Волков, К. Н., В. Н. Емельянов, И. Е. Капранов, and И. В. Тетерина. "Lagrangian coherent vortex structures and their numerical visualization." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 3 (July 25, 2018): 293–313. http://dx.doi.org/10.26089/nummet.v19r328.

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Рассматриваются вопросы, связанные с реализацией и физико-математическим сопровождением вычислительных экспериментов по исследованию течений жидкости и газа, содержащих лагранжевые когерентные вихревые структуры. Обсуждаются методы и инструменты, предназначенные для визуализации вихревых течений, возникающих в различных практических приложениях. Приводятся примеры визуального представления решений ряда задач вихревой газовой динамики, полученных при помощи лагранжевых подходов к описанию течений жидкости и газа. Помимо традиционных подходов к визуализации вихревых течений, основанных на постро
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35

GREEN, M. A., C. W. ROWLEY, and G. HALLER. "Detection of Lagrangian coherent structures in three-dimensional turbulence." Journal of Fluid Mechanics 572 (January 23, 2007): 111–20. http://dx.doi.org/10.1017/s0022112006003648.

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We use direct Lyapunov exponents (DLE) to identify Lagrangian coherent structures in two different three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. We find that despite additional computational cost, the DLE method has several advantages over Eulerian methods, including greater detail and the ability to define structure boundaries without relying on a preselected threshold. As a further advantage, the DLE method requires no velocity derivatives, which
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36

Rempel, Erico L., Abraham C. L. Chian, Axel Brandenburg, Pablo R. Muñoz, and Shawn C. Shadden. "Coherent structures and the saturation of a nonlinear dynamo." Journal of Fluid Mechanics 729 (July 19, 2013): 309–29. http://dx.doi.org/10.1017/jfm.2013.290.

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AbstractEulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean-field dynamo, produced by direct numerical simulations of the three-dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied: the kinematic stage, where a seed magnetic field undergoes exponential growth; and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, in addition to providing information on the chaotic mixin
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37

Ivić, Stefan, Iva Mrša Haber, and Tarzan Legović. "Lagrangian coherent structures in the Rijeka Bay current field." Acta Adriatica 58, no. 3 (2017): 373–89. http://dx.doi.org/10.32582/aa.58.3.1.

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Some of the major European oil supply routes pass through the Adriatic Sea representing a potential to endanger the whole basin with an oil spill. Particularly high ecological vulnerability of Rijeka Bay is due to its geospatial characteristics as semi-enclosed basin. The simulated onemonth sea surface velocity field of Rijeka Bay was analyzed using Lagrangian coherent structures (LCSs) to assess the diffusion and chaotic advection of passive pollutants (dye). LCSs were extracted by the Finite-Time Lyapunov Exponents (FTLE), hypergraphs, Lagrangian advection alone and advection-diffusion metho
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38

Nolan, Peter J., Hosein Foroutan, and Shane D. Ross. "Pollution Transport Patterns Obtained Through Generalized Lagrangian Coherent Structures." Atmosphere 11, no. 2 (2020): 168. http://dx.doi.org/10.3390/atmos11020168.

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Identifying atmospheric transport pathways is important to understand the effects of pollutants on weather, climate, and human health. The atmospheric wind field is variable in space and time and contains complex patterns due to turbulent mixing. In such a highly unsteady flow field, it can be challenging to predict material transport over a finite-time interval. Particle trajectories are often used to study how pollutants evolve in the atmosphere. Nevertheless, individual trajectories are sensitive to their initial conditions. Lagrangian Coherent Structures (LCSs) have been shown to form the
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39

Jiang, Xianyang. "Lagrangian Identification of Coherent Structures in Wall-Bounded Flows." Advances in Applied Mathematics and Mechanics 11, no. 3 (2019): 640–52. http://dx.doi.org/10.4208/aamm.2018.s08.

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40

Beron-Vera, F. J., M. J. Olascoaga, and G. J. Goni. "Oceanic mesoscale eddies as revealed by Lagrangian coherent structures." Geophysical Research Letters 35, no. 12 (2008): n/a. http://dx.doi.org/10.1029/2008gl033957.

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41

Prants, S. V., M. Yu Uleysky, and M. V. Budyansky. "Lagrangian coherent structures in the ocean favorable for fishery." Doklady Earth Sciences 447, no. 1 (2012): 1269–72. http://dx.doi.org/10.1134/s1028334x12110062.

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42

Haller, G., and G. Yuan. "Lagrangian coherent structures and mixing in two-dimensional turbulence." Physica D: Nonlinear Phenomena 147, no. 3-4 (2000): 352–70. http://dx.doi.org/10.1016/s0167-2789(00)00142-1.

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43

Peacock, Thomas, and George Haller. "Lagrangian coherent structures: The hidden skeleton of fluid flows." Physics Today 66, no. 2 (2013): 41–47. http://dx.doi.org/10.1063/pt.3.1886.

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44

Froyland, Gary. "Dynamic isoperimetry and the geometry of Lagrangian coherent structures." Nonlinearity 28, no. 10 (2015): 3587–622. http://dx.doi.org/10.1088/0951-7715/28/10/3587.

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45

Onu, K., F. Huhn, and G. Haller. "LCS Tool: A computational platform for Lagrangian coherent structures." Journal of Computational Science 7 (March 2015): 26–36. http://dx.doi.org/10.1016/j.jocs.2014.12.002.

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46

Beron-Vera, Francisco J., María J. Olascoaga, Michael G. Brown, Huseyin Koçak, and Irina I. Rypina. "Invariant-tori-like Lagrangian coherent structures in geophysical flows." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 1 (2010): 017514. http://dx.doi.org/10.1063/1.3271342.

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47

Wang, N., U. Ramirez, F. Flores, and S. Datta‐Barua. "Lagrangian coherent structures in the thermosphere: Predictive transport barriers." Geophysical Research Letters 44, no. 10 (2017): 4549–57. http://dx.doi.org/10.1002/2017gl072568.

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48

Fazanaro, Filipe I., Diogo C. Soriano, Ricardo Suyama, Marconi K. Madrid, Romis Attux, and José Raimundo de Oliveira. "Information Generation and Lagrangian Coherent Structures in Multiscroll Attractors*." IFAC Proceedings Volumes 45, no. 12 (2012): 93–98. http://dx.doi.org/10.3182/20120620-3-mx-3012.00010.

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49

Schindler, B., R. Fuchs, S. Barp, et al. "Lagrangian Coherent Structures for Design Analysis of Revolving Doors." IEEE Transactions on Visualization and Computer Graphics 18, no. 12 (2012): 2159–68. http://dx.doi.org/10.1109/tvcg.2012.243.

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50

Karrasch, Daniel, and Johannes Keller. "A Geometric Heat-Flow Theory of Lagrangian Coherent Structures." Journal of Nonlinear Science 30, no. 4 (2020): 1849–88. http://dx.doi.org/10.1007/s00332-020-09626-9.

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