main.bib

@ARTICLE{haller00:_lagran,
  AUTHOR       = {Haller, George and Yuan, Guocheng},
  DOI          = {10.1016/S0167-2789(00)00142-1},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  MONTH        = {12},
  NUMBER       = {3--4},
  PAGES        = {352--370},
  TITLE        = {Lagrangian coherent structures and mixing in two-dimensional turbulence},
  VOLUME       = {147},
  YEAR         = {2000},
}

@ARTICLE{peacock13:_lagran,
  AUTHOR       = {Peacock, Thomas and Haller, George},
  DOI          = {10.1063/PT.3.1886},
  JOURNALTITLE = {Physics Today},
  MONTH        = {2},
  NUMBER       = {2},
  PAGES        = {41--47},
  TITLE        = {Lagrangian coherent structures: The hidden skeleton of fluid flows},
  VOLUME       = {66},
  YEAR         = {2013},
}

@ARTICLE{haller15:_langr_coher_struc,
  ABSTRACT     = {Typical fluid particle trajectories are sensitive to changes in their initial conditions. This makes the assessment of flow models and observations from individual tracer samples unreliable. Behind complex and sensitive tracer patterns, however, there exists a robust skeleton of material surfaces, Lagrangian Coherent Structures (or LCSs), shaping those patterns. Free from the uncertainties of single trajectories, LCSs frame, quantify, and even forecast key aspects of material transport. A number of diagnostic quantities have been proposed to visualize LCSs. More recent mathematical approaches identify LCSs precisely through their impact of these surfaces on fluid deformation. This review focuses on the latter developments, illustrating them on applications to geophysical fluid dynamics.},
  AUTHOR       = {Haller, George},
  DOI          = {10.1146/annurev-fluid-010313-141322},
  JOURNALTITLE = {Annual Review of Fluid Mechanics},
  PAGES        = {137--161},
  TITLE        = {Lagrangian Coherent Structures},
  VOLUME       = {47},
  YEAR         = {2015},
}

@ARTICLE{beron-vera13:_objec_agulh,
  AUTHOR       = {Beron-Vera, Francisco Javier and Wang, Yan and Olascoaga, María J. and Goni, Gustavo J. and Haller, George},
  DOI          = {10.1175/JPO-D-12-0171.1},
  JOURNALTITLE = {Journal of Physical Oceanography},
  MONTH        = {7},
  NUMBER       = {7},
  PAGES        = {1426--1438},
  TITLE        = {Objective detection of oceanic eddies and the Agulhas leakage},
  VOLUME       = {43},
  YEAR         = {2013},
}

@ARTICLE{koh02:_hyper,
  AUTHOR       = {Koh, Tieh-Yong and Legras, Bernard},
  DOI          = {10.1063/1.1480442},
  JOURNALTITLE = {Chaos},
  MONTH        = {6},
  NUMBER       = {2},
  PAGES        = {382--394},
  TITLE        = {Hyperbolic lines and the stratospheric polar vortex},
  VOLUME       = {12},
  YEAR         = {2002},
}

@ARTICLE{wilson09:_lagran_reynol,
  AUTHOR       = {Wilson, Megan M. and Peng, Jifeng and Dabiri, John O. and Eldredge, Jeff D.},
  DOI          = {10.1088/0953-8984/21/20/204105},
  JOURNALTITLE = {Journal of Physics: Condensed Matter},
  NUMBER       = {20},
  PAGES        = {204105:1--9},
  PAGETOTAL    = {9},
  TITLE        = {Lagrangian coherent structures in low Reynolds number swimming},
  VOLUME       = {21},
  YEAR         = {2009},
}

@ARTICLE{tallapragada11:_lagran,
  AUTHOR       = {Tallapragada, Phanindra and Ross, Shane David and Schmale, Burton III, David Garner},
  DOI          = {10.1063/1.3624930},
  JOURNALTITLE = {Chaos},
  NUMBER       = {3},
  PAGES        = {33122:1--16},
  TITLE        = {Lagrangian coherent structures are associated with fluctuations in airborne microbial populations},
  VOLUME       = {21},
  YEAR         = {2011},
}

@ARTICLE{huhn12:_south_indian_ocean_count_madag,
  AUTHOR       = {Huhn, Florian and von Kameke, Alexandra and Pérez-Muñuzuri, Vicente and Olascoaga, María J. and Beron-Vera, Francisco Javier},
  DOI          = {10.1029/2012GL051246},
  JOURNALTITLE = {Geophysical Research Letters},
  NUMBER       = {6},
  PAGES        = {L06602:1--6},
  PAGETOTAL    = {6},
  TITLE        = {The impact of advective transport by the South Indian Ocean Countercurrent on the Madagascar plankton bloom},
  VOLUME       = {39},
  YEAR         = {2012},
}

@ARTICLE{tang10:_accur_lagran_hong_kong_inter_airpor,
  AUTHOR       = {Tang, Wenbo and Chan, Pak Wai and Haller, George},
  DOI          = {10.1063/1.3276061},
  JOURNALTITLE = {Chaos},
  NUMBER       = {1},
  PAGES        = {17502:1--8},
  TITLE        = {Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport},
  VOLUME       = {20},
  YEAR         = {2010},
}

@ARTICLE{gawlik09:_lagran,
  AUTHOR       = {Gawlik, Evan S. and Marsden, Jerrold Eldon and du Toit, Philip C. and Campagnola, Stefano},
  DOI          = {10.1007/s10569-008-9180-3},
  JOURNALTITLE = {Celestial Mechanics and Dynamical Astronomy},
  MONTH        = {3},
  NUMBER       = {3},
  PAGES        = {227-249},
  TITLE        = {Lagrangian coherent structures in the planar elliptic restricted three-body problem},
  VOLUME       = {103},
  YEAR         = {2009},
}

@INPROCEEDINGS{ali07:_lagran_partic_dynam_approac_crowd,
  ABSTRACT  = {This paper proposes a framework in which Lagrangian particle dynamics is used for the segmentation of high density crowd flows and detection of flow instabilities. For this purpose, a flow field generated by a moving crowd is treated as an aperiodic dynamical system. A grid of particles is overlaid on the flow field, and is advected using a numerical integration scheme. The evolution of particles through the flow is tracked using a flow map, whose spatial gradients are subsequently used to setup a Cauchy Green deformation tensor for quantifying the amount by which the neighboring particles have diverged over the length of the integration. The maximum eigenvalue of the tensor is used to construct a finite time Lyapunov exponent (FTLE) field, which reveals the Lagrangian coherent structures (LCS) present in the underlying flow. The LCS divide flow into regions of qualitatively different dynamics and are used to locate boundaries of the flow segments in a normalized cuts framework. Any change in the number of flow segments over time is regarded as an instability, which is detected by establishing correspondences between flow segments over time. The experiments are conducted on a challenging set of videos taken from Google Video and a National Geographic documentary.},
  AUTHOR    = {Ali, Saad and Shah, Mubarak},
  BOOKTITLE = {IEEE Conference on Computer Vision and Pattern Recognition},
  DOI       = {10.1109/CVPR.2007.382977},
  KEYWORDS  = {gradient methods;image motion analysis;image segmentation;integration;object detection;stability;Cauchy Green deformation tensor;Lagrangian particle dynamics approach;crowd flow segmentation;finite time Lyapunov exponent;flow map;flow stability analysis;numerical integration scheme;spatial gradient method;Bridges;Cities and towns;Computer vision;Fluid dynamics;Lagrangian functions;Layout;Safety;Stability analysis;Tensile stress;Videos},
  MONTH     = {6},
  PAGES     = {1-6},
  TITLE     = {A Lagrangian Particle Dynamics Approach for Crowd Flow Segmentation and Stability Analysis},
  YEAR      = {2007},
}

@ARTICLE{hadjighasem13:_detec_kam,
  AUTHOR       = {Hadjighasem, Alireza and Farazmand, Mohammad Mehdi and Haller, George},
  DOI          = {10.1007/s11071-013-0823-x},
  EPRINT       = {1302.1732},
  EPRINTCLASS  = {nlin.CD},
  EPRINTTYPE   = {arXiv},
  JOURNALTITLE = {Nonlinear Dynamics},
  MONTH        = {7},
  NUMBER       = {1--2},
  PAGES        = {689--704},
  TITLE        = {Detecting invariant manifolds, attractors, and generalized KAM tori in aperiodically forced mechanical systems},
  VOLUME       = {73},
  YEAR         = {2013},
}

@ARTICLE{haller01:_distin,
  AUTHOR       = {Haller, George},
  DOI          = {10.1016/S0167-2789(00)00199-8},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  NUMBER       = {4},
  PAGES        = {248-277},
  TITLE        = {Distinguished material surfaces and coherent structures in three-dimensional fluid flows},
  VOLUME       = {149},
  YEAR         = {2001},
}

@ARTICLE{haller11:_lagran_coher_struc,
  AUTHOR       = {George Haller},
  DOI          = {10.1016/j.physd.2010.11.010},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  MONTH        = {3},
  NUMBER       = {7},
  PAGES        = {574-598},
  TITLE        = {A variational theory of hyperbolic Lagrangian Coherent Structures},
  VOLUME       = {240},
  YEAR         = {2011},
}

@ARTICLE{norgard12:_secon_lagran_coher_struc,
  AUTHOR       = {Norgard, Greg and Bremer, Peer-Timo},
  DOI          = {10.1016/j.physd.2012.05.006},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  MONTH        = {9},
  NUMBER       = {18},
  PAGES        = {1475-1476},
  TITLE        = {Second derivative ridges are straight lines and the implications for computing Lagrangian Coherent Structures},
  VOLUME       = {241},
  YEAR         = {2012},
}

@ARTICLE{beron-vera10:_invar_lagran,
  AUTHOR       = {Beron-Vera, Francisco Javier and Olascoaga, María J. and Brown, Michael G. and Koçak, Hüseyin and Rypina, Irina I.},
  DOI          = {10.1063/1.3271342},
  JOURNALTITLE = {Chaos},
  MONTH        = {3},
  NUMBER       = {1},
  PAGES        = {17514:1--13},
  TITLE        = {Invariant-tori-like Lagrangian coherent structures in geophysical flows},
  VOLUME       = {20},
  YEAR         = {2010},
}

@ARTICLE{farazmand12:_comput_lagran,
  AUTHOR       = {Farazmand, Mohammad Mehdi and Haller, George},
  DOI          = {10.1063/1.3690153},
  JOURNALTITLE = {Chaos},
  NUMBER       = {1},
  PAGES        = {13128:1--12},
  TITLE        = {Computing Lagrangian coherent structures from their variational theory},
  VOLUME       = {22},
  YEAR         = {2012},
}

@ARTICLE{haller12:_geodes_theor_trans_barrier_two_dimen_flows,
  AUTHOR       = {Haller, George and Beron-Vera, Francisco Javier},
  DOI          = {10.1016/j.physd.2012.06.012},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  MONTH        = {10},
  NUMBER       = {20},
  PAGES        = {1680-1702},
  TITLE        = {Geodesic Theory of Transport Barriers in Two-Dimensional Flows},
  VOLUME       = {241},
  YEAR         = {2012},
}

@ARTICLE{haller13:_coher_lagran,
  AUTHOR       = {Haller, George and Beron-Vera, Francisco Javier},
  DOI          = {10.1017/jfm.2013.391},
  EPRINT       = {1308.2352},
  EPRINTCLASS  = {physics.ao-ph},
  EPRINTTYPE   = {arXiv},
  JOURNALTITLE = {Journal of Fluid Mechanics},
  MONTH        = {9},
  PAGES        = {R4:1--10},
  TITLE        = {Coherent Lagrangian vortices: the black holes of turbulence},
  VOLUME       = {731},
  YEAR         = {2013},
}

@ARTICLE{haller14:_adden_coher_lagran,
  AUTHOR       = {Haller, George and Beron-Vera, Francisco Javier},
  DOI          = {10.1017/jfm.2014.441},
  EPRINT       = {1406.1493},
  EPRINTCLASS  = {physics.ao-ph},
  EPRINTTYPE   = {arXiv},
  JOURNALTITLE = {Journal of Fluid Mechanics},
  MONTH        = {9},
  PAGES        = {R3:1--4},
  TITLE        = {Addendum to ‘Coherent Lagrangian vortices: the black holes of turbulence’},
  VOLUME       = {755},
  YEAR         = {2014},
}

@ARTICLE{farazmand13:_attrac_lagran,
  AUTHOR       = {Farazmand, Mohammad Mehdi and George Haller},
  DOI          = {10.1063/1.4800210},
  EPRINT       = {1301.4951},
  EPRINTCLASS  = {math.DS},
  EPRINTTYPE   = {arXiv},
  JOURNALTITLE = {Chaos},
  NUMBER       = {2},
  PAGES        = {23101:1--11},
  TITLE        = {Attracting and repelling Lagrangian coherent structures from a single computation},
  VOLUME       = {23},
  YEAR         = {2013},
}

@ARTICLE{blazevski14:_hyper_ellip_trans_barrier_three,
  AUTHOR       = {Blazevski, Daniel and Haller, George},
  DOI          = {10.1016/j.physd.2014.01.007},
  EPRINT       = {1306.6497},
  EPRINTCLASS  = {math.DS},
  EPRINTTYPE   = {arXiv},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  MONTH        = {4},
  PAGES        = {46-62},
  TITLE        = {Hyperbolic and Elliptic Transport Barriers in Three-Dimensional Unsteady Flows},
  VOLUME       = {273--274},
  YEAR         = {2014},
}

@ARTICLE{farazmand14:_shearless,
  AUTHOR       = {Farazmand, Mohammad Mehdi and Blazevski, Daniel and Haller, George},
  DOI          = {10.1016/j.physd.2014.03.008},
  EPRINT       = {1308.6136},
  EPRINTCLASS  = {math.DS},
  EPRINTTYPE   = {arXiv},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  MONTH        = {6},
  PAGES        = {44-57},
  TITLE        = {Shearless transport barriers in unsteady two-dimensional flows and maps},
  VOLUME       = {278--279},
  YEAR         = {2014},
}

@THESIS{lekien03:_time,
  AUTHOR      = {Lekien, François},
  INSTITUTION = {California Institute of Technology},
  TITLE       = {Time-dependent dynamical systems and geophysical flows},
  TYPE        = {phdthesis},
  URL         = {http://resolver.caltech.edu/CaltechETD:etd-04082003-180353},
  YEAR        = {2003},
}

@THESIS{toit10:_trans,
  ANNOTATION  = {Newman - Software for computing FTLE in geophysical applications},
  AUTHOR      = {du Toit, Philip C.},
  INSTITUTION = {California Institute of Technology},
  TITLE       = {Transport and separatrices in time-dependent flows},
  TYPE        = {phdthesis},
  URL         = {http://resolver.caltech.edu/CaltechTHESIS:10072009-165901284},
  YEAR        = {2010},
}

@INCOLLECTION{ameli14:_devel_effic_flexib_pipel_lagran,
  AUTHOR    = {Ameli, Siavash and Desai, Yogin and Shadden, Shawn C.},
  BOOKTITLE = {Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications},
  CROSSREF  = {bremer14:_topol_method_data_analy_visual},
  DOI       = {10.1007/978-3-319-04099-8\_13},
  PAGES     = {201-215},
  PUBLISHER = {Springer},
  TITLE     = {Development of an Efficient and Flexible Pipeline for Lagrangian Coherent Structure Computation},
  YEAR      = {2014},
}

@BOOK{truesdell04,
  AUTHOR    = {Truesdell, Clifford Ambrose and Noll, Walter},
  DOI       = {10.1007/978-3-662-13183-1},
  EDITION   = {third},
  PUBLISHER = {Springer},
  TITLE     = {The non-linear field theories of mechanics},
  YEAR      = {2004},
}

@INPROCEEDINGS{delmarcelle94,
  AUTHOR    = {Delmarcelle, Thierry and Hesselink, Lambertus},
  BOOKTITLE = {Visualization, 1994., Visualization '94, Proceedings., IEEE Conference on},
  DOI       = {10.1109/VISUAL.1994.346326},
  MONTH     = {10},
  PAGES     = {140-147},
  TITLE     = {The topology of symmetric, second-order tensor fields},
  YEAR      = {1994},
}

@BOOK{arnold89:_mathem,
  AUTHOR    = {Arnold, Vladimir Igorevich},
  DOI       = {10.1007/978-1-4757-2063-1},
  PUBLISHER = {Springer},
  SERIES    = {Graduate Texts in Mathematics},
  TITLE     = {Mathematical Methods of Classical Mechanics},
  VOLUME    = {60},
  YEAR      = {1989},
}

@ARTICLE{karrasch14:_autom_lagran,
  AUTHOR       = {Karrasch, Daniel and Huhn, Florian and Haller, George},
  DOI          = {10.1098/rspa.2014.0639},
  EPRINT       = {1404.3109},
  EPRINTCLASS  = {math.DS},
  EPRINTTYPE   = {arXiv},
  JOURNALTITLE = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  MONTH        = {1},
  NUMBER       = {2173},
  TITLE        = {Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows},
  VOLUME       = {471},
  YEAR         = {2014},
}

@ARTICLE{shadden05:_defin_lagran_lyapun,
  AUTHOR       = {Shadden, Shawn C. and Lekien, Francois and Marsden, Jerrold Eldon},
  DOI          = {10.1016/j.physd.2005.10.007},
  JOURNALTITLE = {Physica D: Nonlinear Phenomena},
  MONTH        = {12},
  NUMBER       = {3--4},
  PAGES        = {271--304},
  TITLE        = {Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows},
  VOLUME       = {212},
  YEAR         = {2005},
}

@ARTICLE{castilloNegrete93:_chaot_rossb,
  AUTHOR       = {del-Castillo-Negrete, Diego and Morrison, Philip J.},
  DOI          = {10.1063/1.858639},
  JOURNALTITLE = {Physics of Fluids A},
  MONTH        = {4},
  NUMBER       = {4},
  PAGES        = {948-965},
  TITLE        = {Chaotic transport by Rossby waves in shear flow},
  VOLUME       = {5},
  YEAR         = {1993},
}

@ARTICLE{conti12:_gpu_apu_finit_time_lyapun_expon,
  AUTHOR       = {Conti, Christian and Rossinelli, Diego and Koumoutsakos, Petros},
  DOI          = {10.1016/j.jcp.2011.10.032},
  JOURNALTITLE = {Journal of Computational Physics},
  MONTH        = {3},
  NUMBER       = {5},
  PAGES        = {2229-2244},
  TITLE        = {GPU and APU computations of Finite Time Lyapunov Exponent fields},
  VOLUME       = {231},
  YEAR         = {2012},
}

@ARTICLE{miron12:_anisot_lagran_coher_struc,
  AUTHOR       = {Miron, Philippe and Vétel, Jérôme and Garon, André and Delfour, Michel and El Hassan, Mouhammad},
  DOI          = {10.1016/j.jcp.2012.06.015},
  JOURNALTITLE = {Journal of Computational Physics},
  MONTH        = {8},
  NUMBER       = {19},
  PAGES        = {6419-6437},
  TITLE        = {Anisotropic mesh adaptation on Lagrangian Coherent Structures},
  VOLUME       = {231},
  YEAR         = {2012},
}

@ARTICLE{olascoaga12:_forec,
  ABSTRACT     = {The lack of reliable forecasts for the spread of oceanic and atmospheric contamination hinders the effective protection of the ecosystem, society, and the economy from the fallouts of environmental disasters. The consequences can be dire, as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010. We present a methodology to predict major short-term changes in environmental contamination patterns, such as oil spills in the ocean and ash clouds in the atmosphere. Our approach is based on new mathematical results on the objective (frame-independent) identification of key material surfaces that drive tracer mixing in unsteady, finite-time flow data. Some of these material surfaces, known as Lagrangian coherent structures (LCSs), turn out to admit highly attracting cores that lead to inevitable material instabilities even under future uncertainties or unexpected perturbations to the observed flow. These LCS cores have the potential to forecast imminent shape changes in the contamination pattern, even before the instability builds up and brings large masses of water or air into motion. Exploiting this potential, the LCS-core analysis developed here provides a model-independent forecasting scheme that relies only on already observed or validated flow velocities at the time the prediction is made. We use this methodology to obtain high-precision forecasts of two major instabilities that occurred in the shape of the Deepwater Horizon oil spill. This is achieved using simulated surface currents preceding the prediction times and assuming that the oil behaves as a passive tracer.},
  AUTHOR       = {Olascoaga, María J. and Haller, George},
  DOI          = {10.1073/pnas.1118574109},
  JOURNALTITLE = {Proceedings of the National Academy of Sciences},
  NUMBER       = {13},
  PAGES        = {4738-4743},
  TITLE        = {Forecasting sudden changes in environmental pollution patterns},
  VOLUME       = {109},
  YEAR         = {2012},
}