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Physica. D, ISSN 0167-2789, 2009, Volume 238, Issue 16, pp. 1507 - 1523
.... For dissipative chaotic flows such a decomposition into invariant regions does not exist; instead, the transfer operator approach detects almost-invariant sets... 
Finite-time Lyapunov exponent | Coherent structure | Invariant manifold | Transport | Almost-invariant set | Transfer operator | FIELDS | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | ATTRACTORS | CHAOTIC STREAMLINES | MAPS | OPERATOR | FLUID-FLOWS | DYNAMICS | APERIODIC FLOWS | CIRCUIT
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2013, Volume 18, Issue 5, pp. 1106 - 1126
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2010, Volume 239, Issue 16, pp. 1527 - 1541
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1089-7682, 2010, Volume 20, Issue 4, pp. 043116 - 043116-10
.... We develop a novel probabilistic methodology based upon transfer operators that automatically detect maximally coherent sets... 
MATHEMATICS, APPLIED | MAPS | MANIFOLDS | FLOWS | POLAR VORTEX | PHYSICS, MATHEMATICAL | ALMOST-INVARIANT SETS | Mathematics - Dynamical Systems
Journal Article
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 2017, Volume 16, Issue 1, pp. 120 - 138
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 03/2017, Volume 27, Issue 3, p. 035804
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport... 
GRAPH | MATHEMATICS, APPLIED | FLUID | ALGORITHM | DYNAMICS | BARRIERS | MANIFOLDS | FLOWS | PHYSICS, MATHEMATICAL | ALMOST-INVARIANT SETS | Mathematics - Dynamical Systems
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2005, Volume 200, Issue 3, pp. 205 - 219
.... Dellnitz, Detecting and locating near-optimal almost-invariant sets and cycles, SIAM J. Sci. Comput. 24 (6) (2003) 1839–1863], focussing on a statistical description... 
Macrostructure | Transitivity | Almost-invariant | Meta-stable | MATHEMATICS, APPLIED | macrostructure | PHYSICS, MULTIDISCIPLINARY | transitivity | meta-stable | almost-invariant | PHYSICS, MATHEMATICAL
Journal Article
Chaos, ISSN 1054-1500, 2015, Volume 25, Issue 8, p. 087409
Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself... 
MATHEMATICS, APPLIED | TRANSPORT | ALMOST-INVARIANT | PHYSICS, MATHEMATICAL
Journal Article
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 2017, Volume 17, Issue 2, pp. 1891 - 1924
.... Finite-time coherent sets are regions of the flow that minimally mix with the remainder of the flow domain over the finite period of time considered... 
Finite element method | Mixing | Lagrangian coherent structure | Finite-time coherent sets | Isoperimetric theory | Dynamic Laplacian | isoperimetric theory | MATHEMATICS, APPLIED | TRANSPORT | finite element method | dynamic Laplacian | DYNAMICAL-SYSTEMS | mixing | finite-time coherent sets | FLOWS | PHYSICS, MATHEMATICAL | ALMOST-INVARIANT SETS
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 12/2017, Volume 360, pp. 36 - 45
We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent... 
Lagrangian data | Coherent structures | Data assimilation | SURFACE CIRCULATION | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | SEQUENTIAL MONTE-CARLO | PARTICLE FILTER | PHYSICS, MATHEMATICAL | ALMOST-INVARIANT SETS | Tracers (Biology) | Analysis | Physics - Atmospheric and Oceanic Physics
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 11/2010, Volume 82, Issue 5, p. 056311
The "edge" of the Antarctic polar vortex is known to behave as a barrier to the meridional (poleward) transport of ozone during the austral winter. This... 
TRANSPORT | APPROXIMATION | MAPS | PHYSICS, FLUIDS & PLASMAS | DYNAMICS | OZONE | PHYSICS, MATHEMATICAL | ALMOST-INVARIANT SETS
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 03/2018, Volume 25, Issue 1, pp. 41 - 46
For certain groups of isometric transformations of the Euclidean plane , negligible and absolutely negligible subsets of this plane are considered and compared... 
Euclidean plane | 28D05 | negligible set | 28A05 | absolutely negligible set | almost invariant set | MATHEMATICS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2008, Volume 136, Issue 2, pp. 687 - 697
Journal Article
Physica. D, ISSN 0167-2789, 2012, Volume 241, Issue 15, pp. 1255 - 1269
... to: (a) identify invariant sets in the state space, and (b) to form coherent structures by aggregating invariant sets that are similar across multiple spatial scales... 
Ergodic partition | Coherent structures | Diffusion modes | Dynamical systems | Trajectory averages | 3-DIMENSIONAL FLUID-FLOWS | DEFINITION | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | DIFFUSION MAPS | TIME | EIGENFUNCTIONS | PHYSICS, MATHEMATICAL | HARMONIC-ANALYSIS | SYSTEMS | ALMOST-INVARIANT SETS | Analysis | Algorithms | Quotients | Mathematical analysis | Coherence | Trajectories | Diffusion | Invariants | Ergodic processes
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 05/2003, Volume 24, Issue 6, pp. 1839 - 1863
.... Rather than characterizing dynamical behavior at the level of trajectories, we consider following the evolution of sets... 
Almost-cycle | Graph partitioning | Almost-invariant set | Minimal cut | Maximal cut | Laplacian matrix | Fiedler vector | Macrostructure | MATHEMATICS, APPLIED | almost-invariant set | minimal cut | macrostructure | BOUNDS | EIGENVECTORS | maximal cut | ALGORITHM | almost-cycle | graph partitioning
Journal Article