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

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

Reviews of modern physics, ISSN 1539-0756, 2017, Volume 89, Issue 2, pp. 1 - 66

This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the...

Physics and Astronomy(all) | STOKES-FLOW | TIME LYAPUNOV EXPONENTS | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | TRANSPORT ENHANCEMENT | BIOLOGICAL-ACTIVITY | FLUID-MECHANICS | LAGRANGIAN COHERENT STRUCTURES | ALMOST-INVARIANT SETS | VOLUME-PRESERVING MAPS | PASSIVE SCALARS

Physics and Astronomy(all) | STOKES-FLOW | TIME LYAPUNOV EXPONENTS | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | TRANSPORT ENHANCEMENT | BIOLOGICAL-ACTIVITY | FLUID-MECHANICS | LAGRANGIAN COHERENT STRUCTURES | ALMOST-INVARIANT SETS | VOLUME-PRESERVING MAPS | PASSIVE SCALARS

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2013, Volume 18, Issue 5, pp. 1106 - 1126

â–º A new set-oriented FTLE definition links probability densities and curve stretching...

Transport and mixing in fluids | Phase space transport | Lagrangian coherent structures | Hyperbolic invariant manifolds | Finite time Lyapunov exponents | Almost invariant sets | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ALMOST-INVARIANT SETS | Tropospheric circulation | Mechanical engineering

Transport and mixing in fluids | Phase space transport | Lagrangian coherent structures | Hyperbolic invariant manifolds | Finite time Lyapunov exponents | Almost invariant sets | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ALMOST-INVARIANT SETS | Tropospheric circulation | Mechanical engineering

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2010, Volume 239, Issue 16, pp. 1527 - 1541

.... In the autonomous setting, such objects are variously known as almost-invariant sets, metastable sets, persistent patterns, or strange eigenmodes, and have proved to be important in a variety of applications...

Coherent set | Almost-invariant set | Lyapunov exponent | Nonautonomous dynamical system | Oseledets subspace | Strange eigenmode | Persistent pattern | Perronâ€“Frobenius operator | Metastable set | Perron-Frobenius operator | MATHEMATICS, APPLIED | LYAPUNOV EXPONENTS | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | ULAMS CONJECTURE | PHYSICS, MATHEMATICAL | TRANSPORT | MAPS | OPERATOR | MANIFOLDS | FLOWS | SPECTRUM | ALMOST-INVARIANT SETS | Numerical analysis | Tracking | Disperse | Coherence | Mathematical models | Autonomous | Dynamical systems | Formalism | Mathematics - Dynamical Systems

Coherent set | Almost-invariant set | Lyapunov exponent | Nonautonomous dynamical system | Oseledets subspace | Strange eigenmode | Persistent pattern | Perronâ€“Frobenius operator | Metastable set | Perron-Frobenius operator | MATHEMATICS, APPLIED | LYAPUNOV EXPONENTS | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | ULAMS CONJECTURE | PHYSICS, MATHEMATICAL | TRANSPORT | MAPS | OPERATOR | MANIFOLDS | FLOWS | SPECTRUM | ALMOST-INVARIANT SETS | Numerical analysis | Tracking | Disperse | Coherence | Mathematical models | Autonomous | Dynamical systems | Formalism | Mathematics - Dynamical Systems

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

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

In this article, we develop a set-oriented numerical methodology which allows us to perform uncertainty quantification (UQ...

Uncertainty quantification | Attractors | Set-oriented numerical methods | MATHEMATICS, APPLIED | uncertainty quantification | APPROXIMATION | POLYNOMIAL CHAOS | set-oriented numerical methods | MANIFOLDS | attractors | PHYSICS, MATHEMATICAL | MULTILEVEL SUBDIVISION TECHNIQUES | ALMOST-INVARIANT SETS | Mathematics - Dynamical Systems

Uncertainty quantification | Attractors | Set-oriented numerical methods | MATHEMATICS, APPLIED | uncertainty quantification | APPROXIMATION | POLYNOMIAL CHAOS | set-oriented numerical methods | MANIFOLDS | attractors | PHYSICS, MATHEMATICAL | MULTILEVEL SUBDIVISION TECHNIQUES | ALMOST-INVARIANT SETS | Mathematics - Dynamical Systems

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

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) 1839â€“1863], focussing on a statistical description...

Macrostructure | Transitivity | Almost-invariant | Meta-stable | MATHEMATICS, APPLIED | macrostructure | PHYSICS, MULTIDISCIPLINARY | transitivity | meta-stable | almost-invariant | PHYSICS, MATHEMATICAL

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

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

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

11.
Full Text
A coherent structure approach for parameter estimation in Lagrangian Data Assimilation

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

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

TRANSPORT | APPROXIMATION | MAPS | PHYSICS, FLUIDS & PLASMAS | DYNAMICS | OZONE | PHYSICS, MATHEMATICAL | ALMOST-INVARIANT SETS

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 2013, Volume 51, Issue 1, pp. 223 - 247

...., fixed points of an associated transfer operator. In addition, global slowly mixing structures, such as almost-invariant sets, which partition phase space...

Approximation | Spectral theory | Vector fields | Eigenvalues | Eigenfunctions | Textual collocation | Trajectories | Eigenvectors | Density | Spectral methods | Escape rate | Spectral method | Ulam's method | Infinitesimal generator | Transfer operator | Almostinvariant set | MATHEMATICS, APPLIED | APPROXIMATION | spectral method | EXPANDING MAPS | transfer operator | almost-invariant set | escape rate | DYNAMICAL-SYSTEMS | infinitesimal generator | MANIFOLDS | OPERATORS | ALMOST-INVARIANT SETS | Operators | Discretization | Estimating | Generators | Dynamical systems | Invariants | Mathematics - Numerical Analysis

Approximation | Spectral theory | Vector fields | Eigenvalues | Eigenfunctions | Textual collocation | Trajectories | Eigenvectors | Density | Spectral methods | Escape rate | Spectral method | Ulam's method | Infinitesimal generator | Transfer operator | Almostinvariant set | MATHEMATICS, APPLIED | APPROXIMATION | spectral method | EXPANDING MAPS | transfer operator | almost-invariant set | escape rate | DYNAMICAL-SYSTEMS | infinitesimal generator | MANIFOLDS | OPERATORS | ALMOST-INVARIANT SETS | Operators | Discretization | Estimating | Generators | Dynamical systems | Invariants | Mathematics - Numerical Analysis

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

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

... \Gamma on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e...

Ergodic theory | Equivalence relation | Mathematical vectors | Central limit theorem | Mathematical theorems | Random variables | Generalized bernoulli shifts | E0-ergodicity | Amenable actions | Almost invariant sets | amenable actions | MATHEMATICS | almost invariant sets | MATHEMATICS, APPLIED | generalized Bernoulli shifts | E-0-ergodicity

Ergodic theory | Equivalence relation | Mathematical vectors | Central limit theorem | Mathematical theorems | Random variables | Generalized bernoulli shifts | E0-ergodicity | Amenable actions | Almost invariant sets | amenable actions | MATHEMATICS | almost invariant sets | MATHEMATICS, APPLIED | generalized Bernoulli shifts | E-0-ergodicity

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

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

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