A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds

DOI10.1007/s00332-017-9397-yzbMath1477.37092arXiv1610.01128OpenAlexW2528596067MaRDI QIDQ2022702

Gary Froyland, Eric Kwok

Publication date: 29 April 2021

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.01128

zbMATH Keywords

transfer operatorLagrangian coherent structureweighted Riemannian manifolddynamic isoperimetric problemdynamic Laplace operatorfinite-time coherent set

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Ergodicity, mixing, rates of mixing (37A25) Turbulent transport, mixing (76F25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Approximation methods and numerical treatment of dynamical systems (37M99) Transport equations (35Q49)

Related Items (7)

DYNAMIC ISOPERIMETRY ON GRAPHS AND WEIGHTED RIEMANNIAN MANIFOLDS ⋮ Detecting the birth and death of finite‐time coherent sets ⋮ A geometric heat-flow theory of Lagrangian coherent structures ⋮ Spatiotemporal analysis using Riemannian composition of diffusion operators ⋮ Barriers to the Transport of Diffusive Scalars in Compressible Flows ⋮ Linear response for the dynamic Laplacian and finite-time coherent sets ⋮ How sensitive are Lagrangian coherent structures to uncertainties in data?

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost-invariant sets and invariant manifolds - connecting probabilistic and geometric descriptions of coherent structures in flows
• Stable manifolds and predictability of dynamical systems
• Nonlinear potential theory and weighted Sobolev spaces
• Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains
• Statistically optimal almost-invariant sets
• Sobolev spaces on Riemannian manifolds
• The volume of a small geodesic ball of a Riemannian manifold
• Advection-diffusion in Lagrangian coordinates
• On Riemannian manifolds admitting a function whose gradient is of constant norm
• An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems
• A geometric heat-flow theory of Lagrangian coherent structures
• A multiscale measure for mixing
• Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
• Coherent Lagrangian vortices: the black holes of turbulence
• Using multiscale norms to quantify mixing and transport
• Dynamic isoperimetry and the geometry of Lagrangian coherent structures
• THE DYNAMICAL SYSTEMS APPROACH TO LAGRANGIAN TRANSPORT IN OCEANIC FLOWS
• An analytical study of transport, mixing and chaos in an unsteady vortical flow
• The development of chaotic advection
• Lagrangian coherent structures from approximate velocity data
• Coherent structures and isolated spectrum for Perron–Frobenius cocycles
• Symplectic maps, variational principles, and transport
• A note on the isoperimetric constant
• Elliptic Partial Differential Equations of Second Order
• On the Approximation of Complicated Dynamical Behavior
• On the isolated spectrum of the Perron-Frobenius operator
• On fast computation of finite-time coherent sets using radial basis functions
• Robust FEM-Based Extraction of Finite-Time Coherent Sets Using Scattered, Sparse, and Incomplete Trajectories
• Transport in time-dependent dynamical systems: Finite-time coherent sets
• Global variational approach to elliptic transport barriers in three dimensions
• Riemannian geometry and geometric analysis

This page was built for publication: A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds