336 citations · 3.5k across the 72 of their papers we have counts for
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Exact Model Reduction by a Slow-Fast Decomposition of Nonlinear Mechanical Systems
George Haller, Sten Ponsioen
We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the most flexible degrees of freedom.…
Efficient Computation of Null-Geodesic with Applications to Coherent Vortex Detection
Mattia Serra, George Haller
Recent results suggest that boundaries of coherent fluid vortices (elliptic coherent structures) can be identified as closed null-geodesics of appropriate Lorentzian metrics define…
Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations
Robert Szalai, David Ehrhardt, George Haller
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots…
Level set formulation of two-dimensional Lagrangian vortex detection methods
Alireza Hadjighasem, George Haller
We propose here the use of the variational level set methodology to capture Lagrangian vortex boundaries in 2D unsteady velocity fields. This method reformulates earlier approaches…
Forecasting Long-Lived Lagrangian Vortices from their Objective Eulerian Footprints
Mattia Serra, George Haller
We derive a non-dimensional metric to quantify the expected Lagrangian persistence of objectively defined Eulerian vortices in two-dimensional unsteady flows. This persistence metr…
An Autonomous Dynamical System Captures all LCSs in Three-Dimensional Unsteady Flows
David Oettinger, George Haller
Lagrangian coherent structures (LCSs) are material surfaces that shape finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation propertie…
Nonlinear normal modes and spectral submanifolds: Existence, uniqueness and use in model reduction
George Haller, Sten Ponsioen
We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-depe…