336 citations · 3.5k across the 72 of their papers we have counts for
6 papers · 2 filters
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…
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…