Analytical Description of Optimally Time-Dependent Modes for Reduced-Order Modeling of Transient Instabilities

The optimally time-dependent (OTD) modes form a time-evolving orthonormal basis that captures directions in phase space associated with transient and persistent instabilities. In the original formu...

[1]  Andrew J Majda,et al.  Conceptual dynamical models for turbulence , 2014, Proceedings of the National Academy of Sciences.

[2]  T. Sapsis,et al.  Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents. , 2017, Chaos.

[3]  H. Kantz,et al.  Extreme Events in Nature and Society , 2006 .

[4]  J. Carr Applications of Centre Manifold Theory , 1981 .

[5]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[6]  Pierre F. J. Lermusiaux,et al.  Dynamically orthogonal field equations for continuous stochastic dynamical systems , 2009 .

[7]  Yves Pomeau,et al.  Prediction of catastrophes: an experimental model. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  A. B. Potapov,et al.  On the concept of stationary Lyapunov basis , 1998 .

[9]  William G. Hoover,et al.  Dense‐fluid Lyapunov spectra via constrained molecular dynamics , 1987 .

[10]  Kunimochi Sakamoto,et al.  Invariant manifolds in singular perturbation problems for ordinary differential equations , 1990, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[11]  Antonio Politi,et al.  Covariant Lyapunov vectors , 2012, 1212.3961.

[12]  H. Posch,et al.  Lyapunov instability of dense Lennard-Jones fluids. , 1988, Physical review. A, General physics.

[13]  D. Solli,et al.  Recent progress in investigating optical rogue waves , 2013 .

[14]  I. Shimada,et al.  A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems , 1979 .

[15]  Francesco Fedele,et al.  On Oceanic Rogue Waves , 2015, 1501.03370.

[16]  Christoph Dellago,et al.  Time-reversal symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Local Gram–Schmidt and covariant Lyapunov vectors and exponents for three harmonic oscillator problems , 2011, 1106.2367.

[18]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[19]  Mohammad Farazmand,et al.  Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems. , 2016, Physical review. E.

[20]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[21]  Ferdinand Verhulst,et al.  A Mechanism for Atmospheric Regime Behavior , 2004 .

[22]  Neil Fenichel Geometric singular perturbation theory for ordinary differential equations , 1979 .

[23]  H. Chaté,et al.  Characterizing dynamics with covariant Lyapunov vectors. , 2007, Physical review letters.

[24]  G. Lapeyre,et al.  Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. , 2002, Chaos.

[25]  U. Frisch FULLY DEVELOPED TURBULENCE AND INTERMITTENCY , 1980 .

[26]  J. Charney,et al.  Multiple Flow Equilibria in the Atmosphere and Blocking , 1979 .

[27]  G. Benettin,et al.  Kolmogorov Entropy and Numerical Experiments , 1976 .

[28]  H. Babaee,et al.  A minimization principle for the description of modes associated with finite-time instabilities , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[29]  H. Posch,et al.  Covariant Lyapunov vectors for rigid disk systems , 2010, Chemical physics.

[30]  Anthony B. Costa,et al.  Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium , 2013, Proceedings of the National Academy of Sciences.

[31]  J. R. E. O’Malley Singular perturbation methods for ordinary differential equations , 1991 .

[32]  Neil Fenichel Persistence and Smoothness of Invariant Manifolds for Flows , 1971 .

[33]  R. Vautard,et al.  A GUIDE TO LIAPUNOV VECTORS , 2022 .

[34]  A. Timmermann,et al.  Increasing frequency of extreme El Niño events due to greenhouse warming , 2014 .

[35]  Eugenia Kalnay,et al.  Ensemble Forecasting at NMC: The Generation of Perturbations , 1993 .

[36]  Themistoklis P. Sapsis,et al.  Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model , 2014, 1401.3397.

[37]  Wiesel Continuous time algorithm for Lyapunov exponents. I. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  Ulrich Parlitz,et al.  Theory and Computation of Covariant Lyapunov Vectors , 2011, Journal of Nonlinear Science.

[39]  G. Radons,et al.  Comparison between covariant and orthogonal Lyapunov vectors. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Steven A. Orszag,et al.  Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method , 1987 .