Reduction and reconstruction for self-similar dynamical systems

No abstract is available for this paper.

• Publication year

  2002

• Venue

  Nonlinearity

• Publication date

  2002-11-01

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/0951-7715/16/4/304
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Focusing revisited: a renormalization/bifurcation approach

  2003cited by this paper
• Effective bifurcation analysis: a time-stepper-based approach

  2002cited by this paper
• 'Coarse' integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods

  2002cited by this paper
• Going with the Flow: a Lagrangian approach to self-similar dynamics and its consequences

  2001influential reference
• The geometric integration of scale-invariant ordinary and partial differential equations

  2001cited by this paper
• Reconstruction equations and the Karhunen—Loéve expansion for systems with symmetry

  2000influential reference
• An Adaptive Newton-Picard Algorithm with Subspace Iteration for Computing Periodic Solutions

  1998cited by this paper
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks

  1997cited by this paper
• Scaling: Self-similarity and intermediate asymptotics

  1996cited by this paper
• Introduction to mechanics and symmetry

  1994cited by this paper
• Lectures on Mechanics

  1993cited by this paper
• Reconstructing phase space from PDE simulations

  1992influential reference
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS

  1991cited by this paper
• Reduction, Symmetry, And Phases In Mechanics

  1990cited by this paper
• Applications of lie groups to differential equations

  1990cited by this paper
• Nature of wave collapse in the critical case

  1988cited by this paper
• APPLICATIONS OF LIE GROUPS TO DIFFERENTIAL EQUATIONS (Graduate Texts in Mathematics)

  1987cited by this paper
• Focusing singularity of the cubic Schrödinger equation.

  1986cited by this paper
• Applications of Lie Groups to Differential Equations

  1986cited by this paper
• Hidden chiral symmetry in the presence of mass terms.

  1986cited by this paper
• Group analysis of differential equations

  1982cited by this paper
• Group analysis of differential equations

  1982cited by this paper
• Linear and Nonlinear Waves. By G. B. WHITHAM. Wiley-Interscience, 1974. 636 pp. $625.75

  1978cited by this paper
• Lectures On Phase Transitions And The Renormalization Group

  1972cited by this paper
• Lie Groups

  year unknowninfluential reference

• High-order empirical interpolation methods for real-time solution of parametrized nonlinear PDEs

  2026cites this paper
• Hilbert Proper Orthogonal Decomposition: a tool for educing advective wavepackets from flow field data

  2025cites this paper
• Petrov–Galerkin Dynamical Low Rank Approximation: SUPG stabilisation of advection-dominated problems

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• Model order reduction via Lie groups

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• Symmetry-reduced model reduction of shift-equivariant systems via operator inference

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• Feature-guided sampling strategy for adaptive model order reduction of convection-dominated problems

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• Petrov-Galerkin Dynamical Low Rank Approximation:SUPG stabilisation of advection-dominated problems

  2024cites this paper
• Forecasting high-dimensional spatio-temporal systems from sparse measurements

  2024cites this paper
• Generative Reduced Basis Method

  2024cites this paper
• Approximation of translation invariant Koopman operators for coupled non-linear systems.

  2024cites this paper
• A reference frame-based microgrid primary control for ensuring global convergence to a periodic orbit

  2024cites this paper
• A robust shifted proper orthogonal decomposition: Proximal methods for decomposing flows with multiple transports

  2024cites this paper
• Data-driven state-space and Koopman operator models of coherent state dynamics on invariant manifolds

  2023cites this paper
• Model Reduction on Manifolds: A differential geometric framework

  2023cites this paper
• Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles

  2022cites this paper
• Front Transport Reduction for Complex Moving Fronts

  2022cites this paper
• Reduced basis methods for time-dependent problems

  2022cites this paper
• Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference

  2022cites this paper
• Symmetry-Aware Autoencoders: s-PCA and s-nlPCA

  2021cites this paper
• Permuted proper orthogonal decomposition for analysis of advecting structures

  2021cites this paper
• Unfolding spatiotemporal dynamics through symmetry reduction based on orbit topology.

  2021cites this paper
• A learning-based projection method for model order reduction of transport problems

  2021cites this paper
• Evolution of Nonlinear Reduced-Order Solutions for PDEs with Conserved Quantities

  2021cites this paper
• Optimization-based modal decomposition for systems with multiple transports

  2020cites this paper
• Lagrangian Reduced Order Modeling of Finite Time Lyapunov Exponents

  2020cites this paper
• Approximation of Traveling Waves by Splitting Methods

  2020cites this paper
• Projection-based model reduction with dynamically transformed modes

  2019cites this paper
• Nonlinear Galerkin Model Reduction for Systems with Multiple Transport Velocities

  2019cites this paper
• Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena

  2019cites this paper
• Overcoming slowly decaying Kolmogorov n-width by transport maps: application to model order reduction of fluid dynamics and fluid-structure interaction problems

  2019cites this paper
• A characteristic dynamic mode decomposition

  2019cites this paper
• Model Order Reduction Framework for Problems with Moving Discontinuities

  2019cites this paper
• Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents

  2018cites this paper
• Topology reconstruction of dynamical networks via constrained Lyapunov equations

  2018cites this paper
• Model reduction for convective problems: formulation and application

  2018cites this paper
• Computation and stability of waves in equivariant evolution equations

  2018cites this paper
• Reduced-order modeling of fluids systems, with applications in unsteady aerodynamics

  2017cites this paper
• Revisiting Diffusion: Self-similar Solutions and the $t^{-1/2}$ Decay in Initial and Initial-Boundary Value Problems

  2017cites this paper
• Dynamics of patterns in equivariant Hamiltonian partial differential equations

  2017cites this paper
• Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows

  2017cites this paper
• Model Order Reduction for Stochastic Dynamical Systems with Continuous Symmetries

  2017cites this paper
• Dimensional Splitting of Hyperbolic Partial Differential Equations Using the Radon Transform

  2017cites this paper
• Generating Random Earthquake Events for Probabilistic Tsunami Hazard Assessment

  2016cites this paper
• Freezing Traveling and Rotating Waves in Second Order Evolution Equations

  2016cites this paper
• Computation and Stability of Traveling Waves in Second Order Evolution Equations

  2016cites this paper
• A Lagrangian Dynamic Mode Decomposition

  2016cites this paper
• Freezing similarity solutions in the multi-dimensional Burgers equation

  2016cites this paper
• An IMEX-RK scheme for capturing similarity solutions in the multidimensional Burgers’s equation

  2016cites this paper
• A characteristic dynamic mode decomposition

  2016cites this paper
• On the Symmetrization in POD-Galerkin Model for Linearized Compressible Flows

  2016cites this paper
• Identifying the Flow Physics and Modeling Transient Forces on Two-Dimensional Wings

  2016cites this paper
• Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures.

  2016cites this paper
• A General Framework for Stochastic Traveling Waves and Patterns, with Application to Neural Field Equations

  2015cites this paper
• Two-dimensional traveling waves arising from planar front interaction in a three-species competition-diffusion system

  2015cites this paper
• Two-dimensional traveling waves arising from planar front interaction in a three-species competition-diffusion system

  2015cites this paper
• An adjoint-based approach for finding invariant solutions of Navier–Stokes equations

  2015cites this paper
• The shifted proper orthogonal decomposition

  2015cites this paper
• The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena

  2015cites this paper
• Relative periodic orbits form the backbone of turbulent pipe flow

  2015cites this paper
• Data-Driven Methods for Interactive Simulation of Complex Phenomena

  2014cites this paper
• Hopf fibrations for turbulent pipe flows

  2014cites this paper
• Stability and Computation of Dynamic Patterns in PDEs

  2014cites this paper
• Symmetry reduction of turbulent pipe flows

  2014cites this paper
• Comoving frames and symmetry-related motions in parallel shear flows

  2014influential citation
• Numerical Bifurcation Theory for High-Dimensional Neural Models

  2014cites this paper
• Coarse graining, dynamic renormalization and the kinetic theory of shock clustering

  2014cites this paper
• Periodic orbit analysis of a system with continuous symmetry--A tutorial.

  2014cites this paper
• Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing

  2013cites this paper
• Symmetry related dynamics in parallel shear flows

  2013influential citation
• Non-polynomial Galerkin projection on deforming meshes

  2013cites this paper
• Low-dimensional models for compressible temporally developing shear layers

  2013cites this paper
• Relativity for Cyclists

  2013cites this paper
• WAVES IN RANDOM NEURAL MEDIA

  2012cites this paper
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  2012cites this paper
• Stability and Freezing of Nonlinear Waves in First Order Hyperbolic PDEs

  2012cites this paper
• Computing Stochastic Traveling Waves

  2012cites this paper
• Cartography of high-dimensional flows: a visual guide to sections and slices.

  2012cites this paper
• Stability and Freezing of Nonlinear Waves in First Order Hyperbolic PDEs

  2012cites this paper
• Model Order Reduction of Nonlinear Dynamical Systems

  2011cites this paper
• Galerkin Models Enhancements for Flow Control

  2011cites this paper
• Numerical Bifurcation Study of Superconducting Patterns on a Square

  2011cites this paper
• A linear stability theory on time-invariant and time-dependent spatial domains with symmetry: the drop splash problem

  2011cites this paper
• Reduction of continuous symmetries of chaotic flows by the method of slices

  2011cites this paper
• Approximating travelling waves by equilibria of non-local equations

  2011cites this paper
• State Estimation for diffusion systems using a Karhunen-Loeve-Galerkin Reduced-Order Model

  2010cites this paper
• Freezing Stochastic Travelling Waves

  2010cites this paper
• Reducing continuous symmetries with linear slices

  2010influential citation
• Continuous symmetry reduction and return maps for high-dimensional flows

  2010influential citation
• Low-Dimensional Modeling for Spatially Developing Free Shear Layers

  2009cites this paper
• Low-dimensional models of a temporally evolving free shear layer

  2009cites this paper
• Dynamics of Patterns in Nonlinear Equivariant PDEs

  2009cites this paper
• RECURRENT SPATIO-TEMPORAL STRUCTURES IN PRESENCE OF CONTINUOUS SYMMETRIES

  2009cites this paper
• Reduction methods for feedback stabilization of fluid flows

  2009cites this paper
• Recurrent spatio-temporal structures in presence of continuous symmetries

  2009cites this paper
• Numerical Approximation of Relative Equilibria for Equivariant PDEs

  2008cites this paper
• Low-dimensional representations for the simulation and control of complex dynamics

  2008cites this paper
• Freezing Multipulses and Multifronts

  2008influential citation
• A simple example using equation-free computation.

  2008cites this paper
• The Effect of Freezing and Discretization to the Asymptotic Stability of Relative Equilibria

  2008cites this paper
• Numerical computation of relative equilibria with Femlab

  2007cites this paper