Coarse-Graining Autonomous ODE Systems by Inducing a Separation of Scales: Practical Strategies and Mathematical Questions

DOI10.1177/1081286508100972zbMath1197.74015OpenAlexW2028732883MaRDI QIDQ3162537

Amit Acharya

Publication date: 19 October 2010

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1081286508100972

zbMATH Keywords

time-averagingcomputational coarse-graining methodologysequential multiscale modeling

Mathematics Subject Classification ID

Micromechanical theories (74A60) Dynamic equations on time scales or measure chains (34N05)

Related Items (4)

Microcanonical entropy and mesoscale dislocation mechanics and plasticity ⋮ Computing singularly perturbed differential equations ⋮ Coarse variables of autonomous ODE systems and their evolution ⋮ Time-averaged coarse variables for multi-scale dynamics

Cites Work

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• Estimating correlation dimension from a chaotic time series: When does plateau onset occur?
• Model reduction via parametrized locally invariant manifolds: Some examples
• On a computational approach for the approximate dynamics of averaged variables in nonlinear ODE systems: toward the derivation of constitutive laws of the rate type
• Parametrized invariant manifolds: a recipe for multiscale modeling?
• Discontinuous and nondifferentiable functions and dimension increase induced by filtering chaotic data
• Ergodic theory of chaos and strange attractors
• Singularly perturbed ordinary differential equations with dynamic limits

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