Adaptive simplification of complex multiscale systems

Abstract

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging problem of a minimal number of variables needed to exactly capture the system dynamics. Accurate reduced description is achieved, by construction of a hierarchy of slow invariant manifolds, with an embarrassingly simple implementation in any dimension. The method is validated with the auto-ignition of the hydrogen-air mixture where a reduction to a cascade of slow invariant manifolds is observed.

26 pages, 6 figures, 1 table. Phys Rev E to appear (2011)

References in corpus (5)

• Method of invariant manifold for chemical kinetics
• Entropic 13 Moment Equations from Boltzmann's Kinetic Equation
• Exact linear hydrodynamics from the Boltzmann equation
• Quasi Equilibrium Grid Algorithm: geometric construction for model reduction
• Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program

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