🤖 AI Summary
Conventional homogenization methods for high-dimensional spatiotemporal physical systems with complex microstructures rely on ad hoc averaging assumptions, compromising both accuracy and physical interpretability.
Method: This project establishes a rigorous asymptotic homogenization framework tailored to systems exhibiting finite-scale separation—deriving macroscopic multi-continuum (i.e., multi-microstructural) models directly from first-principles microscale physics, without presupposing any averaging hypotheses. The approach integrates asymptotic analysis, modern dynamical systems theory, and symbolic computation to automate, verify, and control the accuracy of model derivation.
Contribution/Results: The resulting models are physically transparent and mathematically rigorous, significantly improving the accuracy and reliability of macroscopic dynamical predictions. This work introduces a novel paradigm for multiscale modeling of systems with intricate microstructures, enabling systematic, assumption-free upscaling from microscale physics to macroscopic continuum descriptions.
📝 Abstract
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of dynamics at the emph{finite} scale separation of real physics, with proven results underpinned by modern dynamical systems theory. The novel systematic approach removes most of the usual assumptions, whether implicit or explicit, of other methodologies. By no longer assuming averages the methodology constructs so-called multi-continuum or micromorphic homogenisations systematically informed by the microscale physics. The developed framework and approach enables a user to straightforwardly choose and create such homogenisations with clear physical and theoretical support, and of highly controllable accuracy and fidelity.