The rapid advances in understanding the very small scales will have an enormous impact on the macro-scale world in which ¿we live.¿ The simulation of multi-scale systems presents the major challenge of computational mechanics. At present, problems in areas as diverse as environmental and geosciences, materials, combustion and biosciences are facing major roadblocks due to multi-scale modelling needs.
Nanotechnology is our first application of interest (one of the lines of the ERA that will have a profound impact in medicine, electronics and materials). This is a novel field that starts the design at the finest scales, where critical phenomena need to be described at the atomistic level. However, nanoscale devices may interact with larger components with longer response times. Therefore, there is a need to simulate systems over an enormous range of scales (atomistic to continuum models). To this end, multi-scale analysis and methods promise great research opportunities.
Further, other fields now in fashion will profit from multi-scale simulation. E.g., improved climate models required to predict the effect of human activities on Earth will incorporate local effects that will be accounted for using multi-scale modelling. We want to develop a general mathematical frame for multi-scale simulation that will improve the current situation (a set of disjoint, ad-hoc and extremely limited methods developed without a general approach). It will provide a common language to formulate and analyse multi-scale methods. With this aim we suggest the extension of the Variational Multi-scale Method to atomistic to continuum modelling.
This method is extremely flexible and with a general motivation. From VMM naturally arises key aspects as inter-scales communication. Further, we want to exp lore model adaptivity in the frame of multi-scale simulation, that is, a criterion for deciding where fine scales must be considered, basic in order to keep the simulation affordable.
Field of science
- /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations
- /natural sciences/physical sciences/classical mechanics/fluid mechanics/fluid dynamics
- /engineering and technology/materials engineering/liquid crystal
- /natural sciences/physical sciences/classical mechanics/solid mechanics
- /engineering and technology/nanotechnology
Call for proposal
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