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Lectures
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
2007/01/15
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Antonio DeSimone (SISSA (International School for Advanced Studies))
Analysis of physical systems involving multiple spatial scales: some case studies
Antonio DeSimone (SISSA (International School for Advanced Studies))
Analysis of physical systems involving multiple spatial scales: some case studies
[ Abstract ]
Variational methods have recently proved to be a powerful tool in deriving macroscopic models for phenomena whose physics is decided at the sub-miccron scale.
We will use two case studies to illustrate this point, namely, that of liquid crystal elastomers and that of superhydrophobic surfaces.
Liquid crystal elastomers are solids which combine the optical properties of liquid crystals with the mechanical properties of rubbery solids. They display phase transformations, material instabilities, and microstructures in a way simalr to shape-memory alloys.
The richness of the underlying material symmetries makes the mathematical analysis of this system particularly rewarding. Recent progress, ranging from analytical relaxation results to numerical simulations of the macroscopic mechanical response will be reviewed.
Variational methods have recently proved to be a powerful tool in deriving macroscopic models for phenomena whose physics is decided at the sub-miccron scale.
We will use two case studies to illustrate this point, namely, that of liquid crystal elastomers and that of superhydrophobic surfaces.
Liquid crystal elastomers are solids which combine the optical properties of liquid crystals with the mechanical properties of rubbery solids. They display phase transformations, material instabilities, and microstructures in a way simalr to shape-memory alloys.
The richness of the underlying material symmetries makes the mathematical analysis of this system particularly rewarding. Recent progress, ranging from analytical relaxation results to numerical simulations of the macroscopic mechanical response will be reviewed.
