Theoretical Mechanics

Members:
Matteo Focardi (Università di Firenze)
Mariano Giaquinta (Scuola Normale Superiore)
Paolo Maria Mariano (Università di Firenze) (coordinator)
Alexander Mielke (WIAS und Humboldt-Universität zu Berlin) (coordinator)
Giuseppe Modica (Università di Firenze)
Domenico Mucci (Università di Parma)

The activity of the research group is focused on the construction and analysis of mathematical models of physical phenomena with special attention to mechanics, in particular the mechanics of complex bodies. The aim is the development of models and appropriate tools from analysis, geometry and function spaces. Instances coming from condensed matter physics and the achievements of advanced technology in the micro- and nanorange indicate the need of re-discussing basic paradigms of classical mechanics. Continuous models require sometimes to be supplemented by statistical methods or quantum mechanics. In particular, the bridging between the different inherent length scales in materials has to be discussed. Open problems are manifold.

Topics covered:
Mechanics of complex bodies (solids and fluids), analysis of evolution equations, mechanics of dissipative processes, variational methods, topological methods in continuum mechanics, Γ-convergence techniques, computational mechanics...

Exchange Programs:
An exchange program is established with the Weierstrass-Institut für Angewandte Analysis und Stochastik (WIAS) at Berlin.

Students:
Undergraduate and graduate students interested in the activities of the research group may develop their theses by following joint programs with other institutions.