PhD research topic - Marcello Ponsiglione
Calculus of Variations
Gamma-convergence, Elasticity, Dislocations, Materials Science, Geometric flows
The first research topic deals with multi-scale variational models for topological singularities in materials science. Vortices in superconductors, XY spin systems, liquid crystals and dislocations in crystals represent prototypical examples. I aim at exploiting the universality character of topological singularities, providing variational models able to describe and predict the common features of several apparently unrelated physical systems. Topological singularities are characterized by concentration of the energy and of the relevant fields, and formation of fascinating microstructures, which strongly influence the physical properties of materials. Their modeling is a central problem in materials science, and a challenging mathematical task. The main goal consists in building up and analyzing macroscopic models, which are rigorously derived by fundamental microscopic theories, rich enough to be predictive, but overcoming the untreatable complexity of discrete and microscopic systems. Calculus of variations is a fruitful framework to this task, providing natural tools for the asymptotic analysis across different length scales, and describing in an efficient way complex phenomena such as the formation and evolution of microstructures, driven by energy minimization .