Molecular structures
We focus on the variational modeling of molecular geometries within the frame of Molecular Mechanics: effective configurations are identified as minimizers of classical configurational potentials. By combining discrete, analytical, and computational techniques, our aim is that of investigating the local and global geometry of ground state configurations, their mechanics, and the emergence of scale effects across scales.
Thermomechanics
The macroscopic behavior of materials results from the complex combination of different phenomena. Inelasticity and phase transformation in solids are inherently coupled with temperature changes. Magnetoelastic and shape-memory materials call for considering electromagnetic effects as well. Our research is aimed at advancing effective descriptions for the macroscopic behavior of complex materials and to analyze the corresponding mathematical formulations from the analytic and the numerical viewpoint.
Evolution equations and SPDEs
We are interested in the many aspects of the analysis of nonlinear evolution equations and stochastic partial differential equations, mostly of parabolic type. Well-posedness theories, variational characterizations, optimal control, and approximations are in focus.