Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Numerical Methods for Innovative Semiconductor Devices

Read more about Numerical Methods for Innovative Semiconductor Devices

Variational Physics Informed Neural Networks: the role of quadratures and test functions

Read more about Variational Physics Informed Neural Networks: the role of quadratures and test functions

Quasistatic Limit of a Dynamic Viscoelastic Model with Memory

Dal Maso G, Sapio F. Quasistatic Limit of a Dynamic Viscoelastic Model with Memory. [Internet]. 2021 . Available from: https://doi.org/10.1007/s00032-021-00343-w

A dynamic model for viscoelasticity in domains with time-dependent cracks

Sapio F. A dynamic model for viscoelasticity in domains with time-dependent cracks. [Internet]. 2021 ;28(6):67. Available from: https://doi.org/10.1007/s00030-021-00729-0

An existence result for the fractional Kelvin–Voigt’s model on time-dependent cracked domains

Caponi M, Sapio F. An existence result for the fractional Kelvin–Voigt’s model on time-dependent cracked domains. [Internet]. 2021 . Available from: https://doi.org/10.1007/s00028-021-00713-2

A dynamic model for viscoelastic materials with prescribed growing cracks

Caponi M, Sapio F. A dynamic model for viscoelastic materials with prescribed growing cracks. [Internet]. 2020 ;199(4):1263 - 1292. Available from: https://doi.org/10.1007/s10231-019-00921-1

High-order spectral element methods for the simulation of compressible turbulent flows

Read more about High-order spectral element methods for the simulation of compressible turbulent flows

The periodic nonlinear Schrodinger (NLS) equations: deterministic and probabilistic approaches

In this course we will study different aspects of the nonlinear and periodic Schrodinger equation, mainly in 2D. We start with Strichartz estimates for the deterministic well-posedness, we then introduce the notion of transfer of energy, and we present few theorems concerning this very active area of research. We then move to the notion of Gibbs measure and its invariance. If we have time we introduce the wave kinetic equation associated to the NLS as well.

Read more about The periodic nonlinear Schrodinger (NLS) equations: deterministic and probabilistic approaches

Consistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows

Strazzullo M, Girfoglio M, Ballarin F, Iliescu T, Rozza G. Consistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows. 2021 .

AN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS

Demo N, Strazzullo M, Rozza G. AN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS. 2021 .

Mathematics