Research Projects

Ongoing Projects


Horizon 2020 - MSCA-RISE-2017

1 Nov 2017 - 31 Oct 2021

Regular and stochastic behaviour in dynamical systems

PRIN 2017

18 Aug 2019 - 18 Feb 2023

Keywords: chaotic systems, weak chaos, integrable systems, limit laws in dynamical systems, stochastic dynamics, applications in mathematical physics, anomalous diffusion, extreme events.


The focus of the project is the study of the long time behaviour in dynamical systems. This is a momentous problem to which the international community has dedicated a tremendous amount of work with an intensity that shows no sign of dwindling. Far-reaching results have been obtained, but limited to special systems:

A) hyperbolic systems (for which the long time behaviour is stochastic in nature and hence naturally described in statistical terms);

B) (piecewise algebraic or rigid) parabolic systems (which enjoy weaker ergodic properties characterised by the rate of convergence of the Birkhoff averages);

C) perturbations of completely integrable systems (elliptic systems) whose ergodic properties are currently beyond our reach hence the emphasis is on the study of invariant sets.

Our goal is to substantially forward the state of the art in all such cases. In case (A) we are concentrating on partially hyperbolic systems and hyperbolic systems with infinite invariant measure (e.g. Farey map) or non compact phase space (e.g. Lorentz gas). In (B) we aim at refining and extending known results beyond the rigid case. As for (C) we want to go beyond the symplectic context in order to make the techniques developed in the Hamiltonian formalism bear on a more general class of systems.

Concluded Projects

MIUR-DAAD Simoncini

MIUR-DAAD Joint Mobility Program

Mar 2018 - Feb 2020

detailed info



1 Feb 2018 - 31 Jan 2020

Mathematical and computational models of European Air Traffic. Tests on simulated agent based models of new air traffic regulations.

Combustion-wave interactions via extended thermodynamics

EU-funded project B-MOB

1 May 2014 - 30 Apr 2016

Keywords: nonlinear wave propagation, extended thermodynamics, wave interaction.


This research project was proposed by Dr. Andrea Mentrelli (AM^2, University of Bologna) and Dr. Gianni Pagnini (Basque Center for Applied Mathematics, BCAM). The Basque Center for Applied Mathematics hosted Dr. Andrea Mentrelli for several research visits in order to benefit from his expertise in the field of nonlinear wave propagation and high-performance computing to study the problems of combustion instability and the related generated noise, which are open issues in aerospace engineering. Lean premixed combustion has been shown to be particularly susceptible to instability arising from the coupling of the unsteady Turbulent Premixed Combustion (TPC) with the acoustic waves generated by the heat release fluctuations. The acoustic waves produced by combustion can be reflected at the boundaries and again interact with the combustion process to produce further unsteady heat release, thereby forming a feedback loop. TPC can be seen as a problem of front propagation, where the front is a reacting interface embedded into a turbulent flow. Literature approaches to TPC traditionally adopted the Eulerian point of view. The investigation of the recently proposed Lagrangian approach was the main focus of this project. The level-set method, which is a powerful tool for tracking moving interfaces, was the framework adopted for the study. The developed model can be considered a randomized level-set method according to the PDF of the particles displacement and the resulting governing equation is the reaction-diffusion equation associated to the level-set (or G-equation). One of the outcome of this research was the development of a software library based on the level-set method useful for the simulation of the evolution of randomized moving fronts.