Sept. 2023 - Sept. 2025
https://www.researchproject.it/
Keywords: Nonlinear waves; Nonlinear Elasticity; Continuum mechanics; Elastography.
The aim of the project is to use nonlinear solid mechanics and rigorous mathematics to understand wave motion in soft tissues. We focus first of all in the framework of the actual technology of transient elastography with the goal to improve elastograms in precision and spatial resolution but we consider also application to shock waves in brain and other soft tissues. The project is organised in three work packages: the first about constitutive modelling, the second about wave propagation issues and the third about computational and algorithmic aspects.
2019 - 2023
https://mcmslot.wordpress.com/
Keywords: Fluid dynamics; Continuum mechanics; Mathematical Physics; Mesoscopic models and extended thermodynamics.
The proposal concerns Continuum Mechanics models in presence of different spatial and temporal scales. We consider three exemplar cases.
The first sees the Boltzmann equation a model one can derive using the principles of Extended Thermodynamics: off-equilibrium phenomena occurring in reactive and polyatomic gases, micromagnetism, semiconductors and the main object of our analysis.
The second involves Reaction Diffusion models and the destabilization mechanisms leading to the formation of coherent structures and to the sub bifurcations: Landau-Lifshitz-Gilbert equation, oscillatory systems with nonlinear diffusion, models for inflammatory diseases are considered.
The third regards the incompressible Navier-Stokes equations in the zero viscosity limit with highly concentrated vorticity data: the main goals being the justification of the Birkhoff-Rott equation and the analysis of the singularities leading to the break-up to the subsequent transition phenomena.
The team, which is made of researchers that have considerably contributed to the field, will be reinforced hiring four post docs.
The project has the potential for a high scientific impact as well as an impact on Future and Emerging technologies.
Aug. 2019 - Feb. 2023
https://site.unibo.it/regular-stochastic-dynamical-systems/en
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.
Feb. 2022 - Sept. 2022
https://site.unibo.it/toc4deep
A transversal approach between Science and Art . A multi-sensory, immersive exploration of the Cosmos, where the most recent astrophysical data are heightened into real works of art, so to allow the public to access scenarios - until now reserved only to researchers - with emotional immediacy.
Partners: VISIT-LAB CINECA- DIP.MATH-UNIBO -INAF
Fiber of the Universe – Cineca Visit Lab
Into the (un)known
Radio Relics in Galaxy Clusters — Collisions — Simulations & VLA won the first prize at NRAO Contest Winners Illustrate Diverse Cosmic Phenomena.
PI: Serena Morigi
ABSTRACT: In immunofluorescence diagnostic systems, cost is often dominated by high-sensitivity CCD cameras used to capture fluorescence images. In this project it is proposed the use of low-cost CMOS sensors that together with advanced variational imaging methods allow the development of a portable diagnostic system that uses multiparametric disposable cartridges with applications to detect and discriminate different serotypes of the Dengue virus in human samples, different food bacteria, both aspects with a strong application potential. Close collaboration with slovenian start-up OREL.doo was conducted, in particular for the serological diagnostic methodology phase. The mathematical reasearch involved the definition of variational models suitable for restoration, super-resolution and segmentation of images produced by the CMOS Prototype (P-CMOS), as well as a strategy for reliable and fast automatic diagnosis.
Feb. 2018 - Jan. 2020
Mathematical and computational models of European Air Traffic. Tests on simulated agent based models of new air traffic regulations.
May 2014 - 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.