Ricerc@Sapienza

The aim of this research project is to join together well established researchers who are interested in mathematical models both under the applicative and under the analytical point of view.
The models we are going to consider are all amenable to a natural asymptotic study, falling in one of two classes. Some models contain a `small' parameter, which is sent to zero in order to achieve a simplification of an otherwise too complex mathematical scheme; this is the case when we investigate the electric response of bio-materials or the behavioUr of a magneto-viscoelastic body, or the energetic response of polycrystalline materials in the context of elasto-plasticity and fracture mechanics, where concurrent different effects need to be considered, sometimes in an intricate geometry. A second kind of asymptotics is simply the study of the large time behavioUr of solutions, for example of soliton solutions or solutions of equations with nonlinear convection.
In this framework, the focus is on various specific themes: new materials also with memory with or without magnetic effects, polycrystals with fine heterogeneities, biological tissues also with electrical effects, current through lattices or even crowd evolution when the crowd itself is modelled as collective entity.
A description of the applied mathematical methods as well as of their interest, under the applicative and analytical points of view, is provided in the following Sections.
In Section 2.A and 2.E the international connections of the participants in this project are given: they are testified also by the publications in Sect 3 [P:1, 3, 5, 6, 8, 9, 11, 14, O: 5, 6, 9, 10, 16-22, 24, 25] and by many Preprints in Sect 2. E, after the List of External Collaborators in the project.
The mathematical physics interest of the proposed research subjects falls into one of the main themes: thermodynamics, diffusion and dynamics, all with applications.

REF.S: (P =PRINCIPAL INVESTIGATOR, O=OTHER PARTICIPANTS)