PROGRAMMA PRIN 2022 - BCALL PRIN2022 D.D. N.104 DEL 2 FEBRUARY 2022

PROJECT TITLE Evolution problems involving interacting scales

CODICE CUP D53D23005880006

Budget: € 141.712

P.I. Giuseppe Maria Coclite

Other Research Units or any Sub-Units

University of Palermo (Maria Carmela Lombardo)

Today it is widely recognized that the behavior of any physical system at a given space-time scale is profoundly governed by laws involving other, often different, scales, and that such laws remain largely unknown. The paradigmatic problem of turbulence in fluids constitutes one of the most tangible manifestations of this reality; however, many other phenomena that are still not fully explained also appear to depend on the cross-scale interaction of the laws governing them. These issues concern both biological and geophysical materials. Understanding these phenomena requires a collective effort from numerous scientific fields, and mathematics plays a fundamental role in identifying the appropriate conceptual framework to advance knowledge.

The research activities were organized into the following work packages:

• WP: Energy transfer in nonlocal evolution equations
• WP: Singularity formation in nonlocal evolution equations
• WP: Local limit of peridynamic theories
• WP: Computational methods for peridynamics
• WP: Stacking faults and partial dislocations in the HCP lattice
• WP: Antiferromagnetic XY model on the triangular lattice
• WP: Frustrated three-dimensional spin systems
• WP: Transition layers for nonlinear RD systems
• WP: Localized solutions for chemotaxis models
• WP: Stability of vortex layers
• WP: Stability and convection in fluid and porous layers

The main tools used to achieve the research objectives were developed starting from classical methods of harmonic analysis, potential theory, analytical fluid dynamics, and computational fluid dynamics.

The two research units organized 11 international workshops and 31 seminars delivered by internationally renowned experts, held 20 seminars at national and international institutions, presented 54 communications at international workshops, and published 61 articles in international journals and 6 preprints.

The Palermo Research Unit organized the intermediate international conference “Multiscale and Nonlocal Problems in PDEs”, held on 20 and 21 June 2024, with the aim of giving the research group the opportunity to present the intermediate results achieved and to discuss the project’s subsequent developments. The Polytechnic University of Bari Research Unit organized the final international conference “Second Workshop on Multiscale and Nonlocal Problems in PDEs”, held on 19 and 20 June 2025, in order to present the results obtained to scholars external to the project.

The Palermo Research Unit entered into a legal agreement concerning the awarding of a type B research fellowship, lasting 12 months and subsequently extended for a further 4 months, to Dr. Alessandra Rizzo, for the performance of research activities within the project entitled “Coherent structures and hydrodynamic and parabolic asymptotic limits”, under the scientific responsibility of Prof. Maria Carmela Lombardo.