The project is devoted to the study of Kinetic Mean Field Games (KMFGs), i.e. the limit of cooperative or non-cooperative games in very large populations, composed of interacting individuals, where each individual has a small influence on the global behaviour of the system and where the behaviour of the system depends on additional (internal) variables. Though the observables of KMFGs do not depend on the additional variables themselves (as they are the moments of the distribution function with respect to these additional variables), such internal variables have to be taken into account in the models and they have an influence in its behaviour. Moreover, since different time scales can be involved in the phenomenon, the kinetic approach allows to treat systems that cannot be modelled by purely macroscopic equations. The methods to be used come from the most recent developments in kinetic theory, as well as from the strategies developed in the last years for macroscopic mean field games. They include: existence theory of nontrivial remarkable states, linear and nonlinear asymptotic stability methods, entropy/entropy dissipation estimates, perturbative methods, renormalized solutions, etc. Our goal is, in particular, to extract information from systems which are far from known steady states. Moreover, through the identification of a scale parameter, we will study the limit, as the parameter tends to zero, of the system. Particular emphasis will be addressed to the numerical simulation of KMFG systems. As the unknown function depends - in principle - on several variables and as the KMFG is in principle both forward and backward in time, the numerical study of kinetic mean field game systems requires new approaches and massive parallelization techniques. The easy access to teraflop-based manycore computing (i.e. either 1-card GPU-like office computing, or clusters of manycores HPC) will allow to handle KMFG equations at the numerical level and produce accurate numerical schemes. Since the modelling is not completely stabilized in many of the problems under consideration, a collaboration with teams of economists or biologists is planned. The research project proposed here foresees the hiring of excellent postdoctoral researchers, coming from national or international high level universities and aims to give a substantial contribution in developing KMFG theory. Our development strategy consists in a fast dissemination of the scientific results that we will obtain. It will be done by producing publications in international reviewed journals and by means of communications in international conferences and workshops. Our works will provide contributions in applied mathematics journals but also, for example, in economics or biology journals. The interaction with industries and agencies is planned. Furthermore, we aim to widespread our results also in non-academic contexts, in order to show how applied mathematics can help the productive world. Finally, we shall create a web site where the pieces of information on the ANR project will be available to the scientific community.

Secondary refrigeration is an effective way to drastically reduce the quantity of primary refrigerant fluid used while improving energy efficiency by storing and transporting energy-dense secondary fluids. These ice slurries, made of ice crystals suspended in aqueous solution, are unfortunately not yet widespread due to an over-investment related to scraped surface or supercooling type generators. Within this COOLISSE project, our objective is thus to participate in the energy optimisation of the refrigeration sector by designing new type of ice slurry generators. Our aim is therefore to develop stainless steel surfaces where formed ice could be carried away by the fluid flow, without rotating scraper blades. These original non-wetting micro/nanostructured surfaces, inspired from nature, displaying anti-icing properties will be obtained by an original and efficient combination of processes: additive manufacturing (to yield micro-structures) and femtosecond laser ablation (to reach nanometer scale roughness) that will allow obtaining a multiscale and very dense textured stainless steel surface. These surfaces will be then infused by inert liquid in order to obtain slippery infused surfaces (SLIPS). The second objective of the project is to develop methods and expertise on the surface characterization under flow at low temperature [-15°C to 0°C]. The potential in anti-icing applications of the designed surfaces will be proven by investigating their action mechanisms on ice formation, analysing the freezing time, adhesion strength and nucleation in the freezing process. In parallel a comprehensive numerical method will be developed to describe the thermal equilibrium state, heat flux and gas-solid-liquid interface changes during freezing and phase change. The environmental impact and potential gain of these new surfaces on slurry fabrication process will also be compared to traditional processes using multiple criteria analyses like Life Cycle Assessment.

We aim to set up a strong research network built around the three collaborators towards a very ambitious and very interdisciplinary project that will be financed by the Horizon Europe program. The project involves approaches from economics, management, administrative sciences, psychology, computer science and mechanical engineering. We will explore how citizens can and should be involved in the design and implementation of smart systems for public services (co-engineering) and policy making (co-governance). We will theoretically and empirically assess some viable methods of aggregating public opinions on the ethical and moral aspects of automated systems and robots in public services. We propose a new methodology for integrating citizens' contribution into the design and governance of smart public services, which will improve on existing approaches that are too technocratic and hypothetical. We will identify the dimensions that explain which utilities could benefit from automation using intelligent systems. These dimensions will allow us to measure whether the citizen approach that we propose is really useful and leads to better designed public services and policies.

With the need to reduce carbon dioxide emissions, the trend is to make lighter auto bodies, yet without sacrificing their aptitude to protect car passengers in case of accidents. Steel manufacturers such as ArcelorMittal are currently developing a new generation of flat carbon steels, especially for automotive applications. However these steels are more exposed, in terms of properties consistency, to process variations than other conventional flat carbon steels. Therefore, adequate measurement tools are required to at least check the production scatter and control it. The objective of this project is to predict qualitatively, and possibly quantitatively, the magnetic response to various parameters of the microstructure of the industrial dual phase steels. For instance: The sensitivity to the perturbation parameters that go along the on-line measurement, and especially the effect of an applied tension or of zinc coating variations; the sensitivity of the elongation resulting from temper rolling; and the sensitivity to the presence of band-type microstructures. The main stages of the modeling will be to first link microstructure and magnetism, using finite elements models in 3D, with the integration of the magneto-mechanic coupling, then to model a measuring device so-called 3MA and link the modifications of the hysteretic cycles, brought forth by the change of microstructure, to the output signal of these devices. This project will allow for exploring the link between microstructure and magnetism and develop a new software: SIVIMM3D.

<< Background >>The aim of our project is to design and implement new methods for mathematics learning that are effective and valid also in distance learning contexts. The need for innovative teaching methodologies is particularly felt in mathematics teaching. As a consequence of the Covid19 pandemic, the majority of students (including many students with an excellent level in other disciplines and an interest in mathematics) have accumulated serious gaps which, if not filled, could have repercussions throughout their university studies. The strategies adopted by higher education institutions are not producing the desired results. Examinations in the first semester in many universities showed two situations: a decrease in grade averages with constant exam difficulty or a maintenance of grade averages with easier exams than in the past.We would also like to organise remedial courses to enable students to fill in past gaps.The project will also pay special attention to the needs of students with special needs, in particular students with hearing problems and disabilities. for such students, distance or hybrid teaching is particularly difficult because hearing is particularly used in this context.The project therefore aims to provide equal opportunities for success to both students without disabilities and students with disabilities.<< Objectives >>The ultimate desired impact is to contribute to the development of young generations. This goal has a great impact at the local, regional, national, European and international levels because a solid preparation of the new generations is the engine of the success of tomorrow's society. This is a very challenging task and we expect that the project and the cooperation among the partners push us in this direction.We want moreover help student with hearing disabilities to overcome their specific difficulties. We will produce permanent intellectual outputs, which will help for improving the mathematics teaching strategies and which will be freely available to the public.<< Implementation >>The activities of the project are logically linked and cover the main aspects for guaranteeing the achievement of the project objectives and the delivery of the planned results.The main goal is to provide a new teaching strategy especially designed for mathematics teaching at the higher education level in the context of the Covid-19 pandemic and beyond. Hence, we first analyze all the aspects of the knowledge transmission and, at the same time, we will identify the most important mathematical skills and knowledge for a student of the 21st century.Moreover, once identified the content of the courses and the psychological mechanisms of learning, we will produce some teaching material and strategies (websites, virtual courses, MOOCs, slides, course notes, applications...).This teaching material and the teaching strategies will be tested on the students of the five participating organizations and the results of these tests will be analyzed in order to improve the intellectual outputs. In parallel, the participating organizations will implement some innovative ways for minimizing the negative effects of isolation and of the reduction of the social component in the teaching of mathematics.Finally, the problem of designing right and effective evaluation strategies will be addressed. These methods, which need to go beyond the standard written exam, must ensure the accuracy of the student’s assessment and prevent fraud.<< Results >>The outcomes of our project include: a better understanding of learning processes, with particular attention to students with hearing disabilities, the design of new teaching methodologies, the production of teaching materials, which are available online in open format, the formation of university lecturers and the improvment of their teaching skills related to online and distance learning for student with and without disabilities.The website hosting our results and the community on a social network will be maintained after the end of the project.We moreover plan to write articles in specialized journals and reports describing our results. We will grant the general public the legal permission to use our work through an open license. We will organise training courses for teachers and three interntional conferences for widespreading our results.