This workshop aims to bring together researchers and experts in kinetic equations to share and discuss the latest advances in the field. It will provide a platform to present current research directions, foster collaboration, and stimulate the exchange of ideas across different communities. Particular attention will be given to exploring future development perspectives from multiple viewpoints, including analytical, modeling, numerical, and applied approaches.

Invited Speakers

• Giacomo Albi – Università di Verona

• Paolo Antonelli – Gran Sasso Science Institute

• Marzia Bisi – Università di Parma

• Giacomo Dimarco – Università di Ferrara

• Maria Groppi – Università di Parma

• Tommaso Tenna – Università di Roma “Sapienza”

• Andrea Tosin – Politecnico di Torino

• Mattia Zanella – IUSS &Università di Pavia

Program

09.45 – 10.00

Registration & opening

Morning Session - SALA DEL CAMINO

10.00 – 11.00

Speaker: Mattia ZANELLA
Title:  Kinetic equations in the physical and life sciences
Abstract: TBA

11.00 – 11.30

Speaker: Andrea TOSIN
Title: Homogeneous Boltzmann-type equations on graphs
Abstract: Homogeneous Boltzmann-type equations are an established tool for modelling interacting multi-agent systems in sociophysics by means of the principles of statistical mechanics and kinetic theory. A customary implicit assumption is that interactions are "all-to-all", meaning that every pair of randomly sampled agents may potentially interact. However, this legacy of classical kinetic theory, developed for collisions among gas molecules, may not be equally applicable to social interactions, which are often influenced by preferential connections between agents. In this seminar, we discuss ongoing research on incorporating graph structures into homogeneous Boltzmann-type equations, thereby accounting for the "some-to-some" nature of social interactions. 

11.30 – 12.00

Speaker: Paolo ANTONELLI
Title: TBA
Abstract: TBA

12.00 – 12.30

Speaker: Marzia BISI
Title: Mutual influence of knowledge and wealth in a multi-population system described by kinetic equations
Abstract: We investigate the evolution of a multi-population system where agents are involved in international trades with possible transfers of individuals from a country to another, and trading interaction rules are influenced by the individual knowledge and vice versa. Starting from a proper microscopic description of single-agent dynamics, we build up the corresponding kinetic model, with suitable transition probabilities in the kernels of Boltzmann-type operators. Macroscopic equations may be derived from the kinetic level, governing the evolution of each population density, mean knowledge and national wealth. A suitable quasi-invariant asymptotic limit of the Boltzmann model leads to a system of simpler Fokker-Planck-type equations, with diffusion and drift operators with respect to both wealth and knowledge variables. Some open issues on the long-time behaviour of such system and possible future research directions are discussed. 

12.30 – 14.30

Lunch

Afternoon Session - AULA 1.17

14.30 – 15.00

Speaker: Maria GROPPI
Title: Kinetic modelling of inert and reactive gas mixtures
Abstract: In this talk we present some recent developments about BGK models for mixtures, obtained in collaboration with M. Bisi, E. Lucchin, A. Macaluso (University of Parma), G. Martalò (University of Pavia).
First, we propose a hybrid Boltzmann-BGK model for mixtures of monatomic gases, that combines the detailed description of collisions given by the Boltzmann integral operators with the simplicity and the numerical manageability of BGK-type relaxation operators. This kinetic model has the same structure of the full Boltzmann equations, with the collision term of each constituent given by a sum of bi-species operators, that may be chosen of Boltzmann or of BGK type. The mixed model fulfills all the desired consistency properties:  conservation properties, positivity of all temperatures, H-theorem, and convergence to a global Maxwellian equilibrium with all species sharing a common mean velocity and a common temperature. The presence of a collision operator for any pair of gaseous components allows for a consistent derivation of evolution equations for the main macroscopic fields in different hydrodynamic regimes, according to the dominant collision process. Specifically, we investigate the classical collision dominated regime, a situation with dominant intra-species collisions, leading to multi-fields macroscopic description, and a mixture with heavy and light particles, leading to a kinetic-fluid description: in all of these frames a Chapman-Enskog procedure allows to obtain an explicit closure of macroscopic equations at Navier-Stokes level, with transport coefficients in agreement with physical expectations.
Then, we present a consistent BGK-type approach for the modeling of chemically reacting gas mixtures,  which mimics the Boltzmann description,  and preserves fundamental physical properties, such as mass, momentum, total energy conservation, and the correct equilibrium Maxwellian distributions, including mass action law.  

15.00 – 15.30

Speaker: Giacomo DIMARCO
Title: TBA
Abstract: TBA

15.30 – 16.00

Speaker: Giacomo ALBI
Title: TBA
Abstract: TBA

16.00 – 16.30

Speaker: Tommaso TENNA
Title: From the multi-species Boltzmann equation to an isentropic two-phase flow model
Abstract: Starting from the microscopic description of gas mixtures, a rigorous kinetic foundation is essential for capturing the complex interfacial dynamics often missed by phenomenological models. In this talk, we investigate the formal hydrodynamic limit of the multispecies Boltzmann equation, specifically in a regime where intra-species collisions are the dominant physical process. By analyzing the asymptotic behavior as the Knudsen numbers approach zero, we derive the isentropic two-phase flow model originally proposed by Romenski and Toro. This derivation provides a justification for multi-velocity and multi-pressure frameworks, allowing for the explicit computation of model coefficients. Furthermore, we demonstrate how this kinetic scaling naturally accounts for the evolution of the volume fraction, bridging the gap between kinetic theory and macroscopic multiphase flow.

16.30 – 18.00

Free discussion

Organizers

• Giorgio Martalò – Università di Pavia

• Mattia Zanella – IUSS & Università di Pavia

We invite anyone interested to attend the workshop to send a mail to

giorgio.martalo@unipv.it