Professeur à l'ESILV et professeur des Universités à l'Université de Pavie (Italie), Francesco Salvarani est un mathématicien, expert reconnu en théorie cinétique.
francesco.salvarani@devinci.fr
Etienne Bernard; Francesco Salvarani
On the Homogenization of the Renewal Equation with Heterogeneous External Constraints Journal Article
In: Acta Applicandae Mathematicae, vol. 187, no. 1, pp. 4, 2023.
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title = {On the Homogenization of the Renewal Equation with Heterogeneous External Constraints},
author = {Etienne Bernard and Francesco Salvarani},
url = {https://link.springer.com/article/10.1007/s10440-023-00594-2},
year = {2023},
date = {2023-10-01},
journal = {Acta Applicandae Mathematicae},
volume = {187},
number = {1},
pages = {4},
abstract = {We study the homogenization limit of the renewal equation with heterogeneous external con- straints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem.},
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Francesco Salvarani; Etienne Bernard
Homogenization of the linear Boltzmann equation with a highly oscillating scattering term in extended phase space Journal Article
In: Applied Mathematics Letters, vol. 143, pp. 108672, 2023.
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title = {Homogenization of the linear Boltzmann equation with a highly oscillating scattering term in extended phase space},
author = {Francesco Salvarani and Etienne Bernard},
url = {https://doi.org/10.1016/j.aml.2023.108672},
year = {2023},
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journal = {Applied Mathematics Letters},
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Frédérique Charles; Annamaria Massimini; Francesco Salvarani
Mathematical and numerical study of a kinetic model describing the evolution of planetary rings Journal Article
In: Computers & Mathematics With Applications, vol. 143, pp. 48-56, 2023.
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author = {Frédérique Charles and Annamaria Massimini and Francesco Salvarani},
url = {https://www.sciencedirect.com/science/article/pii/S0898122123001724},
year = {2023},
date = {2023-08-01},
journal = {Computers & Mathematics With Applications},
volume = {143},
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Thomas Borsoni; Laurent Boudin; Francesco Salvarani
Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions Journal Article
In: Journal Of Mathematical Analysis And Applications, vol. 517, no. 1, pp. 126579, 2023.
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title = {Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions},
author = {Thomas Borsoni and Laurent Boudin and Francesco Salvarani},
url = {https://www.sciencedirect.com/science/article/pii/S0022247X22005935?via%3Dihub},
year = {2023},
date = {2023-01-01},
journal = {Journal Of Mathematical Analysis And Applications},
volume = {517},
number = {1},
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abstract = {In this paper, we investigate a compactness property of the linearized Boltzmann operator in the context of a polyatomic gas whose molecules undergo resonant collisions. The peculiar structure of resonant collision rules allows to tensorize the problem into a velocity-related one, neighbouring the monatomic case, and an internal energy-related one. Our analysis is based on a specific treatment of the internal energy contributions. We also propose a geometric variant of Grad's proof of the same compactness property in the monatomic case.},
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Laurent Boudin; Alex Rossi; Francesco Salvarani
A kinetic model of polyatomic gas with resonant collisions Journal Article
In: Ricerche Di Matematica, 2022.
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author = {Laurent Boudin and Alex Rossi and Francesco Salvarani},
url = {https://doi.org/10.1007/s11587-022-00733-1},
year = {2022},
date = {2022-09-01},
journal = {Ricerche Di Matematica},
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Laurent Boudin; Francesco Salvarani; Emmanuel Trélat
Exponential Convergence Towards Consensus for Non-Symmetric Linear First-Order Systems in Finite and Infinite Dimensions Journal Article
In: Siam Journal On Mathematical Analysis, vol. 54, no. 3, pp. 2727-2752, 2022.
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title = {Exponential Convergence Towards Consensus for Non-Symmetric Linear First-Order Systems in Finite and Infinite Dimensions},
author = {Laurent Boudin and Francesco Salvarani and Emmanuel Trélat},
url = {https://epubs.siam.org/doi/abs/10.1137/21M1416102},
year = {2022},
date = {2022-05-01},
journal = {Siam Journal On Mathematical Analysis},
volume = {54},
number = {3},
pages = {2727-2752},
abstract = {We consider finite and infinite-dimensional first-order consensus systems with time- constant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows us to define a weighted mean corresponding to the consensus and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate.},
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Giulia Braghini; Francesco Salvarani
Effects of Hidden Opinion Manipulation in Microblogging Platforms Journal Article
In: Advances In Complex Systems, vol. 24, no. 5, pp. 2150009, 2021.
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title = {Effects of Hidden Opinion Manipulation in Microblogging Platforms},
author = {Giulia Braghini and Francesco Salvarani},
url = {https://www.worldscientific.com/doi/abs/10.1142/S0219525921500090},
year = {2021},
date = {2021-11-01},
journal = {Advances In Complex Systems},
volume = {24},
number = {5},
pages = {2150009},
abstract = {This paper studies a model for describing opinions' evolution in a community linked by microblogging directed network systems. The network can evolve in time by means of the creation and the deletion of some connections. When a connexion is created, the individuals have access to the whole history of posts written by the corresponding author and, when a connexion is destroyed, all the posts written by the corresponding author become invisible. The agents' opinions are described by a set of continuous opinion variables in the closed interval Omega=[-1,1]. They represent the agreement (or disagreement) of the corresponding agent with respect to a binary question (such as a referendum or an election with two candidates). The model takes into account the effects on public opinion caused by the sign and the intensity of the initial opinions of the agents, their activity in microblogging platforms the presence of leaders and the possible manipulations of the visibility of the posts by the microblogging platform owner. The model is written as a system of integro-differential equations and simulated by using a Runge-Kutta method. We show that hidden manipulation can have an important impact on the public opinion formation and that very mild interventions of the network owner may induce major effects on the population. In our simulations, the effect of hidden manipulation is shown to be more efficient in driving the public opinion than the action of a leader, in the case of bounded confidence models and for short-time intervals.},
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Nastassia Pouradier Duteil; Francesco Salvarani
Kinetic approach to the collective dynamics of the rock paper scissors binary game Journal Article
In: Applied Mathematics And Computation, vol. 388, pp. 125496, 2021.
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url = {https://www.sciencedirect.com/science/article/pii/S0096300320304549#!},
year = {2021},
date = {2021-01-01},
journal = {Applied Mathematics And Computation},
volume = {388},
pages = {125496},
abstract = {This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness.},
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Etienne Bernard; Francesco Salvarani
Optimal Estimate of the Spectral Gap for the Degenerate Goldstein-Taylor Model Journal Article
In: Journal Of Statistical Physics, vol. 181, pp. 1470-1471, 2020.
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year = {2020},
date = {2020-11-01},
journal = {Journal Of Statistical Physics},
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Frédérique Charles; Francesco Salvarani
Mathematical and numerical study of a dusty Knudsen gas mixture Journal Article
In: Acta Applicandae Mathematicae, vol. 168, no. 1, pp. 17-31, 2020.
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title = {Mathematical and numerical study of a dusty Knudsen gas mixture},
author = {Frédérique Charles and Francesco Salvarani},
url = {https://link.springer.com/article/10.1007/s10440-019-00277-x},
year = {2020},
date = {2020-08-01},
journal = {Acta Applicandae Mathematicae},
volume = {168},
number = {1},
pages = {17-31},
abstract = {We consider a mixture composed of a gas and dust particles in a very rarefied setting. Whereas the dust particles are individually described, the surrounding gas is treated as a Knudsen gas, in such a way that interactions occur only between gas particles and dust by means of diffuse reflection phenomena. After introducing the model, we prove the existence and the uniqueness of the solution and provide a numerical strategy for the study of the equations. At the numerical level, we focus our attention on the phenomenon of energy transfer between the gas and the moving dust particles.},
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Olga Mula; Francesco Salvarani; Harsha Hutridurga
Homogenization in the energy variable for a neutron transport model. Journal Article
In: Asymptotic Analysis, vol. 117, no. 1-2, pp. 1-25, 2020.
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title = {Homogenization in the energy variable for a neutron transport model.},
author = {Olga Mula and Francesco Salvarani and Harsha Hutridurga},
url = {https://content.iospress.com/articles/asymptotic-analysis/asy191544},
year = {2020},
date = {2020-03-01},
journal = {Asymptotic Analysis},
volume = {117},
number = {1-2},
pages = {1-25},
abstract = {This article addresses the homogenization of linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit. We also provide some numerical experiments to illustrate our results. In the Appendix, we treat a related case of the harmonic oscillator.},
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Benjamin Anwasia; Marzia Bisi; Ana Jacinta Soares; Francesco Salvarani
On the Maxwell- Stefan diffusion limit for reactive mixture of polyatomic gases in non-isothermal setting Journal Article
In: Kinetic And Related Models, vol. 13, no. 1, pp. 63-95, 2020.
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title = {On the Maxwell- Stefan diffusion limit for reactive mixture of polyatomic gases in non-isothermal setting},
author = {Benjamin Anwasia and Marzia Bisi and Ana Jacinta Soares and Francesco Salvarani},
url = {https://www.aimsciences.org/article/doi/10.3934/krm.2020003},
year = {2020},
date = {2020-02-01},
journal = {Kinetic And Related Models},
volume = {13},
number = {1},
pages = {63-95},
abstract = {In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of the model are derived in the diffusive limit of a kinetic system of Boltzmann equations for the considered mixture, in the general non-isothermal setting. The asymptotic analysis of the kinetic system is performed under a reactive-diffusive scaling for which mechanical collisions are dominant with respect to chemical reactions. The resulting system couples the Maxwell-Stefan equations for the diffusive fluxes with the evolution equations for the number densities of the chemical species and the evolution equation for the temperature of the mixture. The production terms due to the chemical reaction and the Maxwell-Stefan diffusion coefficients are moreover obtained in terms of general collision kernels and parameters of the kinetic model.},
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Ana Jacinta Soares; Francesco Salvarani
On the relaxation of the Maxwell-Stefan system to linear diffusion Journal Article
In: Applied Mathematics Letters, vol. 85, pp. 15-21, 2018.
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title = {On the relaxation of the Maxwell-Stefan system to linear diffusion},
author = {Ana Jacinta Soares and Francesco Salvarani},
url = {https://www.sciencedirect.com/science/article/abs/pii/S089396591830154X},
year = {2018},
date = {2018-11-01},
journal = {Applied Mathematics Letters},
volume = {85},
pages = {15-21},
abstract = {In this note, we rigorously prove the relaxation limit of the Maxwell-Stefan system to a
system of heat equations when all binary diffusion coefficients tend to the same positive value.},
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Francesco Salvarani
Recent Advances in Kinetic Equations and Applications Book
Springer, 2021, ISBN: 978-3-030-82946-9.
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issn = {978-3-030-82946-9},
year = {2021},
date = {2021-01-01},
volume = {48},
pages = {XI, 393},
publisher = {Springer},
series = {Springer INdAM Series},
abstract = {The volume covers most of the topics addressed and discussed during the Workshop INdAM "Recent advances in kinetic equations and applications", which took place in Rome (Italy), from November 11th to November 15th, 2019.
The volume contains results on kinetic equations for reactive and non-reactive mixtures and on collisional and non-collisional Vlasov equations for plasmas.
Some contributions are devoted to the study of phase transition phenomena, of kinetic problems with non-trivial boundary conditions and hierarchies of models.
The book, addressed to researchers interested in the mathematical and numerical study of kinetic equations, provides an overview of recent advances in the field and future research directions.},
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Francesco Salvarani
Kinetic models for complex systems Conference
Modelling, analysis and numerical methods of complex dynamics, Marseille, France, 2023.
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Francesco Salvarani
On the homogenization of the linear Boltzmann equation Conference
Seminario EDP, Universidad Autónoma de Madrid, Spain, 2023.
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Francesco Salvarani
Homogenization of linear kinetic equations with highly oscillating scattering terms Conference
Seminario de Análisis Matemático y Matemática Aplicada, Madrid, Spain, 2023.
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Francesco Salvarani
Exponential convergence to consensus in finite and infinite dimensions Conference
Japan-France Joint Workshop ?Interacting Particle Systems and Fluid Mechanics : Theory and Applications?, Institut Français du Japon-Kansai, Kyoto, Japan, 2022.
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Francesco Salvarani
Kinetic description of polyatomic gases undergoing resonant collisions Conference
Particle Systems and PDEs X, Braga, Portugal, 2022.
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Francesco Salvarani
Applied Analysis, Complex Systems & Dynamics Seminar, Graz, Austria, 2022.
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Francesco Salvarani
Particle Systems and PDEs IX, Braga, Portugal, 2021.
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Francesco Salvarani
Matematica e vaccinazione: prevedere conseguenze collettive a partire da scelte individuali Conference
Presentation conference of the new members of the National Virgilian Academy., Mantua, Italy, 2021.
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Francesco Salvarani
On the homogenization problem for the linear Boltzmann equation Conference
Workshop 2020 Partial differential equations, Prague, Czech Republic, 2020.
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Francesco Salvarani
On reactive gaseous mixtures: the kinetic description and the Maxwell-Stefan diffusion limit Conference
Energy department seminar, Politecnico di Torino Turin, Italy, 2020.
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Francesco Salvarani
On the homogenization problem for the linear Boltzmann equation Conference
Particles Systems and PDE VIII, Lisbon, Portugal, 2019.
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Francesco Salvarani
On the homogenization problem for the linear Boltzmann equation Conference
Kyoto University seminar, Kyoto, Japan, 2019.
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