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49 results on '"BOUDIN, LAURENT"'

1. Compactness of linearized Boltzmann operators for polyatomic gases

Author

Bernhoff, Niclas, Boudin, Laurent, Čolić, Milana, and Grec, Bérénice

Subjects
Mathematics - Analysis of PDEs
Abstract

In this article, we recall various existing kinetic models of non-reactive polyatomic gases. We also review the results, all recently obtained, about the compactness of the associated linearized Boltzmann operator, and briefly investigate the mixture case. Eventually, with a specific collision kernel, we present a discussion about the physical relevance of the assumptions used to obtain the compactness results.

Published
2024

3. Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions

Author

Borsoni, Thomas, Boudin, Laurent, and Salvarani, Francesco

Subjects
Mathematics - Functional Analysis
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 contributions due to the internal energy of the molecules. We also propose a geometric variant of Grad's proof of the same compactness property in the monatomic case.

Published
2022

4. Energy method for the Boltzmann equation of monatomic gaseous mixtures

Author

Boudin, Laurent, Grec, Bérénice, Pavić-Čolić, Milana, and Simić, Srboljub

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a global equilibrium is decomposed into the sum of a macroscopic and a microscopic part, for which we obtain a priori estimates at both lower and higher orders. These estimates are obtained under a suitable smallness assumption. The assumption can be justified a posteriori in the higher-order case, leading to the closure of the corresponding estimate.

Published
2021

5. Exponential convergence towards consensus for non-symmetric linear first-order systems in finite and infinite dimensions

Author

Boudin, Laurent, Salvarani, Francesco, and Trélat, Emmanuel

Subjects
Mathematics - Analysis of PDEs
Abstract

We consider finite and infinite-dimensional first-order consensus systems with timeconstant 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 to define a weighted mean corresponding to the consensus, and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate.

Published
2021

7. Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distributions

Author

Bondesan, Andrea, Boudin, Laurent, Briant, Marc, and Grec, Bérénice

Subjects
Mathematical Physics, Mathematics - Analysis of PDEs
Abstract

We consider the Boltzmann operator for mixtures with cutoff Maxwellian, hard potentials, or hard spheres collision kernels. In a perturbative regime around the global Maxwellian equilibrium, the linearized Boltzmann multi-species operator $\mathbf{L}$ is known to possess an explicit spectral gap $\lambda_{\mathbf{L}}$, in the global equilibrium weighted $L^2$ space. We study a new operator $\mathbf{L^\varepsilon}$ obtained by linearizing the Boltzmann operator for mixtures around local Maxwellian distributions, where all the species evolve with different small macroscopic velocities of order $\varepsilon$, $\varepsilon >0$. This is a non-equilibrium state for the mixture. We establish a quasi-stability property for the Dirichlet form of $\mathbf{L^\varepsilon}$ in the global equilibrium weighted $L^2$ space. More precisely, we consider the explicit upper bound that has been proved for the entropy production functional associated to $\mathbf{L}$ and we show that the same estimate holds for the entropy production functional associated to $\mathbf{L^\varepsilon}$, up to a correction of order $\varepsilon$., Comment: 22 pages

Published
2018

11. Fluid-kinetic modelling for respiratory aerosols with variable size and temperature∗

Author

Boudin Laurent, Grandmont Céline, Grec Bérénice, Martin Sébastien, Mecherbet Amina, and Noël Frédérique

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939
Abstract

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.

Published
2020
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15. A kinetic model of polyatomic gas with resonant collisions

Author

Boudin, Laurent, Rossi, Alex, and Salvarani, Francesco

Abstract

We propose a kinetic model describing a polyatomic gas undergoing resonant collisions, in which the microscopic internal and kinetic energies are separately conserved during a collision process. This behaviour has been observed in some physical phenomena, for example in the collisions between selectively excited CO2molecules. We discuss the model itself, prove the related H-theorem and show that, at the equilibrium, two temperatures are expected. We eventually present a numerical illustration of the model and its main properties.

Published
2024
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17. A coupled model for the dynamics of gas exchanges in the human lung with Haldane and Bohr's effects

Author

Boudin, Laurent, Grandmont, Céline, Grec, Bérénice, Martin, Sébastien, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract
Abstract

We propose an integrated dynamical model for oxygen and carbon dioxide transfer from the lung into the blood, coupled with a lumped mechanical model for the ventilation process, for healthy patients as well as in pathological cases. In particular, we focus on the Bohr and Haldane effects, which induce a nonlinear coupling between the oxygen and the carbon dioxide. We also take into account the dead space volume, which requires a special attention in the pathological cases.

Published
2022

24. Concentration effects in a kinetic model with wealth and knowledge exchanges

Author

Boudin, Laurent, Trussardi, Lara, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université de Vienne, and universite de Vienne

Subjects
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [MATH]Mathematics [math]
Abstract

Using a kinetic equation of Boltzmann type, we describe the effect of knowledge and wealth exchange in a closed community, where all the interactions inside the population are binary. We model the evolution of the distribution function f = f (t, x, v) of agents with wealth v and knowledge x at time t. Some numerical experiments demonstrating, among other things, clustering effects, are presented, and some more asymptotic studies are performed.

Published
2020

28. Fluid-kinetic modelling for respiratory aerosols with variable size and temperature.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Boudin, Laurent, Grec, Bérénice, Martin, Sébastien, Mecherbet, Amina, and Noël, Frédérique

Subjects
AIR flow, PARTICLES, RESPIRATORY organs, NAVIER-Stokes equations, VLASOV equation, COMPUTER simulation of biological systems
Abstract

Copyright of ESAIM: Proceedings & Surveys is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Published
2020
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31. Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium maxwell distributions.

Author

Bondesan, Andrea, Boudin, Laurent, Briant, Marc, and Grec, Bérénice

Subjects
MAXWELL-Boltzmann distribution law, DIRICHLET forms, KINETIC theory of gases, NON-equilibrium reactions
Abstract

We consider the Boltzmann operator for mixtures with cutoff Maxwellian, hard potential, or hard-sphere collision kernels. In a perturbative regime around the global Maxwellian equilibrium, the linearized Boltzmann multi-species operator LL is known to possess an explicit spectral gap λLλL, in the global equilibrium weighted L2L2 space. We study a new operator LεLε obtained by linearizing the Boltzmann operator for mixtures around local Maxwellian distributions, where all the species evolve with different small macroscopic velocities of order εε, ε>0ε>0. This is a non-equilibrium state for the mixture. We establish a quasi-stability property for the Dirichlet form of LεLε in the global equilibrium weighted L2L2 space. More precisely, we consider the explicit upper bound that has been proved for the entropy production functional associated to LL and we show that the same estimate holds for the entropy production functional associated to LεLε, up to a correction of order εε. [ABSTRACT FROM AUTHOR]

Published
2020
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33. A numerical scheme for the one-dimensional pressureless gases system

Author

Boudin, Laurent, Mathiaud, Julien, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Numerical simulation of biological flows (REO), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), DAM Île-de-France (DAM/DIF), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Centre de Mathématiques et de Leurs Applications (CMLA), and École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]
Abstract

International audience; In this work, we investigate the numerical solving of the one-dimensional pressureless gases system. After briefly recalling the mathematical framework of the duality solutions introduced by Bouchut and James, we point out that the upwind scheme for the density and momentum does not satisfy the one-sided Lipschitz (OSL) condition on the expansion rate required for the duality solutions. Then we build a diffusive scheme which allows to recover the OSL condition by following a strategy previously described for the continuous model.

Published
2012

47. A MATHEMATICAL AND NUMERICAL ANALYSIS OF THE MAXWELL-STEFAN DIFFUSION EQUATIONS.

Author

Boudin, Laurent, Grec, Bérénice, and Salvarani, Francesco

Subjects
GAS mixtures, SPECTRUM analysis, MATHEMATICAL analysis, NUMERICAL solutions to heat equation, DIFFUSION, HEAT flux, MOLECULES
Abstract

We consider the Maxwell-Stefan model of diffusion in a multi-component gaseous mixture. After focusing on the main differences with the Fickian diffusion model, we study the equations governing a three-component gas mixture. Mostly in the case of a tridiagonal diffusion matrix, we provide a qualitative and quantitative mathematical analysis of the model. We develop moreover a standard explicit numerical scheme and investigate its main properties. We eventually include some numerical simulations underlining the uphill diffusion phenomenon. [ABSTRACT FROM AUTHOR]

Published
2012
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48. Aerosol deposition in a ventilator circuit: comparison between experimental results and numerical computations

Author

Ayman Moussa, Thomas Duparque, Céline Grandmont, Michael Grasseau, Marc Thiriet, Laurent Boudin, Patrice Diot, Laurent Vecellio, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Numerical simulation of biological flows (REO), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Pathologies Respiratoires : Protéolyse et Aérosolthérapie, Université de Tours (UT)-Institut National de la Santé et de la Recherche Médicale (INSERM), DTF-Aerodrug, DTF, Université de Tours-Institut National de la Santé et de la Recherche Médicale (INSERM), and Boudin, Laurent

Subjects
[SDV.MHEP.PSR] Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract, [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2009

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