Pierre Degond

Université Toulouse III - Paul Sabatier

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Sara Merino-Aceituno

University of Vienna

Fabrice Deluzet

Institut de Mathématiques de Toulouse

Amic Frouvelle

Centre de Recherche en Mathématiques de la Décision

Christian Ringhofer

Arizona State University

Jian‐Guo Liu

Duke University

Diane Peurichard

Sorbonne Université

Mohammed Lemou

Centre National de la Recherche Scientifique

Marie-Hélène Vignal

Institut de Mathématiques de Toulouse

Giacomo Dimarco

University of Ferrara

Pierre-Arnaud Raviart

Sorbonne Université

Cooperative Institutions

Centre National de la Recherche Scientifique

159

Université Toulouse III - Paul Sabatier

Université de Toulouse

Institut de Mathématiques de Toulouse

Institut national de recherche en informatique et en automatique

Imperial College London

Institut National des Sciences Appliquées de Toulouse

Sorbonne Université

École Polytechnique

Commissariat à l'Énergie Atomique et aux Énergies Alternatives

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Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour

Journal of Mathematical Biology (2022)

Pierre Degond Sophie Hecht Michèle Romanos Ariane Trescases

Elongation

10.1007/s00285-022-01784-6

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Citations (4)

A kinetic description of anisotropic fluids with multivalued internal energy

European Journal of Mechanics - B/Fluids (2003)

Pierre Degond Mohammed Lemou José Luis López

Kinetic Theory

Internal energy

Operator (biology)

10.1016/s0997-7546(03)00060-8

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Citations (2)

On a hierarchy of macroscopic models for semiconductors

Journal of Mathematical Physics (1996)

N. Ben Abdallah Pierre Degond

This paper shows that various models of electron transport in semiconductors that have been previously proposed in the literature can be connected one with each other by the diffusion approximation methodology. We first investigate the diffusion limit of the semiconductor Boltzmann equation towards the so-called ‘‘spherical harmonic expansion model,’’ under the assumption of dominant elastic scattering. Then, this model is again connected, either to the energy-transport model or to a ‘‘periodic spherical harmonic expansion model’’ through a diffusion approximation, respectively making electron–electron or phonon scattering large. We provide the mathematical background which makes the Hilbert expansions associated with these various diffusion limits rigorous.

Harmonic

Heavy traffic approximation

Convection–diffusion equation

10.1063/1.531567

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Citations (247)

A PLASMA EXPANSION MODEL BASED ON THE FULL EULER–POISSON SYSTEM

Mathematical Models and Methods in Applied Sciences (2007)

Pierre Crispel Pierre Degond Marie-Hélène Vignal

In this paper, we consider a quasi-neutral plasma expanding in the vacuum gap separating two electrodes. During the expansion, some particles are emitted from the plasma-vacuum interface and form a beam in the vacuum. Starting from the two-fluid full Euler–Poisson model, we derive an asymptotic model. This asymptotic model consists of a quasi-neutral model in the plasma region, a Child–Langmuir law in the beam region and connection relations at the plasma-beam interface. For this model, we propose a numerical scheme which accounts for the motion of the plasma-beam interface and is much more efficient than the resolution of the original two-fluid Euler–Poisson problem. We demonstrate the efficiency of the model by means of numerical simulations for two different one-dimensional test cases.

Poisson's equation

10.1142/s0218202507002224

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Citations (26)

Mach-number uniform asymptotic-preserving gauge schemes for compressible flows

HAL (Le Centre pour la Communication Scientifique Directe) (2007)

Pierre Degond Shi Jin J.-G. Liu

We present novel algorithms for compressible flows that are efficient for all Mach numbers. The approach is based on several ingredients: semi-implicit schemes, the gauge decomposition of the velocity field and a second order formulation of the density equation (in the isentropic case) and of the energy equation (in the full Navier-Stokes case). Additionally, we show that our approach corresponds to a micro-macro decomposition of the model, where the macro field corresponds to the incompressible component satisfying a perturbed low Mach number limit equation and the micro field is the potential component of the velocity. Finally, we also use the conservative variables in order to obtain a proper conservative formulation of the equations when the Mach number is order unity. We successively consider the isentropic case, the full Navier-Stokes case, and the isentropic Navier-Stokes-Poisson case. In this work, we only concentrate on the question of the time discretization and show that the proposed method leads to Asymptotic Preserving schemes for compressible flows in the low Mach number limit.

Isentropic process

Poisson's equation

Compressible flow

Source

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Citations (41)

The Child‐Langmuir asymptotics for semiconductors including phonon interactions

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (1997)

Pierre Degond Youchun Qiu

Presents a simplified mathematical model of electron transport in a one‐dimensional semiconductor device of N + ‐ N ‐ N + type. The model is based on a singular perturbation approach of the kinetic equation which describes the transport processes. This so‐called Child‐Langmuir asymptotics is obtained by assuming that the injected electrons at the N + ‐ N junction on the source side have a very weak energy compared with what they are able to gain under the influence of the electric field. Formally establishes the limit model when a realistic collision model for electron‐phonon interaction is considered. Compares the results with both experiments and particle simulations.

10.1108/03321649710182896

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Citations (2)

Simulation of non equilibrium plasmas with a numerical noise reduced particle in cell method

AIP conference proceedings (2011)

Pierre Degond Fabrice Deluzet Giacomo Dimarco Gérard Gallice Pietro Santagati

An innovative Particle In Cell method, aimed at reducing the numerical noise characterising classical PIC schemes, has been investigated in the framework of ionospheric plasma simulations. The numerical model is composed of a kinetic equation for the plasma coupled with the Maxwell‐Faraday law driving the evolution in the magnetic field.

Particle-in-cell

Faraday cage

Particle (ecology)

10.1063/1.3562793

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Citations (2)

Correction to: Coupled Self-Organized Hydrodynamics and Stokes Models for Suspensions of Active Particles

Journal of Mathematical Fluid Mechanics (2020)

Pierre Degond Sara Merino-Aceituno Fabien Vergnet Hui Yu

This note provides a list of errata and their correction for Reference [1].

10.1007/s00021-020-00519-1

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Towards a Kinetic Model of Turbulent Incompressible Fluids

Birkhäuser Basel eBooks (2001)

Pierre Degond Mohammed Lemou

A turbulence model for incompressible fluids is derived from kinetic theory. The kinetic model involves a relaxation time type collision operator which describes the relaxation of the probability distribution function (pdf) towards an isotropic pdf on a time scaleT.The dependence ofTupon the kinetic turbulent energy can be tuned in such a way that both the so called "viscous subrange" (dominated by molecular viscosity) and the "inertial range" (obeying the Kolmogorov law) can be described.

Kinetic Theory

10.1007/978-3-0348-8370-2_31

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Citations (1)

An asymptotic preserving scheme for the two-fluid Euler–Poisson model in the quasineutral limit

Journal of Computational Physics (2006)

Pierre Crispel Pierre Degond Marie-Hélène Vignal

Poisson's equation

10.1016/j.jcp.2006.09.004

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Citations (90)