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Publications (by subject)


Emergence and self-organization in complex systems

Micro-macro passage in models of complex systems

Self-Organized Hydrodynamics

P. Degond, G. Dimarco, T. B. N. Mac, Hydrodynamics of the Kuramoto-Vicsek model of rotating self-propelled particles,  Mathematical Models and Methods in Applied Sciences, 24 (2014) pp. 277–325manuscript on arXiv.

P. Degond, A. Frouvelle, J.-G. Liu,S. Motsch, L. Navoret, Macroscopic models of collective motion and self-organization, Séminaire Laurent Schwartz - EDP et applications (2012-2013), exposé n°1, (27 p.). manuscript on arXiv

P. Degond, J-G. Liu, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Mathematical Models and Methods in Applied Sciences, 22, Suppl. 1 (2012), 1140001 (18 pages).  manuscript on HAL ; manuscript on arXiv

P. Degond, J-G. Liu, S. Motsch, V. Panferov, Hydrodynamic models of self-organized dynamics: derivation and existence theory,Methods and Applications of Analysis20 (2013), 089-114. manuscript on HAL ; manuscript on arXiv

P. Degond, T. Yang, Diffusion in a continuum model of self-propelled particles with alignment interaction, Mathematical Models and Methods in Applied Sciences, 20, Suppl. (2010), pp. 1459-1490 and http://arxiv.org/abs/1002.2716


P. Degond, S. Motsch,  Continuum limit of self-driven particles with orientation interaction, Mathematical Models and Methods in Applied Sciences  18, Suppl. (2008), pp. 1193-1215. http://dx.doi.org/10.1142/S0218202508003005, manuscript on arxiv

P. Degond, S. Motsch,  Macroscopic limit of self-driven particles with orientation interaction, C. R. Acad. Sci. Paris, Ser I.  345 (2007), pp. 555-560. http://dx.doi.org/10.1016/j.crma.2007.10.024


Phase transitions

E. A. Carlen, M. C.Carvalho, P. Degond, B. Wennberg, A Boltzmann model for rod alignment and schooling fish. Submitted. Manuscript on arXiv

P. Degond, A. Frouvelle, G. Raoul, Local stability of perfect alignment for a spatially homogeneous kinetic model. Submitted.Manuscript on arXiv. 

P. Degond, A. Frouvelle,  J.-G. Liu, Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, submitted, manuscript on arxiv

P. Degond, A. Frouvelle, J.-G. Liu, A note on phase transitions for the Smoluchowski equation with dipolar potential, Proceedings of Hyp2012 - the 14th International Conference on Hyperbolic Problems held in Padova, Italy, June 25-28 2012, AIMS, 2013, to appearmanuscript on arXiv

A. Barbaro, P. Degond, Phase transition and diffusion among socially interacting self-propelled agents,Discrete and Continuum Dynamical Systems B, to appear. manuscript on arXiv

P. Degond, A. Frouvelle, J-G. Liu, Macroscopic limits and phase transition in a system of self-propelled particles, Journal of Nonlinear Science 23 (2013), pp. 427-456manuscript on HALmanuscript on arXiv


Propagation of chaos

E. Carlen, R. Chatelin, P. Degond, and B Wennberg, Kinetic hierarchy and propagation of chaos in biological swarm models, Physica D 260 (2013), 90-111.  manuscript on HALmanuscript on arXiv

E. Carlen, P. Degond, and B Wennberg, Kinetic limits for pair-interaction driven master equations and biological swarm models, Mathematical Models and Methods in Applied Sciences, 23 (2013), pp. 1339-1376. manuscript on arxiv

 


Applications


Economics and social sciences

P. Degond, J.-G. Liu, C. Ringhofer, Evolution of wealth in a nonconservative economy driven by local Nash equilibria. Submitted.Manuscript on arXiv

P. Degond, J.-G. Liu, C. Ringhofer, Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria, Journal of Statistical Physics154 (2014), pp. 751-780.. Manuscript on arXiv

P. Degond, J.-G. Liu, C. Ringhofer, Large-scale dynamics of Mean-Field Games driven by local Nash equilibria (previously: A Nash equilibrium macroscopic closure for kinetic models coupled with Mean-Field Games), Journal of Nonlinear Science 24 (2014), pp. 93-115manuscript (first version) on arXiv


Network and network formation models

P. Degond, M. Herty, J.-G. Liu, Flow on sweeping networks, to appear in Multiscale Modeling and SimulationManuscript on arXiv

E. Boissard, P. Degond, S. Motsch, Trail formation based on directed pheromone deposition, Journal of Mathematical Biology, 66 (2013), pp. 1267-1301..  manuscript on HAL ; manuscript on arXiv


Crowd dynamics

P. Degond, C. Appert-Rolland, J. Pettre, G. Theraulaz, Vision-based macroscopic pedestrian models, Kinetic and Related Models6 (2013), 809-839. Manuscript on arXiv

S. Motsch, M. Moussaïd, E. G. Guillot, M. Moreau, J. Pettré, G. Theraulaz, C. Appert-Rolland, P. Degond, Pedestrian counterflow drives cluster dynamics and traffic efficiency, submitted. 

P. Degond, C. Appert-Rolland, M. Moussaid, J. Pettre, G. Theraulaz, A hierarchy of heuristic-based models of crowd dynamics, Journal of Statistical Physics152 (2013), pp. 1033-1068. manuscript on arXiv

P. Degond, J. Hua, Self-Organized Hydrodynamics with congestion and path formation in crowds, Journal of Computational Physics, 237 (2013), pp. 299–319, manuscript on arxiv

M. Moussaïd, E. G. Guillot, M. Moreau, J. Fehrenbach, O. Chabiron, S. Lemercier, J. Pettré, C. Appert-Rolland, P. Degond, G. Theraulaz, Traffic Instabilities in Self-organized Pedestrian Crowds, PLoS Computational Biology, 8 (2012), e1002442 (open access)

O. Chabiron, J. Fehrenbach, P. Degond, M. Moussaıd, J. Pettre, S. Lemercier, Lane detection in pedestrian motion and entropy-based order index, First International Conference on Pattern Recognition Applications and Methods, accepted. 

S. Lemercier, A. Jelic, R. Kulpa, J. Hua, J. Fehrenbach, P. Degond, C. Appert-Rolland, S. Donikian, J. Pettré, Realistic following behaviors for crowd simulation, Computer Graphics Forum, Vol. 31, pp. 489–498, May 2012Online version

S. Lemercier, A. Jelic, J. Hua, J. Fehrenbach, P. Degond, C. Appert-Rolland, S. Donikian, J. Pettré, Un modèle de suivi réaliste pour la simulation de foules, Revue Électronique Francophone d’Informatique Graphique, 5 (2011), pp. 67–76. 

C. Appert-Rolland, P. Degond, S. Motsch, Two-way multi-lane traffic model for pedestrians in corridors, Networks and Heterogeneous Media, 6 (2011), 351-381. http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6434 and manuscript on HAL, manuscript on arXiv.


Herds 

P. Degond, J. Hua, L. Navoret, Numerical simulations of the Euler system with congestion constraint, Journal of Computational Physics, 230 (2011), pp. 8057-8088.http://www.sciencedirect.com/science/article/pii/S0021999111004153 and http://arxiv.org/abs/1008.4045

P. Degond, L. Navoret, R. Bon, D. Sanchez, Congestion in a macroscopic model of self-driven particles modeling gregariousness, J. Stat. Phys., 138 (2010), pp. 85-125. DOI: 10.1007/s10955-009-9879-x  and  http://arxiv.org/PS_cache/arxiv/pdf/0908/0908.1817v1.pdf

L. Navoret, R. Bon, P. Degond, J. Gautrais, D. Sanchez, G. Theraulaz,  Analogies between social interactions models and supply chains, in 'Progress in Industrial Mathematics at ECMI 2008' (A. D. Fitt, J. Norbury, H. Ockendon \& E. Wilson (eds.)), Mathematics in Industry, vol 15, part 2, Springer, 2010, pp. 535--540, http://dx.doi.org/10.1007/978-3-642-12110-4_84


Fish schools

P. Degond, S. Motsch, A macroscopic model for a system of swarming agents using curvature control, Journal of Statistical Physics, 143 (2011), pp. 685-714.  http://dx.doi.org/10.1007/s10955-011-0201-3 and http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.5405v1.pdf

P. Degond, S. Motsch,  Large scale dynamics of the Persistent Turning Walker model of fish behavior, J. Stat. Phys.,  131 (2008), pp. 989-1021. http://dx.doi.org/10.1007/s10955-008-9529-8, manuscript on arxiv


Car traffic

P. Degond, M. Delitala,  Modelling and simulation of vehicular traffic jam formation, Kinetic and Related Models  1 (2008), pp. 279-293. http://www.aimsciences.org/journals/doIPChk.jsp?paperID=3291&mode=full

F. Berthelin, P. Degond, V. Le Blanc, S. Moutari, J. Royer, M. Rascle,  A Traffic-Flow Model with Constraints for the Modeling of Traffic Jams, Mathematical Models and Methods in Applied Sciences  18, Suppl. (2008), pp.  1269-1298. http://dx.doi.org/10.1142/S0218202508003030

F. Berthelin, P. Degond, M. Delitala, M. Rascle,  A model for the formation and evolution of traffic jams, Arch. Rat. Mech. Anal., 187 (2008), pp. 185-220. http://dx.doi.org/10.1007/s00205-007-0061-9


Supply chains

P. Degond, C. Ringhofer,  Stochastic dynamics of long supply chains with random breakdowns, SIAM J. Appl. Math.  68 (2007), pp. 59-79. http://dx.doi.org/10.1137/060674302

P. Degond, S. Göttlich, M. Herty, A. Klar,  A network model for supply chains with multiple policies, SIAM J. Multiscale Modeling and Simulation,  6 (2007), pp. 820-837.  http://dx.doi.org/10.1137/060670316

D. Armbruster, P. Degond, C. Ringhofer,  Kinetic and fluid models for supply chains supporting policy attributes, Bulletin of the Institute of Mathematics, Academia Sinica (New Series),  2 (2007), pp. 433-460. http://www.math.sinica.edu.tw/bulletin_ns/20072/2007215.pdf

D. Armbruster, P. Degond, C. Ringhofer,  A model for the dynamics of large queuing networks and supply chains, SIAM J. Appl. Math.  66 (2006), pp. 896-920. http://dx.doi.org/10.1137/040604625

D. Armbruster, P. Degond, C. Ringhofer,  Continuum models for interacting machines, 'Networks of interacting machines: production organization in complex industrial systems and biological cells', D. Armbruster, K. Kaneko and A. Mikhailov (eds), World Scientific, 2005. 



Numerical methods for asymptotic problems

Asymptotic Preserving methods

Quasineutrality in plasmas

P. Degond, F. Deluzet, D. Savelief, Numerical approximation of the Euler-Maxwell model in the quasineutral limit, Journal of Computational Physics, 231 (2012), pp. 1917-1946. manuscript on HALmanuscript on arXiv.

P. Degond, Asymptotic-Preserving Schemes for Fluid Models of Plasmas, to appear in the collection 'Panoramas et Syntheses' of the SMFmanuscript on HALmanuscript on arXiv

P. Degond, H. Liu, D. Savelief, M-H. Vignal, Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit, Journal of Scientific Computing, 51 (2012), pp. 59–86. manuscript on arXiv

 R. Belaouar, N. Crouseilles, P. Degond, E. Sonnendrücker,   An asymptotically stable semi-lagrangian scheme in the quasi-neutral limit, Journal of Scientific Computing, 41 (2009), pp. 341-365. DOI: 10.1007/s10915-009-9302-4  and   http://hal.archives-ouvertes.fr/docs/00/18/93/83/PDF/paperquasiN.pdf
 
P. Degond, F. Deluzet, L. Navoret, A-B. Sun, M-H.Vignal, Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality, J. Comput. Phys., 229 (2010), pp. 5630–5652,  http://dx.doi.org/10.1016/j.jcp.2010.04.001  and  http://hal.archives-ouvertes.fr/hal-00359356/fr/
 
P. Degond, J-G. Liu, M-H. Vignal,  Analysis of an asymptotic preserving scheme for the Euler-Poison system in the quasineutral limit, SIAM J. Numer. Anal.  46 (2008), pp. 1298-1322. http://dx.doi.org/10.1137/070690584
 
P. Crispel, P. Degond, M-H. Vignal,  A plasma expansion model based on the full Euler-Poisson system, Mathematical Models and Methods in Applied Sciences,  17 (2007), pp. 1129-1158. http://dx.doi.org/10.1142/S0218202507002224

P. Crispel, P. Degond, M-H. Vignal,  An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit, J. Comp. Phys.,  223 (2007), pp. 208-234. http://dx.doi.org/10.1016/j.jcp.2006.09.004

P. Degond, F. Deluzet, L. Navoret,  An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality, C. R. Acad. Sci. Paris, Ser I, 343 (2006), pp. 613-618. http://dx.doi.org/10.1016/j.crma.2006.09.033

P. Crispel, P. Degond, M-H. Vignal,  Quasi-neutral fluid models for current-carrying plasmas, J. Comput. Phys.,  205 (2005), pp. 408-438. http://dx.doi.org/10.1016/j.jcp.2004.11.011

P. Crispel, P. Degond, M-H. Vignal,  An asymptotically stable discretization for the Euler-Poisson system in the quasineutral limit, C. R. Acad. Sci. Paris, Ser I,    341 (2005), pp. 341-346. http://dx.doi.org/10.1016/j.crma.2005.07.008

P. Crispel, P. Degond, C. Parzani, M-H. Vignal,  Trois formulations d'un modèle de plasma quasi-neutre avec courant non-nul, C. R. Acad. Sci. Paris, Ser I,    338 (2004), pp. 327-332. http://dx.doi.org/10.1016/j.crma.2003.11.029

P. Degond, C. Parzani, M-H. Vignal,  On plasma expansion in vacuum, in 'Free Boundary Problems: Theory and Applications', P. Colli, C. Verdi and A. Visintin (eds), International Series of Numerical Mathematics, vol 147, Birkhäuser Verlag, Basel, 2004, pp.  103-112.

P. Degond, C. Parzani, M-H. Vignal,  Plasma expansion in vacuum: modeling the breakdown of quasineutrality, SIAM Multiscale Modeling and Simulation  2 (2003) pp. 158-178. http://dx.doi.org/10.1137/030600333

P. Degond, C. Parzani, M-H. Vignal,  A one-dimensional model of plasma expansion, Mathematical and Computer Modelling,  38 (2003), pp. 1093-1099. http://dx.doi.org/10.1016/S0895-7177(03)90109-9

P. Degond, C. Parzani, M-H. Vignal,  Un modèle d'expansion de plasma dans le vide, C. R. Acad. Sci. Paris, Ser I,    335 (2002), pp. 399-404. http://dx.doi.org/10.1016/S1631-073X(02)02479-2

  
 

Strongly anisotropic diffusion problems ; application to large magnetic fields in plasmas

S. Brull, P. Degond, F. Deluzet, A. Mouton, Asymptotic-Preserving scheme for a bi-fluid Euler-Lorentz model, Kinetic and Related Models 4 (2011), pp. 991 - 1023. http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6730 and manuscript on HALmanuscript on arXiv.

P. Degond, Asymptotic-Preserving Schemes for Fluid Models of Plasmas, to appear in the collection 'Panoramas et Syntheses' of the SMFmanuscript on HALmanuscript on arXiv

P. Degond, A. Lozinski, J. Narski & C. Negulescu, An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition, Journal of Computational Physics,231 (2012), pp. 2724-2740. http://arxiv.org/abs/1102.0904

S. Brull, P. Degond, F. Deluzet, Degenerate anisotropic elliptic problems and magnetized plasma simulations, Communications in Computational Physics (CICP), 11 (2012), pp. 147-178  and http://arxiv.org/abs/1010.5968 

P. Degond, F. Deluzet, A. Lozinski, J. Narski & C. Negulescu, Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations, Communications in Mathematical Sciences, 10 (2012), pp. 1-31. and http://arxiv.org/abs/1008.3405

P. Degond, S. Hirstoaga, M-H. Vignal, The Vlasov model under large magnetic fields in the low-Mach number regime. http://hal.archives-ouvertes.fr/hal-00384345/fr/ and http://fr.arxiv.org/abs/0905.2400
 
P. Degond, F. Deluzet, C. Negulescu, An Asymptotic-Preserving scheme for strongly anisotropic problems, Multiscale Model. Simul., 8 (2010), pp. 645-666. http://dx.doi.org/10.1137/090754200 and  http://fr.arxiv.org/abs/0903.4984
 
P. Degond, F. Deluzet, A. Sangam, M-H. Vignal,  An asymptotic preserving scheme for the Euler equations in a strong magnetic field,  J. Comput. Phys., 228 (2009), pp. 3540-3558. http://arxiv.org/abs/0809.1527 and http://dx.doi.org/10.1016/j.jcp.2008.12.040

C. Besse, J. Claudel, P. Degond, F. Deluzet, G. Gallice, C. Tessieras,  Numerical simulations of the ionospheric striation model in a non-uniform magnetic field, Computer Physics Communications,  176 (2007), pp. 75-90. http://dx.doi.org/10.1016/j.cpc.2006.07.022

C. Besse, P. Degond, H-J. Hwang, R. Poncet,  Nonlinear instability of the two-dimensional striation model about smooth steady states, Comm. PDE.,  32 (2007), pp.  1017-1041. http://dx.doi.org/10.1080/03605300701454750

C. Besse, J. Claudel, P. Degond, F. Deluzet, G. Gallice, C. Tessieras,  Instability of the ionospheric plasma: modeling and analysis, SIAM Appl. Math.  65 (2005), pp. 2178-2198. http://dx.doi.org/10.1137/040606582

C. Besse, P. Degond, F. Deluzet, J. Claudel, G. Gallice, C. Tessieras,  Ionospheric plasmas: model derivation, stability analysis and numerical simulations, in 'Numerical Methods for Hyperbolic and Kinetic Problems', S. Cordier, T. Goudon, M. Gutnic, E. Sonnendrücker (eds), European Mathematical Society, Zürich, 2005.

C. Besse, J. Claudel, P. Degond, F. Deluzet, G. Gallice, C. Tessieras,  A model hierarchy for ionospheric plasma modeling, Mathematical Models and Methods in Applied Sciences  14 (2004), pp. 393-415. http://dx.doi.org/10.1142/S0218202504003283

C. Tessieras, J. Claudel, P. Degond, G. Gallice,  Striations dans l'ionosphère: phénoménologie et simulation numérique, Chocs (revue scientifique et technique de la Direction des Applications Militaires, Commissariat à l'Energie Atomique),  26 (2002), pp. 71-83.

 
 
 

All-speed schemes for compressible fluids

P. Degond, J. Hua, Self-Organized Hydrodynamics with congestion and path formation in crowds, Journal of Computational Physics, 237 (2013), pp. 299–319

F. Cordier, P. Degond, A. Kumbaro, Phase appearance or disappearance in two-phase flows, Journal of Scientific Computing58 (2014), pp. 115-148. manuscript on HALmanuscript on arXiv

F. Cordier, P. Degond, A. Kumbaro, An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations, Journal of Computational Physics, 231 (2012), pp. 5685–5704 manuscript on HAL. ; manuscript on arXiv

P. Degond, L. Navoret, J. Hua, Numerical simulations of the Euler system with congestion constraint, Journal of Computational Physics, 230 (2011), pp. 8057-8088. http://www.sciencedirect.com/science/article/pii/S0021999111004153 and http://arxiv.org/abs/1008.4045

P. Degond, M. Tang, All speed scheme for the low mach number limit of the Isentropic Euler equation, Communications in Computational Physics, 10 (2011), pp. 1-31. http://www.global-sci.com/issue/abstract/readabs.php?vol=10&page=1&issue=1&ppage=31&year=2011 and http://arxiv.org/PS_cache/arxiv/pdf/0908/0908.1929v1.pdf
 
P. Degond, S. Jin, J-G. Liu,  Mach-number uniform asymptotic-preserving gauge schemes for compressible flows, Bulletin of the Institute of Mathematics, Academia Sinica (New Series)  2 (2007), pp. 851-892. http://www.math.sinica.edu.tw/bulletin_ns/20074/2007403.pdf
 
 
 

Other applications of AP-methods

P. Degond, S. Jin, M. Tang,  On the time-splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit, SIAM J. Sci. Comput.,  30 (2008), pp. 2466-2487. 10.1137/070700711
 
P. Degond, S. Gallego, F. Méhats,  An asymptotic-preserving scheme for the Schrödinger equation in the semi-classical limit, C. R. Acad. Sci. Paris, Ser I.  345 (2007), pp. 531-536. http://dx.doi.org/10.1016/j.crma.2007.10.014
 
 


Multiscale methods

B. P. Muljadi, J. Narski, A. Lozinski, P. Degond, Non-conforming multiscale finite element method for Stokes flows in heterogeneous media. Part 1: methodologies and numerical experiments. Submitted. Manuscript on arXiv

P. Degond, A. Lozinski, B. P. Muljadi, J. Narski, Crouzeix-Raviart MsFEM with Bubble Functions for Diff.usion and Advection-Diff.usion in Perforated Media. submitted. Manuscript on arXiv

P. Degond, G Dimarco, Fluid simulations with localized Boltzmann upscaling by Direct Simulation Monte-Carlo,  Journal of Computational Physics, 231 (2012), pp. 2414-2437http://arxiv.org/abs/1011.3456

P. Degond, G. Dimarco, L. Mieussens, A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects, J. Comput. Phys., 229 (2010), pp. 4907–4933, http://dx.doi.org/10.1016/j.jcp.2010.03.009 and http://arxiv.org/pdf/0908.0206

P. Degond, G. Dimarco, L. Pareschi, The Moment Guided Monte Carlo Method, International Journal for Numerical Methods in Fluids, 67 (2011), pp. 189-213.  http://onlinelibrary.wiley.com/doi/10.1002/fld.2345/abstract and http://arxiv.org/pdf/0908.0261

P. Degond, G. Dimarco, L. Mieussens,  A moving interface method for dynamic kinetic-fluid coupling, J. Comput. Phys.  227 (2007), pp. 1176-1208. http://dx.doi.org/10.1016/j.jcp.2007.08.027

P. Degond, J-G. Liu, L. Mieussens,  Macroscopic fluid models with localized kinetic upscaling effects, SIAM J. Multiscale Modeling and Simulation,  5 (2006), pp. 940-979. http://dx.doi.org/10.1137/060651574
 
P. Degond, S. Jin, L. Mieussens,  A smooth transition model between kinetic and hydrodynamic equations, J. Comput. Phys.,  209 (2005), pp. 665-694 .  http://dx.doi.org/10.1016/j.jcp.2005.03.025

N. Crouseilles, P. Degond, M. Lemou,  A hybrid kinetic-fluid model for solving the Vlasov-BGK equation, J. Comput. Phys.,  203 (2005), pp. 572-601. http://dx.doi.org/10.1016/j.jcp.2004.09.006

P. Degond, S. Jin,  A smooth transition model between kinetic and diffusion equations, SIAM Numerical Analysis  42 (2005), pp. 2671-2687. http://dx.doi.org/10.1137/S0036142903430414

N. Crouseilles, P. Degond, M. Lemou,  A hybrid kinetic-fluid model for solving the gas dynamics Boltzmann-BGK equation, J. Comput. Phys.,  199 (2004), pp. 776-806. http://dx.doi.org/10.1016/j.jcp.2004.03.007

N. Crouseilles, P. Degond, M. Lemou,  Hybrid kinetic/fluid models for nonequilibrium systems, C. R. Acad. Sci. Paris, Ser I,    336 (2003), pp. 359-364. http://dx.doi.org/10.1016/S1631-073X(03)00033-5

 
 
 

Other topics

Micro-macro passage in physical systems 


Hall Magnetohydrodynamics

D. Chae, P. Degond, J.-G. Liu, Well-posedness for Hall-magnetohydrodynamics, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaireappeared onlinemanuscript on arXiv

M. Acheritogaray, P. Degond, A. Frouvelle, J-G. Liu, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinetic and Related Models 4 (2011), pp. 901-918. http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6726 and manuscript on HAL ; manuscript on arXiv .


Electrical discharges and arcs

J-C. Mateo-Velez, P. Degond, F. Rogier, A. Séraudie, F. Thivet,  Modelling wire-to-wire corona discharge action on aerodynamics and comparison to experiment, J. Phys. D: Appl. Phys.  41 (2008) 035205 (11p.). http://dx.doi.org/10.1088/0022-3727/41/3/035205

P. Degond, B. Lucquin-Desreux,  Mathematical models of electrical discharges in air at atmospheric pressure: a derivation from asymptotic analysis, Int. J. Computing Science and Mathematics,  1 (2007), pp. 58-97. http://dx.doi.org/10.1504/IJCSM.2007.013764 
 
J-C. Matéo-Velez, F. Rogier, F. Thivet, P. Degond,  Numerical modeling of plasma-flow interaction, Proceeding of the ICCS 2006 (International Conference on Computational Science), Reading (UK), May 28-31, 2006. http://dx.doi.org/10.1007/11758525_1

P. Degond, G. Quinio, F. Rogier,  Asymptotic analysis of a simple ionization kinetics of air flows at atmospheric pressure, Journal of Physics D: Applied Physics  38 (2005), pp. 1371-1382. http://dx.doi.org/10.1088/0022-3727/38/9/008

J-C. Matéo-Velez, F. Thivet, F. Rogier, G. Quinio, P. Degond,  Numerical modelling of corona discharges and their interaction with aerodynamics, proceedings de la conference 'European Conference for aerospace sciences (EUCASS), July 4-7th 2005, Moscow.

P. Crispel, P. Degond, M-H. Vignal, J-F. Roussel, E. Amorim, D. Payan, M. Cho,  Secondary arc description on satellite solar generators, proceedings de la 9th spacecraft charging technology conference, 4-8 April 2005, Tsukuba, Japan.

J-C. Matéo-Velez, F. Thivet, P. Degond,  Modélisation élémentaire du vent ionique dans une décharge couronne, comptes rendus du congrès annuel de la société française d'électrostatique, juin 2004.

 

 

Energy-transport models for plasmas and semiconductors

 I. Choquet, P. Degond, B. Lucquin-Desreux,  A strong ionization model in plasma physics, Mathematical and Computer Modelling, 49 (2009), pp. 88-113. http://dx.doi.org/10.1016/j.mcm.2007.06.035
 
P. Degond,  Asymptotic continuum models for plasmas and disparate mass gaseous binary mixtures, in 'Material substructures in complex bodies: from atomic level to continuum', G. Capriz, P-M. Mariano (eds), Elsevier, Amsterdam, 2007. http://dx.doi.org/10.1016/B978-008044535-9/50002-9

I. Choquet, P. Degond, B. Lucquin-Desreux,  A hierarchy of diffusion models for partially ionized plasmas, Discrete and Continuous Dynamical Systems, Series B.,  8 (2007), pp. 735-772. http://www.aimsciences.org/journals/pdfs.jsp?paperID=2747&mode=full

I. Choquet, P. Degond, C. Schmeiser,  Energy-Transport models for charge carriers involving impact ionization in semiconductors, Transp. Theory Stat. Phys.  32 (2003), pp. 99-132. http://dx.doi.org/10.1081/TT-120019039

P. Degond, D. Levermore, C. Schmeiser,  A note on the energy-transport limit of the semiconductor Boltzmann equation, in 'Transport in Transition Regimes', N. Ben Abdallah et al (eds), The IMA Volumes in Mathematics and Applications, vol 135, Springer, 2003.

 
P. Degond, A. Jüngel, P. Pietra,  Numerical discretization of energy-transport models for semiconductors with non-parabolic band structure, SIAM on Scientific Computing  22 (2000), pp. 986-1007. http://dx.doi.org/10.1137/S1064827599360972
 
P. Degond, S. Génieys,  A. Jüngel,  A steady-state system in non-equilibrium thermodynamics  including thermal and electrical effects, Math. Methods in the Applied Sciences  21 (1998), pp. 1399-1413. http://www3.interscience.wiley.com/journal/10007607/abstract
 
P. Degond, S. Génieys et A. Jüngel,  A system of parabolic equations in nonequilibrium  thermodynamics including thermal and electrical effects, Journal de Mathématiques Pures et  Appliquées.  76 (1997), pp. 991-1015. http://dx.doi.org/10.1016/S0021-7824(97)89980-1

P. Degond, S. Génieys et A. Jüngel,  Symmetrization and entropy inequality for general diffusion  equations, C. R. Acad. Sci. Paris, Ser I,    325 (1997), pp. 963-968. http://dx.doi.org/10.1016/S0764-4442(97)89087-8

P. Degond, S. Génieys et A. Jüngel,  An existence result for a strongly coupled parabolic system  arising in nonequilibriium thermodynamics, C. R. Acad. Sci. Paris, Ser I, 325 (1997), pp. 227-232.  http://dx.doi.org/10.1016/S0764-4442(97)84605-8

P. Degond, S. Génieys,  A. Jüngel,  An existence and uniqueness result for  the stationary  energy-transport model in semiconductor theory, C. R. Acad. Sci. Paris, Ser I, 324 (1997), pp. 867-872. http://dx.doi.org/10.1016/S0764-4442(97)86960-1

P. Degond, B. Lucquin-Desreux,  Transport coefficients of plasmas and disparate mass binary  gases, Transp. Theory and Stat. Phys.  25 (1996), pp. 595-633. http://dx.doi.org/10.1080/00411459608222915
 
N. Ben Abdallah, P. Degond, S. Génieys,  An energy-transport model for semiconductors  derived from the Boltzmann equation, J. Stat. Phys.  84 (1996), pp. 205-231. http://dx.doi.org/10.1007/BF02179583 

P. Degond, B. Lucquin-Desreux,  The asymptotics of collision operators for two species of  particles of disparate masses, Mathematical Models and Methods in Applied Sciences   6 (1996),  pp. 405-436. http://dx.doi.org/10.1142/S0218202596000158

P. Degond, B. Lucquin-Desreux,  Comportement hydrodynamique d'un mélange gazeux formé  de deux espèces de particules de masses très différentes,  C. R. Acad. Sci. Paris, Ser I,    322 (1996) pp.  405-410.

 

Fokker-Planck-SHE (Spherical Harmonics Expansion) models for plasmas and semiconductors

N. Ben Abdallah, P. Degond, F. Deluzet, V. Latocha, R. Talaalout, M-H. Vignal,  Diffusion limits of kinetic models, in 'Hyperbolic problems: theory, numerics, applications', T. Y. Hou and E. Tadmor (eds), Springer, 2003, pp. 3-17.

P. Degond,  An infinite system of diffusion equations arising in transport theory: the coupled spherical harmonics expansion model,  Mathematical Models and Methods in Applied Sciences  11 (2001), pp. 903-932.  http://dx.doi.org/10.1142/S0218202501001173

P. Degond,    Mathematical modelling of microelectronics semiconductor devices, Proceedings of the Morningside Mathematical Center, Beijing, AMS/IP Studies in Advanced Mathematics, AMS Society and International Press, 2000, pp. 77-109.

P. Degond, C. Schmeiser,  Kinetic boundary layers and fluid-kinetic coupling in  semiconductors, Transp. Theory and Stat. Phys.  28 (1999), pp. 31-55. http://dx.doi.org/10.1080/00411459908214514
 
N. Ben Abdallah, P. Degond,  On a hierarchy of macroscopic models for semiconductors, J. Math. Phys.  37 (1996), pp. 3306-3333.
 
 
 

Diffusion and Hydrodynamic limits

P. Degond, S. Goettlich, A. Klar, M. Seaid, A. Unterreiter,  Derivation of a kinetic model from a stochastic particle system, Kinetic and Related Models.,  1 (2008), pp. 557-572. doi:  10.3934/krm.2008.1.557 

I. Choquet, P. Degond, C. Schmeiser,  Hydrodynamic models for charge carriers, Comm. Math. Sci.  1 (2003), pp. 74-86. http://www.intlpress.com/CMS/journal/v1i1/choquet.pdf

P. Degond, A. Klar,  A relaxation approximation for transport equations in the diffusive limit, Appl. Math. Lett.  15 (2002), pp. 131-135. http://dx.doi.org/10.1016/S0893-9659(01)00106-9

P. Degond, T. Goudon et F. Poupaud,  Diffusion limit for non homogeneous and non micro-reversible processes, Indiana University Math. J.  49 (2000), pp. 1175-1198. http://dx.doi.org/10.1512/iumj.2000.49.1936

 
 

Diffusion by solid boundaries: applications to plasmas

P. Degond, C. Parzani, M-H. Vignal,  A Boltzmann model for trapped particles in a surface potential, SIAM J. Multiscale Modeling and Simulation,  5 (2006), pp. 364-392. http://dx.doi.org/10.1137/050642897

P. Degond  Transport of trapped particles in a surface potential, in Studies in Mathematics and its Applications, Vol. 31, D. Cioranescu et J. L. Lions (eds), Elsevier, 2002, pp. 273-296. http://dx.doi.org/10.1016/S0168-2024(02)80014-5

P. Degond, V. Latocha, S. Mancini, A. Mellet,  Diffusion dynamics of an electron gas confined between two plates,  Methods and Applications of Analysis.   9 (2002), pp. 127-150. http://www.intlpress.com/MAA/p/2002/09_1/MAA-09-1-127-150.pdf

V. Latocha, L. Garrigues, P. Degond, J. P. Boeuf,  Numerical Simulation of Electron Transport in the Channel Region of a Stationary Plasma Thruster, Plasma sources sci. Technol.  11 (2002), pp. 104-114. http://dx.doi.org/10.1088/0963-0252/11/1/313

P. Degond, S. Mancini,  Diffusion driven by collisions with the boundary, Asymptotic Analysis  27 (2001), pp. 47-73.

P. Degond, R. Talaalout, M. H. Vignal,  Electron transport and secondary emission in a surface of a solar cell, comptes rendus de la conférence 'multipactor, RF and DC corona and passive intermodulation in space RF hardware', ESTEC, Noordwijk, The Netherlands, Sept 4-6, 2000.

 
P. Degond, V. Latocha, L. Guarrigues, J. P. Boeuf,  Electron Transport in Stationary Plasma  Thrusters, Transp. Theory and Stat. Phys  27 (1998), pp. 203-221. http://dx.doi.org/10.1080/00411459808205621

P. Degond,  A model of near-wall conductivity and its application to plasma thrusters, SIAM J. Applied Math  58 (1998), pp. 1138-1162. http://dx.doi.org/10.1137/S0036139996300897

P. Degond,  Un modèle de conductivité pariétale : application au moteur à propulsion ionique, C.  R. Acad. Sci. Paris, Ser I,     322 (1996) pp. 797-802.

 
 

Diffusion by interfaces: applications to semiconductor super-lattices

P. Degond, K. Zhang,  A scattering matrix model of semiconductor superlattices in multidimensional wave-vector space and its diffusion limit, Chin. Ann. Math.  24B (2003), pp. 167-190. http://dx.doi.org/10.1142/S0252959903000165

N. Ben Abdallah, P. Degond, A. Mellet and F. Poupaud,  Electron transport in semiconductor superlattices, Quarterly Appl. Math.  61 (2003), pp. 161-192.

P. Degond, K. Zhang,  Diffusion approximation of a scattering matrix model of a semiconductor superlattice,  SIAM J. Appl. Math.  63 (2002), pp. 279-298. http://dx.doi.org/10.1137/S0036139999360015

P. Degond, C. Schmeiser,  Macroscopic models for semiconductor heterostructures, J.  Math. Phys  39 (1998), pp. 1-30.
 
 
 

High-field diffusion models

P. Degond, B. Wennberg,  Mass and energy balance laws derived from high-field limits of thermostatted Boltzmann equations, Commun. Math. Sci.,  5 (2007), pp. 355-382. http://www.intlpress.com/CMS/p/2007/issue5-2/CMS-5-2-355-382.pdf

IP. Degond, A. Jüngel,  High field approximations of the energy-transport model for semiconductors with non parabolic band structure, Zeitschrifts für Angewandte Mathematik und Physik  52 (2001), PP. 1053-1070. http://dx.doi.org/10.1007/PL00001583

N. Ben Abdallah, P. Degond,  P. Markowich, C. Schmeiser,  High-field approximations of the Spherical Harmonics Expansion model for semiconductors, Zeitschrifts für Angewandte Mathematik und Physik  52 (2001), pp. 201-230. http://dx.doi.org/10.1007/PL00001544
 
P. Degond, A. Nouri, C. Schmeiser,  Macroscopic models for ionization in the presence of strong electric fields,  Transp. Theory and Stat. Phys.,  29 (2000), pp. 551-561. http://dx.doi.org/10.1080/00411450008205891
 
 

Quantum systems

P. Degond, S. Gallego, F. Méhats, C. Ringhofer,  Quantum hydrodynamic and diffusion models derived from the entropy principle, in 'Quantum Transport: modelling, analysis and asymptotics - lectures given at the CIME summer school held in Cetraro (Italy), September 11-16, 2006' (N. Ben Abdallah & G. Frosali (eds.)), Lectures Notes in Mathematics vol. 1946, Springer, 2008, pp. 111-168. http://dx.doi.org/10.1007/978-3-540-79574-2_3
 
P. Degond, S. Gallego, F. Méhats, C. Ringhofer,  Quantum diffusion models derived from the entropy principle, in 'Progress in industrial mathematics at ECMI 2006' (L L. Bonilla, M. M. Moscoso, G. Platero, J. M. Vega (eds.)), Mathematics in Industry, vol 12, Springer, 2008, pp. 106--122.   http://dx.doi.org/10.1007/978-3-540-71992-2_6

P. Degond, S. Gallego, F. Méhats,  On quantum hydrodynamic and quantum energy-transport models, Commun. Math. Sci.  5 (2007), pp. 887-908. http://www.intlpress.com/CMS/p/2007/issue5-4/CMS-5-4-A8-Degond.pdf

J-P. Bourgade, P. Degond, N. Mauser, C. Ringhofer,  Quantum corrections to semiclassical transport in nanoscale devices using entropy principles, J. Comput. Electron.  6 (2007), pp. 117-120. http://dx.doi.org/10.1007/s10825-006-0062-1
 
P. Degond, S. Gallego, F. Méhats,  Simulation of a resonant tunneling diode using an entropic quantum drift-difusion model, J. Comput. Electron.  6 (2007), pp. 133-136. http://dx.doi.org/10.1007/s10825-006-0088-4

P. Degond, S. Gallego, F. Méhats,  Isothermal quantum hydrodynamics: derivation, asymptotic analysis and simulation, SIAM J. Multiscale Modeling and Simulation,  6 (2007), pp. 246-272. http://dx.doi.org/10.1137/06067153X

 P. Degond, S. Gallego, F. Méhats,  An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes, J. Comp. Phys.,  221 (2007), pp. 226-249. http://dx.doi.org/10.1016/j.jcp.2006.06.027

P. Degond ,,S. Gallego, F. Méhats, On a New Isothermal Quantum Euler Model: Derivation, Asymptotic Analysis and Simulation, Lecture notes in Computer Sciences, Berlin, Heidelberg, 2007, pp. 939-946. http://dx.doi.org/10.1007/978-3-540-72584-8_123

J-P. Bourgade, P. Degond, F. Méhats, C. Ringhofer,  On quantum extensions to classical Spherical Harmonics Expansion / Fokker-Planck models, J. Math. Phys.,  47 (2006), 043302 (26 pages). http://link.aip.org/link/?JMAPAQ/47/043302/1

P. Degond, F. Méhats, C. Ringhofer,  Quantum energy-transport and drift-diffusion models, J. Stat. Phys.  118 (2005), pp. 625-667. 

P. Degond, F. Méhats, C. Ringhofer,  Quantum hydrodynamic models derived from the entropy principle, Contemporary Mathematics,  371 (2005), pp. 107-131.

P. Degond, C. Ringhofer,  Quantum moment hydrodynamics and the entropy principle, J. Stat. Phys.  112 (2003), pp. 587-628. http://dx.doi.org/10.1023/A:1023824008525

P. Degond, C. Ringhofer,  Binary quantum collision operators conserving mass momentum and energy, C. R. Acad. Sci. Paris, Ser I,    336 (2003), pp. 785-790. http://dx.doi.org/10.1016/S1631-073X(03)00185-7

P. Degond, C. Ringhofer,  A note on quantum moment hydrodynamics and the entropy principle, C. R. Acad. Sci. Paris, Ser I,    335 (2002), pp. 967-972. http://dx.doi.org/10.1016/S1631-073X(02)02595-5 

 
 

Relativistic systems

V. Bagland, P. Degond, M. Lemou,  Moment systems derived from relativistic kinetic equations, J. Stat. Phys.,  125 (2006), pp. 617-655. http://dx.doi.org/10.1007/s10955-006-9173-0
 
 
 

Wave-particle collisions and applications to cometary flows and turbulence

P. Degond, M. Lemou, J-L. Lòpez,  A kinetic description of anisotropic fluids with multivalued internal energy, European Journal of Mechanics B/fluids  22 (2003), pp. 487-509. http://dx.doi.org/10.1016/S0997-7546(03)00060-8
 
P. Degond, M. Lemou and J. L. Lopez,  Fluids with multivalued internal energy, the anistropic case, in 'Transport in Transition Regimes', N. Ben Abdallah et al (eds), The IMA Volumes in Mathematics and Applications, vol 135, Springer, 2003. 
 
P. Degond, M. Lemou,  Turbulence models for incompressible fluids derived from kinetic theory, J. Math. Fluid Mech.  4 (2002), pp. 257-284. http://dx.doi.org/10.1007/s00021-002-8545-8

P. Degond et M. Lemou,  On the viscosity and thermal conduction of fluids with multivalued internal energy,  European J. Mech. B/fluids  20 (2001), pp. 303-327. http://dx.doi.org/10.1016/S0997-7546(00)01095-5

P. Degond, M. Lemou,  Towards a kinetic model of turbulent incompressible fluid, in 'Hyperbolic problems, theory, numerics, applications', H. Freistuhler and G. Warnecke (eds), International series of Numerical mathematics, Vol 140, Birkhäuser, 2001, pp. 297-306.

P. Degond, J. L. Lopèz, F. Poupaud, C. Schmeiser,  Existence of solutions of a kinetic equation modeling cometary flows, J. Stat. Phys.  96 (1999), pp. 361-376. http://dx.doi.org/10.1023/A:1004584719071
 
P. Degond, J. L. Lopez, P. F. Peyrard,  On the macroscopic dynamics induced by a model  wave-particle collision operator, Continuum Mechanics and Thermodynamics  10 (1998), pp. 153-178. http://dx.doi.org/10.1007/s001610050087

P. Degond, P. F. Peyrard,  Un modèle de collisions ondes-particules en physique des plasmas :  application à la dynamique des gaz, C. R. Acad. Sci. Paris, Ser I,     323 (1996) pp. 209-214.

 
 

Polymers

P. Degond, A. Lozinski and R. G. Owens, Kinetic models for dilute solutions of dumbbells in non-homogeneous flows revisited, Journal of Non-Newtonian Fluid Mechanics, 165 (2010), pp. 509–518, http://dx.doi.org/10.1016/j.jnnfm.2010.02.007 and http://arxiv.org/abs/1001.2406
 
P. Degond, H. Liu, Kinetic models for polymers with inertial effects, Networks and Heterogeneous Media, 4 (2009), pp. 625-647. http://dx.doi.org/10.3934/nhm.2009.4.625  and  http://arxiv.org/abs/0901.1909 .

P. Degond, M. Lemou and M. Picasso,  Constitutive relations for viscoelastic fluid models derived from kinetic theory, in 'Dispersive transport equations and multiscale models' N. Ben Abdallah et al (eds), The IMA Volumes in Mathematics and Applications, vol 136, Springer, 2004, pp. 77-89.

 P. Degond, M. Lemou, M. Picasso,  Viscoelastic fluid models derived from kinetic equations for polymers, SIAM J. Appl. Math.  62 (2002), pp. 1501-1519. http://dx.doi.org/10.1137/S0036139900374404


 

 

Homogenization

Homogenization in rarefied gases and Knudsen pumps

K. Aoki, P. Charrier, P. Degond, A hierarchy of models related to nanoflows and surface diffusion, Kinetic and Related Models, 4 (2011), pp. 53-85. http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5855 and http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.5406v1.pdf

K. Aoki, P. Degond, L. Mieussens,  Numerical simulations of rarefied gases in curved channels: thermal creep, circulating flow and pumping effect, Communications in Computational Physics, 6 (2009), pp. 919-954. http://www.global-sci.com/issue/abstract/readabs.php?vol=6&page=919&issue=5&ppage=954&year=2009
 
K. Aoki, P. Degond, L. Mieussens, S. Takata, H. Yosida,  A diffusion model for rarefied flows in curved channels, SIAM Multiscale Model. Simul.  6 (2008), pp. 1281-1316. http://dx.doi.org/10.1137/070690328

K. Aoki, P. Degond, L. Mieussens, M. Nishioka, S. Takata,  Numerical simulation of Knudsen pump using the effect of curvature of the channel, Proceedings of the 25th international symposium on rarefied gas dynamics, M. S. Ivanov and A. K. Rebrov (eds), Novosibirsk publishing house of the Siberian branch of the Russian Academy of Sciences, 2007.

C. J. T. Laneryd, K. Aoki, P. Degond, M. Mieussens,  Thermal creep of slightly rarefied gas through a channel with curved boundary, Proceedings of the 25th international symposium on rarefied gas dynamics, M. S. Ivanov and A. K. Rebrov (eds), Novosibirsk publishing house of the Siberian branch of the Russian Academy of Sciences, 2007.

K. Aoki, P. Degond, S. Takata, H. Yosida,  Diffusion models for Knudsen compressors, Phys. Fluids.  19 (2007), 117103 (20 pages). http://link.aip.org/link/?PHFLE6/19/117103/1

K. Aoki, P. Degond,  Homogenization of a flow in a periodic channel of small section, SIAM Multiscale Modeling and Simulation  1 (2003), pp. 304-334. http://dx.doi.org/10.1137/S1540345902409931

 

Homogenization in quantum systems and Einstein rate equations

F. Castella, P. Degond, T. Goudon,  Large time dynamics of a classical system subject to a fast varying force, Commun. Math. Phys.  276 (2007), pp. 23-49. http://dx.doi.org/10.1007/s00220-007-0339-7

F. Castella, P. Degond, T. Goudon,  Asymptotic problems for wave-particle interactions: quantum and classical models, Nonlinearity  20 (2007), pp. 1677-1720. http://dx.doi.org/10.1088/0951-7715/20/7/008

F. Castella, P. Degond, T. Goudon,  Diffusion dynamics of classical systems driven by an oscillatory force, J. Stat. Phys.,  124 (2006), pp. 913-950. http://dx.doi.org/10.1007/s10955-006-9071-5
 
B. Bidégaray-Fesquet, F. Castella, P. Degond,  From Bloch model to the rate equations, Discrete and Continuous Dynamics Systems  11 (2004), pp. 1-26. http://www.aimsciences.org/journals/pdfs.jsp?paperID=567&mode=full

C. Besse, B. Bidégaray-Fesquet, A. Bourgeade, P. Degond, O. Saut,  A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP, ESAIM: M2AN  38 (2004), pp. 321-344. http://dx.doi.org/10.1051/m2an:2004015

F. Castella, P. Degond,  Convergence of the von-Neumann equation towards  the quantum Boltzmann equation in a deterministic framework, C. R. Acad. Sci. Paris, Ser I,    329 (1999), pp. 231-236. http://dx.doi.org/10.1016/S0764-4442(00)88599-7

 

 

Schrödinger-Poisson systems with scattering states or Wigner-Poisson systems

M. Baro, N. Ben Abdallah, P. Degond, A. El Ayyadi,  A 1D coupled Schr\"odinger drift-diffusion model including collisions, J. Comput. Phys.,  203 (2005), pp. 129-153.  http://dx.doi.org/10.1016/j.jcp.2004.08.009

P. Degond, A. El Ayyadi,  A coupled Schrödinger Drift-Diffusion model for quantum semiconductor device simulations, J. Comput. Phys.  181 (2002), pp. 222-259. http://dx.doi.org/10.1006/jcph.2002.7122

N. Ben Abdallah, P. Degond and I. Gamba,  Coupling one-dimensional time-dependent classical and quantum transport models, J. Math. Phys.  43 (2002), pp. 1-24. http://link.aip.org/link/?JMAPAQ/43/1/1

N. Ben Abdallah, P. Degond and I. Gamba,  Inflow boundary conditions for the time-dependent one-dimensional Schrödinger equation,  C. R. Acad. Sci. Paris, Ser I,    331 (2000), pp. 1023-1028. http://dx.doi.org/10.1016/S0764-4442(00)01759-6

N. Ben Abdallah, P. Degond, P. Markowich,  On a one-dimensional Schrödinger-Poisson  scattering model, Zeitschrifts f\"{ur Angewandte Mathematik und Physik  48 (1997), pp. 135-155. http://dx.doi.org/10.1007/PL00001463

P. Degond, P. A. Markowich,  A Mathematical Analysis of Quantum Transport in Three  Dimensional Crystals, Annali di  Matematica Pura ed Applicata   160 (1991), pp. 171-191. http://dx.doi.org/10.1007/BF01764126

P. Degond, P. A. Markowich,  A Quantum Transport Model for Semiconductors : the Wigner- Poisson Problem on a Bounded Domain, RAIRO Modélisation Mathématique et Analyse Numérique   6 (1990),  pp. 697-709.

A. Arnold, P. Degond, P. A. Markowich, H. Steinrück,   The Wigner-Poisson Problem in a  Crystal, Appl. Math. Lett.  2 (1989), pp. 187-191. http://dx.doi.org/10.1016/0893-9659(89)90019-0

 

 

Entropic numerical methods for Boltzmann and Fokker-Planck Landau operators

C. Buet, S. Cordier, P. Degond,  Regularized Boltzmann operators, Computer and Mathematics  with applications   35 (1998), pp. 55-74. http://dx.doi.org/10.1016/S0898-1221(97)00258-7
 
C. Buet, S. Cordier, P. Degond, M. Lemou,  Fast algorithms for numerical conservative and  entropy approximations of the Fokker-Planck-Landau equation, J. Comput. Phys.  133 (1997), pp.  310-322. http://dx.doi.org/10.1006/jcph.1997.5669
 
P. Degond, B. Lucquin-Desreux,  An Entropy Scheme for the Fokker-Planck collision Operator  of Plasma Kinetic Theory, Numer. Mathematik.  68 (1994), pp. 239-262. http://dx.doi.org/10.1007/s002110050059
 

 

Child-Langmuir law

M-J. Càceres, J-A. Carrillo, P. Degond,  The Child-Langmuir limit for semiconductors: a numerical validation, M2AN  36 (2002), pp. 1161-1176. http://dx.doi.org/10.1051/m2an:2003011
 
N. Ben Abdallah, P. Degond,  F. Méhats,  The Child-Langmuir asymptotics for magnetized  flows,  Asymptotic Analysis  20 (1999), pp. 97-132.
 
N. Ben Abdallah, P. Degond, F. Méhats,  Mathematical models of magnetic insulation, Physics of plasmas  5 (1998), pp. 1522-1534.
 
N. Ben Abdallah, P. Degond,  P. Markowich,  The quantum Child-Langmuir problem,  Nonlinear Analysis, Theory, Methods and Applications   31 (1998), pp. 629-648. http://dx.doi.org/10.1016/S0362-546X(97)00429-X
 
P. Degond, Y. Qiu,  The Child-Langmuir asymptotics for semiconductors including phonon  interaction, COMPEL (Computer Electronics) 16 (1997), pp. 157-175. http://dx.doi.org/10.1108/03321649710182896

P. Degond, F. Poupaud, A. Yamnahakki,  Particle simulation and asymptotic analysis of  kinetic equations for modelling a Schottky diode, RAIRO Modélisation Mathématique et Analyse Numérique  30 (1996), pp. 763-795.

P. Degond, F. Poupaud, C. Schmeiser, A. Yamnahakki,  Asymptotic analysis of kinetic  equations for modeling a Schottky diode, Asymptotic Analysis   13 (1996), pp. 79-94.

N. Ben Abdallah, P. Degond, A. Yamnahakki,  The Child-Langmuir law as a model for electron  transport in semiconductors, Solid State Electronics   39 (1996), pp. 737-744. http://dx.doi.org/10.1016/0038-1101(95)00149-2

P. Degond, S. Jaffard, F. Poupaud,  P. A. Raviart,  The Child-Langmuir Asymptotics of the  Vlasov-Poisson Equation for Cylindrically or Spherically Symmetric Diodes ; part 2 : analysis of the  reduced problem and determination of the Child-Langmuir current, Math. Methods in the Appl.  Sciences  19 (1996), pp. 313-340. http://www3.interscience.wiley.com/journal/17591/abstract
  
P. Degond, S. Jaffard, F. Poupaud,  P. A. Raviart,  The Child-Langmuir Asymptotics of the  Vlasov-Poisson Equation for Cylindrically or Spherically Symmetric Diodes ; part 1 : statement of the  problem and basic estimates, Math. Methods in the Appl. Sciences  19 (1996), pp. 287-312.

N. Ben Abdallah, P. Degond,  The Child-Langmuir law in the kinetic theory of charged particles ;  Part 3, semiconductor models, in  "Mathematical Problems in semiconductor physics", P. Marcati, P.  Markowich and R. Natalini (eds), Pitman research notes in Mathematics, Longman, 1996.

N. Ben Abdallah, P. Degond,  The Child-Langmuir Law for the Boltzmann Equation of  Semiconductors, SIAM J. on Mathematical Analysis.  26 (1995), pp. 364-398. http://dx.doi.org/10.1137/S0036141093246567

P. Degond,  Macroscopic models of charged-particle transport derived from kinetic theory,  proceedings of the third ICIAM, Hamburg 95.

N. Ben Abdallah, P. Degond, C. Schmeiser,  On a Mathematical Model for Hot Carrier Injection  in Semiconductors, Mathematical Methods in the Applied Sciences  17, pp. 1193-1212  (1994). http://dx.doi.org/10.1002/mma.1670171503

N. Ben Abdallah, P. Degond,  On the Child-Langmuir Law for Semiconductors, in  "Semiconductors, part 2", W. M. Coughran Jr., J. Cole, P. Lloyd, J. K. White eds, The IMA  volumes in Mathematics and its applications, vol 59, Springer Verlag, New-York, 1994.

P. Degond,  The Child-Langmuir Law in the Kinetic Theory of Charged-Particles. Part 1,  Electron Flows in vacuum, in "Advances in Kinetic Theory" (B. Perthame, ed), pp. 3-44, World  Scientific, Singapore, 1994.

P. Degond, P. A. Raviart,  On a  Penalization of the Child-Langmuir Emission Condition for the  One-Dimensional Vlasov-Poisson Equation, Asymptotic Analysis.  6 (1992), pp. 1-27.

P. Degond, P. A. Raviart,  An Asymptotic Analysis of the One-Dimensional Vlasov-Poisson  System : the Child-Langmuir Law, Asymptotic Analysis   4 (1991), pp. 187-214.

  
 
 

Hyperbolic systems (hydrodynamics, Maxwell, etc.): theory and numerics

P. Degond,  P. F. Peyrard, G. Russo, Ph. Villedieu,  Polynomial upwind schemes for hyperbolic systems,  C. R. Acad. Sci. Paris, Ser I,    328 (1999), pp. 479-483. http://dx.doi.org/10.1016/S0764-4442(99)80194-3

S. Cordier, P. Degond, P. A. Markowich, C. Schmeiser,  Travelling wave analysis of an  isothermal Euler-Poisson model, Annales de la faculté des sciences de Toulouse, 5 (1996), pp. 599- 643. http://afst.cedram.org/afst-bin/fitem?id=AFST_1996_6_5_4_599_0

F. Assous, P. Degond, J. Segré,  Numerical approximation of the Maxwell equations in  inhomogeneous media by a P1 conforming finite element method, J. Comput. Phys.  128 (1996),  pp. 363-380. http://dx.doi.org/10.1006/jcph.1996.0217

S. Cordier, P. Degond, P. A. Markowich, C. Schmeiser,  Travelling wave analysis and jump  relation for the Euler-Poisson model in the quasineutral limit, Asymptotic Analysis.  11 (1995), pp.  209-240.

S. Cordier, P. Degond, P. A. Markowich, C. Schmeiser,  Travelling waves analysis and jump  relations for a fluid model of quasineutral plasma, C. R. Acad. Sci. Paris, Ser I, 318 (1994), pp.  929-934.

S. Cordier, P. Degond, P. A. Markowich, C. Schmeiser,  Travelling waves analysis of an  isothermal Euler Poisson model for plasmas, C. R. Acad. Sci. Paris, Ser I,     318 (1994), pp. 801- 806.

F. Assous, P. Degond, E. Heintzé, P. A. Raviart, J. Segré,  On a Finite-Element Method for  Solving the Three-Dimensionnal Maxwell Equations, J. Comput. Phys.  109 (1993), pp. 222-237. http://dx.doi.org/10.1006/jcph.1993.1214

P. Degond, P. A. Markowich,  A Steady-State Potential  Flow Model for Semiconductors,   Annali di  Matematica Pura ed Applicata. 165 (1993), pp. 87-98. http://dx.doi.org/10.1007/BF01765842 
 
P. Degond, P. A. Raviart,  An analysis of the Darwin model of approximation to Maxwell's  equations,  Forum Mathematicum   4 (1992), pp. 13-44.
 P. Degond, P. A. Markowich,  On a One-Dimensional Steady-State Hydrodynamic Model for  Semiconductors, Appl. Math. Lett.  3 (1990), pp. 25-29. http://dx.doi.org/10.1016/0893-9659(90)90130-4


 

Particle methods

F. Assous, P. Degond, J. Segré,  A new scheme to treat the numerical Tcherenkov instability  for electromagnetic simulations, J. Comput. Phys.  138 (1997), pp. 171-192.  http://dx.doi.org/10.1006/jcph.1997.5818
 
F. Assous, P. Degond, J. Segré,  A Particle-tracking Method for the 3D Electromagnetic PIC codes on Unstructured  Meshes, Computer Physics Communications,  72 (1992), pp. 105-114. http://dx.doi.org/10.1016/0010-4655(92)90142-L

A. Adolf, P. Degond, F. Hermeline, J. Marilleau, P. A. Raviart, J. Segré,  New PIC codes on  unstructured meshes applied to the simulation of a photcathode injector, Nuclear Instruments and  Methods in Physics Research  A304 (1991), pp. 297-299. http://dx.doi.org/10.1016/0168-9002(91)90871-M

P. Degond, F. Hermeline, P. A. Raviart, J. Segré,  Numerical Modelling of Axisymmetric  Electron Beam Devices Using a Coupled Particle-Finite Element Method, IEEE Trans. on Magnetics    27 (1991), pp. 4177-4180.

P. Degond, F. J. Mustieles,  A Deterministic Particle Method for the Kinetic Model of  Semiconductors: the Homogeneous Field Model, Solid State Electron.  34 (1991), pp. 1335-1345. http://dx.doi.org/10.1016/0038-1101(91)90027-V

P. Degond, F. Guyot-Delaurens, F. J. Mustieles, F. Nier,  Semiconductor Modelling via the  Boltzmann Equation, in " Mathematical Aspects of Fluid and Plasma Dynamics", G. Toscani, V.  Boffi, S. Rionero (eds), Lecture Notes in Mathematics vol1460, Springer, Berlin, 1991. http://dx.doi.org/10.1007/BFb0091363
 
P. Degond, F. Guyot-Delaurens, F. J. Mustieles, F. Nier,  Particle Simulation of Bidimensional  Electron Transport Parallel to a Heterojunction Interface, COMPEL (Computation in Electrical and  Electronic Engineering)   9 (1990), pp. 109-116. http://dx.doi.org/10.1108/eb010068

P. Degond, F. Guyot-Delaurens,  Particle Simulations of the Semiconductor Boltzmann Equation  for One Dimensionnal Inhomogeneous Structures, J. Comput. Phys.  90 (1990), pp. 65-97. http://dx.doi.org/10.1016/0021-9991(90)90197-9

P. Degond, F. J. Mustieles,  A Deterministic Approximation of Diffusion Equations using  Particles, SIAM J. on Scientific and Statistical Computing  11 (1990), pp. 293-310. http://dx.doi.org/10.1137/0911018

P. Degond, F. Guyot-Delaurens, F. J. Mustieles,  Semiconductor Modelling via the Boltzmann  Equation, in "Computing Methods in Applied Sciences and Engineering", R. Glowinski, A.  Lichnewsky (eds), SIAM, Philadelphia, 1990.

P. Degond, F. Poupaud, B. Niclot, F. Guyot,  Semiconductor Modelling via the Boltzmann  Equation, in "Computational Aspects of VLSI Design with an Emphasis on Semiconductor Device  simulation ", R. E. Bank (ed), Lectures in Applied Mathematics, Vol 25, AMS,  Providence, (1990).

P. Degond, F. J. Mustieles, B. Niclot,   A Quadrature Approximation of the Boltzmann Collision  Operator in Axisymmetric Geometry and its Application to Particle Methods, in "nonlinear  Hyperbolic Equations - Theory, Computation Methods and Applications", J. Ballmann and R. Jeltsch  (eds), Viewveg, Braunschweig, 1989.

P. Degond, S. Mas-Gallic,  The Weighted Particle Method for Convection-Diffusion Equations,  Part 2: the Anisotropic Case, Math. Comput.  53 (1989), pp. 509-525.

P. Degond, S. Mas-Gallic,  The Weighted Particle Method for Convection-Diffusion Equations,  Part 1: the Case of an Isotropic Viscosity, Math. Comput.  53 (1989), pp. 485-507.

P. Degond, B. Niclot,  Numerical Analysis of the Weighted Particle Method Applied to the  Semiconductor Boltzmann Equation, Numer. Math.  55 (1989), pp. 599-618. http://dx.doi.org/10.1007/BF01398918
 
B. Niclot, P. Degond, F. Poupaud,  Deterministic Particle Simulations of the Boltzmann  Transport Equation of Semiconductors, J. Comput. Phys.  78 (1988), pp. 313-349). http://dx.doi.org/10.1016/0021-9991(88)90053-8
 

 

Mathematical theory of Vlasov-Poisson et Vlasov-Poisson-Fokker-Planck

P. Degond,  Macroscopic limits of the Boltzmann equation: a review in Modeling and computational methods for kinetic equations, P. Degond, L. Pareschi, G. Russo (eds), Modeling and Simulation in Science, Engineering and Technology Series, Birkhauser, 2003, pp. 3-57.

P. Degond, M. Lemou,  Dispersion relations of the linearized Fokker-Planck equation, Archives  of Rational Mechanics and Analysis 138 (1997), pp. 137-167. http://dx.doi.org/10.1007/s002050050038

P. Degond, M. Lemou,  Relations de dispersion pour l'équation de Fokker-Planck linéarisée, C.  R. Acad. Sci. Paris, Ser I,    321 (1995) pp. 413-417.

P. Degond, P. A. Raviart,  The paraxial approximation of the Vlasov-Maxwell equations,  Mathematical Models and Methods in Applied Sciences,  3 (1993), pp. 513-562. http://dx.doi.org/10.1142/S0218202593000278

P. Degond, B. Lucquin-Desreux,  The Fokker-Planck Asymptotics of the Boltzmann Collision  Operator in the Coulomb Case, Mathematical Models and Methods in Applied Sciences,   2 (1992), pp 167-182. http://dx.doi.org/10.1142/S0218202592000119

P. Degond,  Solutions Stationnaires Explicites du Système de Vlasov-Maxwell Relativiste, C. R.  Acad. Sc. Paris, Ser I,     310 (1990), pp. 607-612.

J. Batt, H. Berestycki, P. Degond, B. Perthame,  Some families of solutions of the Vlasov- Poisson system,  Arch. Rational Mech. Anal.  104  (1988) pp. 79-103. http://dx.doi.org/10.1007/BF00256933
 
P. Degond, S. Mas-Gallic,   Existence of Solutions and Diffusion Approximation for a Model  Fokker-Planck Equation, Transp. Theory Stat. Phys.  16 (1987) pp. 589-636. http://dx.doi.org/10.1080/00411458708204307 
 
P. Degond,  Global Existence of Solutions for the Vlasov-Fokker-Planck Equation in 1 and 2  Space Dimensions, An. Scient. Ec. Norm. Sup.  19 (1986) pp. 519-542.

P. Degond,  Local Existence of Solutions of the Vlasov-Maxwell Equations and Convergence to  the Vlasov-Poisson Equations for Infinite Light Velocity, Math. Meth. in the Appl. Sci.,  8  (1986) pp.533-558.

P. Degond,  Spectral Theory of the Linearized Vlasov-Poisson Equation, Trans. AMS   294  (1986) pp. 435-453.

C. Bardos, P. Degond, F. Golse,  A Priori Estimates and Existence Results for the Vlasov and  Boltzmann Equations, in "Non-linear Systems of Partial Differential Equations in Applied  Mathematics", B. Nicolaenko, D. D. Holm, J. M. Hyman (eds) , Lectures in Applied Mathematics,  AMS, Providence, Rhode Island, 1986.

P. Degond,  Régularité de la Solution des Equations Cinétiques en Physique des Plasmas,  Comptes Rendus du "Séminaire Equations aux Dérivées Partielles 1985-1986", Ecole Polytechnique,  1986.

C. Bardos, P. Degond :  Global Existence for the Vlasov-Poisson Equation, Ann. Inst. Henri  Poincaré, Analyse Non Linéaire   2 (1985) pp. 101-118.

P. Degond,  Existence Locale des Solutions de l'Equation de Vlasov-Maxwell et Approximation  par les Solutions de l'Equation de Vlasov-Poisson, C. R. Acad. Sc. Paris, Ser I, 301 (1985) pp.  877-880.

C. Bardos, Ha Tien Ngoan, P. Degond,  Existence Globale des Solutions des Equations de  Vlasov-Poisson relativistes en Dimension 3, C. R. Acad. Sc. Paris, Ser I,     301 (1985) pp. 265- 268.

P. Degond,  Existence Globale des Solutions de l'Equation de Vlasov-Fokker-Planck en  Dimension 1 et 2, C. R. Acad. Sc. Paris, Ser I,     301 (1985) pp. 73-76.

C. Bardos, P. Degond,  Existence Globale et Comportement Asymptotique de l'Equation de  Vlasov-Poisson, C. R. Acad. Sc. Paris, Ser I,     297 (1983) pp. 321-324.

P. Degond,  Apparition de Résonances pour l'Equation de Vlasov-Poisson Linéarisée, C. R. Acad  Sc. Paris, Ser I,   296 (1983) pp. 969-972.
 
 

 

Edited books

Dispersive transport equations and multiscale models, Ben Abdallah N., Arnold A., Degond P., Gamba I.M., Glassey R.T., Levermore C.D., Ringhofer C. (Eds.), The IMA Volumes in Mathematics and Applications, vol 136, Springer, 2004.

Modeling and computational methods for kinetic equations, P. Degond, L. Pareschi, G. Russo (eds), Modeling and Simulation in Science, Engineering and Technology Series, Birkhauser, 2003.

Transport in Transition Regimes, Ben Abdallah N., Arnold A., Degond P., Gamba I.M., Glassey R.T., Levermore C.D., Ringhofer C. (Eds.), The IMA Volumes in Mathematics and Applications, vol 135, Springer, 2003.

 

Vulgarisation articles

 
Interview in the special issue 'Rien n'arrête les mathématiques', Journal du CNRS, 245, june 2010 (c.f. article 'La physique accro aux maths', pp. 23-24).
 
P. Degond, G. Theraulaz, Les mathématiques de la complexité, Paul Sabatier, Magazine scientifique, 17 (2009), p. 7.
 
P. Degond, V. Genot,  Mettre en équations la valse des particules autour de la Terre, Paul Sabatier, Magazine scientifique,  6 (2006), p. 7.
 
C. Tessieras, J. Claudel, P. Degond, G. Gallice, Striations dans l'ionosphère: phénoménologie et simulation numérique, Chocs (Revue Scientifique et Technique de la Direction des Applications Militaires, Commissariat à l'Energie Atomique), 26 (2002), pp. 71-83.
 
P. Degond  Des électrons aux satellites,  la Recherche,  341, april 2001, p. 64.

N. Ben Abdallah, P. Degond,  De l'infiniment petit à l'infiniment grand, CNRS info, mai 2000, pp. 23-24.

P. Degond,  B. Perthame,  Modèles Cinétiques et Equation de Boltzmann, Images des Mathématiques, Le Courrier du CNRS, supplément au vol  76 (1990), pp. 44-49



Table des matières

  1. 1 Emergence and self-organization in complex systems
    1. 1.1 Micro-macro passage in models of complex systems
      1. 1.1.1 Self-Organized Hydrodynamics
      2. 1.1.2 Phase transitions
      3. 1.1.3 Propagation of chaos
    2. 1.2 Applications
      1. 1.2.1 Economics and social sciences
      2. 1.2.2 Network and network formation models
      3. 1.2.3 Crowd dynamics
      4. 1.2.4 Herds 
      5. 1.2.5 Fish schools
      6. 1.2.6 Car traffic
      7. 1.2.7 Supply chains
  2. 2 Numerical methods for asymptotic problems
    1. 2.1 Asymptotic Preserving methods
      1. 2.1.1 Quasineutrality in plasmas
      2. 2.1.2 Strongly anisotropic diffusion problems ; application to large magnetic fields in plasmas
      3. 2.1.3 All-speed schemes for compressible fluids
      4. 2.1.4 Other applications of AP-methods
    2. 2.2 Multiscale methods
  3. 3 Other topics
    1. 3.1 Micro-macro passage in physical systems 
      1. 3.1.1 Hall Magnetohydrodynamics
      2. 3.1.2 Electrical discharges and arcs
      3. 3.1.3 Energy-transport models for plasmas and semiconductors
      4. 3.1.4 Fokker-Planck-SHE (Spherical Harmonics Expansion) models for plasmas and semiconductors
      5. 3.1.5 Diffusion and Hydrodynamic limits
      6. 3.1.6 Diffusion by solid boundaries: applications to plasmas
      7. 3.1.7 Diffusion by interfaces: applications to semiconductor super-lattices
      8. 3.1.8 High-field diffusion models
      9. 3.1.9 Quantum systems
      10. 3.1.10 Relativistic systems
      11. 3.1.11 Wave-particle collisions and applications to cometary flows and turbulence
      12. 3.1.12 Polymers
    2. 3.2 Homogenization
      1. 3.2.1 Homogenization in rarefied gases and Knudsen pumps
      2. 3.2.2 Homogenization in quantum systems and Einstein rate equations
    3. 3.3 Schrödinger-Poisson systems with scattering states or Wigner-Poisson systems
    4. 3.4 Entropic numerical methods for Boltzmann and Fokker-Planck Landau operators
    5. 3.5 Child-Langmuir law
    6. 3.6 Hyperbolic systems (hydrodynamics, Maxwell, etc.): theory and numerics
    7. 3.7 Particle methods
    8. 3.8 Mathematical theory of Vlasov-Poisson et Vlasov-Poisson-Fokker-Planck
  4. 4 Edited books
  5. 5 Vulgarisation articles

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