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Publications

  1. P.-A. Bliman, N. Nguyen, N. Vauchelet, Efficacy of the Sterile Insect Technique in the presence of inaccessible areas: A study using two-patch models, submitted.
  2. S. Latrach, E. Ogier-Denis, N. Vauchelet, H. Zaag, Mathematical study of the spread and blocking in inflammatory bowel disease, submitted.
  3. L. Almeida, J Bellver Arnau, G. Peltier, N. Vauchelet, Optimal strategies for mosquitoes replacement strategy: influence of the carrying capacity on spatial releases, submitted.
  4. L. Almeida, P.-A. Bliman, N. Nguyen, N. Vauchelet, Steady-state solutions for a reaction-diffusion equation with Robin boundary conditions: Application to the control of dengue vectors, Eur. J. Appl. Math. Published online 2023:1-27.
  5. L. Almeida, A. Leculier, N. Vauchelet, Analysis of the "Rolling carpet" strategy to eradicate an invasive species, SIAM J. Math. Anal. 55(1), pp. 275-309 (2023).
  6. L. Almeida, J. Estrada, N. Vauchelet, Wave blocking in a bistable system by local introduction of a population: application to sterile insect techniques on mosquito populations, Mathematical Modelling of Natural Phenomena, 2022, 17, 22.
  7. L. Almeida, M. Duprez, Y. Privat, N. Vauchelet, Optimal strategies for the sterile mosquitoes technique, J. Differential Equations, 311, p 229-266 (2022).
  8. G. Bretti, L. Gosse, N. Vauchelet, Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport, ESAIM: Math. Mod. Num. Analysis, 55(6), 2949-2980 (2021).
  9. M. Duprez, R. Hélie, Y. Privat, N. Vauchelet, Optimization of spatial control strategies for population replacement, application to Wolbachia, ESAIM, Control Optim. Calc. Var. 27, No. 74, Special Issue in honor of Enrique Zuazua's 60th birthday, 30 p. (2021).
  10. B. Fabrèges, F. Lagoutière, S. Tran Tien, N. Vauchelet, Relaxation limit of the aggregation equation with pointy potential, Axioms, Special Issue Differential Models, Numerical Simulations and Applications, 2021, 10(2), 108.
  11. L. Almeida, P.-A. Bliman, G. Nadin, B. Perthame, N. Vauchelet, Final size and convergence rate for an epidemic in heterogeneous population, Math. Models and Meth. in Appl. Sci., Vol. 31, No 5 (2021), 1021-1051.
  12. P.-A. Bliman, M. Duprez, Y. Privat, N. Vauchelet, Optimal immunity control by social distancing for the SIR epidemic model, J. Optim. Theory Appl. (2021), 189 (2), pp 408-436.
  13. N. Vauchelet, S. Yasuda, Numerical scheme for kinetic transport equation with internal state, Multiscale Model. Simul. (2021), Vol 19, No 1, pp 184-207.
  14. M. Marulli, V. Milisic, N. Vauchelet, Reduction of a model for sodium exchanges in kidney nephron, Netw. Heterog. Media 16, No. 4, 609-636 (2021).
  15. T. Debiec, B. Perthame, M. Schmidtchen, N. Vauchelet, Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension, J. Math. Pures Appl. (9) 145 (2021), 204-239.
  16. G. Bretti, L. Gosse, N. Vauchelet, L-splines as dissipative limits of kinetic models, Vietnam J. Math. 49, no 3, 651-671 (2021).
  17. M. Marulli, A. Edwards, V. Milisic, N. Vauchelet, On the role of the epithelium in a model of sodium exchange in renal tubules, Math. Biosci. 321 (2020), 108308.
  18. L. Gosse, N. Vauchelet, A truly two-dimensional, asymptotic preserving scheme for a discrete model of radiative transfer, SIAM J. Numer. Anal. 58 (2), 1092-1116 (2020).
  19. P. Degond, S. Hecht, N. Vauchelet, Incompressible limit of a continuum model of tissue growth for two cell populations, Netw. Heterog. Media (2020) Vol 15, issue 1, 57-85.
  20. F. Delarue, F. Lagoutière, N. Vauchelet, Convergence analysis of upwind type schemes for the aggregation equation with pointy potential, Ann. Henri Lebesgue (2020) 3, 217-260.
  21. B. Perthame, N. Vauchelet, Z. Wang, The Flux-Limited Keller-Segel system; properties and derivation from kinetic equations, Rev. Mat. Iberoam. 36, No 2, 357-386 (2020).
  22. L. Almeida, M. Duprez, Y. Privat, N. Vauchelet, Control strategies on mosquitos population for the fight against arboviruses, Math. Biosci. Eng. (Special Issue), 2019, 16(6) : 6274-6297.
  23. L. Almeida, Y. Privat, M. Strugarek, N. Vauchelet, Optimal releases for population replacement strategies, application to Wolbachia, SIAM J. Math. Anal. 51 (2019), no 4, 3170-3194.
  24. M. Strugarek, L. Dufour, N. Vauchelet, L. Almeida, B. Perthame, D. Villela, Oscillatory regimes in a mosquito population model with larval feedback on egg hatching, J. Biol. Dyn. 13 (2019) no 1, 269-300.
  25. L. Gosse, N. Vauchelet, Some examples of kinetic schemes whose diffusion limit is Il'in's exponential-fitting, Numer. Math. 141 (2019), no 3, 627-680.
  26. M. Strugarek, N. Vauchelet, J. P. Zubelli, Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model, Math. Biosci. Eng. 15 (2018), no 4, 961-991.
  27. G. Nadin, M. Strugarek, N. Vauchelet, Hindrances to bistable front propagation: application to Wolbachia invasion, J. Math. Biol. 76 (2018), no 6, 1489-1533.
  28. S. Hecht, N. Vauchelet, Incompressible limit of a mechanical model for tissue growth with non-overlapping constraint, Commun. Math. Sci. (2017) Vol. 15, No 7, 1913-1932.
  29. C. Jourdana, P. Pietra, N. Vauchelet, A classical-quantum coupling strategy for a hierarchy of one dimensional models for semiconductors, Monatsh. Math. 184 (2017), no 4, 563-596.
  30. F. Delarue, F. Lagoutière, N. Vauchelet, Convergence order of upwind type schemes for transport equations with discontinuous coefficients, J. Math. Pures Appl. (9) 108 (2017), no 6, 918-951.
  31. N. Vauchelet, E. Zatorska, Incompressible limit of the Navier-Stokes model with a growth term, Nonlinear Anal. 163 (2017), 34-59.
  32. L. Gosse, N. Vauchelet, Hydrodynamic singular regimes in 1+1 kinetic models and spectral numerical methods, J. Math. Anal. Appl. 445 (2017), no 1, 564-603.
  33. C. Emako-Kazianou, J. Liao, N. Vauchelet, Synchronising and non-synchronising dynamics for a two-species aggregation model, DCDS-B (2017) Vol 22, no 6, 2121-2146.
  34. N. Outada, N. Vauchelet, T. Akrid, M. Khaladi, From kinetic theory of multicellular systems to hyperbolic tissue equations: asymptotic limits and computing, Math. Models and Meth. in Appl. Sci., Vol. 26, no 14 (2016), 2709-2734.
  35. M. Strugarek, N. Vauchelet, Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type, SIAM J. Appl. Math. 76 (2016) no 5, 2068-2080.
  36. B. Perthame, M. Tang, N. Vauchelet, Derivation of a bacterial run-and-tumble kinetic equation from a model with biochemical pathway, J. Math. Biol. 73 (2016), no 5, 1161-1178.
  37. C. Emako-Kazianou, C. Gayrard, A. Buguin, L. Neves de Almeida, N. Vauchelet, Traveling pulses for a two-species chemotaxis model, PLoS Comput. Biol. 2016, Vol 12 Issue 4, e1004843 (open access).
  38. L. Gosse, N. Vauchelet, Numerical high-field limits in two-stream kinetic models and 1D aggregation equations, SIAM J. Sci. Comput., 38(1) (2016), A412-A434.
  39. J. A. Carrillo, F. James, F. Lagoutière, N. Vauchelet, The Filippov characteristic flow for the aggregation equation with mildly singular potentials, J. Differential Equations, 260 (2016) no 1, 304-338.
  40. F. James, N. Vauchelet, Equivalence between duality and gradient flow solutions for one-dimensional aggregation equations, Disc. Cont. Dyn. Syst., Vol 36, no 3 (2016), 1355-1382.
  41. C. Jourdana, N. Vauchelet, Hybrid fluid-quantum coupling for the simulation of the transport of partially quantized particles in a DG-MOSFET, Nanoscale Syst.: Math. Model. Theory Appl. (2015) 4, 1-17.
  42. B. Perthame, N. Vauchelet, Incompressible limit of mechanical model of tumor growth with viscosity, Phil. Trans. R. Soc. A 373 (2015): 20140283.
  43. C. Emako, L. Neves de Almeida, N. Vauchelet, Existence and diffusive limit of a two-species kinetic model of chemotaxis, Kin. Rel. Models. Vol 8 no 2 (2015), 359-380.
  44. F. James, N. Vauchelet, Numerical methods for one-dimensional aggregation equations, SIAM J. Numer. Anal. Vol 53 no 2 (2015), 895-916.
  45. B. Perthame, F. Quiros, M. Tang, N. Vauchelet, Derivation of a Hele-Shaw type system from a cell model with active motion, Interfaces and Free Boundaries 16 (2014), 489-508.
  46. B. Perthame, M. Tang, N. Vauchelet, Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient, Math. Models and Meth. in Appl. Sci., Vol 24, No 13 (2014), 2601-2626.
  47. P. Pietra, N. Vauchelet, Numerical simulations of an energy-transport model for partially quantized particles, Comm. Math. Sci., Vol 12, no 1 (2014), 99-123.
  48. M. Tang, N. Vauchelet, I. Cheddadi, I. Vignon-Clementel, D. Drasdo, B. Perthame, Composite waves for a cell population system modelling tumor growth and invasion, Chinese Annals of Math. Ser. B, Vol 34, no 2 (2013), 295-318.
  49. F. James, N. Vauchelet, Chemotaxis : from kinetic equations to aggregate dynamics, Nonlinear Differ. Equ. Appl. (NoDEA), Vol 20, Issue 1 (2013), 101-127.
  50. C. Jourdana, N. Vauchelet, Analysis of a diffusive effective mass model for nanowires, Kin. Rel. Models, Vol 4 no 4 (2011), 1121-1142.
  51. F. James, N. Vauchelet, A remark on duality solutions for some weakly nonlinear scalar conservation laws, C. R. Acad. Sci. Paris, Ser. I 349 (2011), 657-661.
  52. B. Perthame, C. Schmeiser, M. Tang, N. Vauchelet, Traveling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities, Nonlinearity 24 (2011) 1253-1270 (featured article).
  53. F. Cerreti, B. Perthame, C. Schmeiser, M. Tang, N. Vauchelet, Waves for an hyperbolic Keller-Segel model and branching instabilities, Math. Models and Meth. in Appl. Sci. 21 (2011), pp. 825-842.
  54. N. Vauchelet, Numerical simulation of a kinetic model for chemotaxis, Kin. Rel. Models., Vol 3, no 3 (2010), 501-528.
  55. N. Vauchelet, Diffusion limit of a kinetic system of partially quantized particles in one dimension, J. Stat. Phys. (2010) 139, 882-914.
  56. N. Vauchelet, J.-P. Dudon, Ch. Besse, Th. Goudon, Comparison of Vlasov solvers for spacecraft simulation, Math. Mod. Num. Analysis (2010) 44, 109--131.
  57. P. Pietra, N. Vauchelet, Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, J. Comput. Elec. (2008) 7:52-65.
  58. N. Vauchelet, Diffusive transport of partially quantized particles : LlogL solutions, Math. Models Methods Appl. Sci. (2008), Vol 18 no 4, 489-510.
  59. N. Ben Abdallah, F. Méhats, N. Vauchelet, Diffusive transport of partially quantized particles : Existence, uniqueness and long time behaviour, Proc. Edinb. Math. Soc.(2006) 49, 513-549.
  60. N. Ben Abdallah, F. Méhats, N. Vauchelet, A note on long time behaviour for the Drift-Diffusion-Poisson system, C.R. Acad. Sci. Paris, Ser. I 339 (2004) 683-688.
  61. N. Ben Abdallah, F. Méhats, N. Vauchelet, Analysis of a Drift-Diffusion-Schrödinger-Poisson model, C.R. Acad. Sci. Paris, Ser. I 335 (2002) 1007-1012.


Proceedings
  1. L. Almeida, J. Estrada, N. Vauchelet, The sterile insect technique used as a barrier control against reinfestation, Radon Ser. Comput. Appl. Math. , 29, De Gruyter, Berlin, 2022, 91–111.
  2. L. Almeida, A. Haddon, C. Kermorvant, A. Léculier, Y. Privat, M. Strugarek, N. Vauchelet, J. Zubelli Optimal release of mosquitoes to control dengue transmission, ESAIM Proc. Surveys 67, CEMRACS 2018, 16-29 (2020).
  3. B. Fabrèges, H. Hivert, K. Le Balc'h, S. Martel, F. Delarue, F. Lagoutière, N. Vauchelet, Numerical schemes for the aggregation equation with pointy potentials, ESAIM Proc. Surveys 65, CEMRACS 2017, EDP Sci., Les Ulis (2019), pp 384-400.
  4. P. A. Bliman, N. Vauchelet, Establishing traveling wave in bistable reaction-diffusion system by feedback, IEEE Control Systems Letter, July 2017, vol 1, issue 1, pp 62-67.
  5. F. Lagoutière, N. Vauchelet, Analysis and simulation of nonlinear and nonlocal transport equations, Innovative algorithms and analysis, Springer INdAM Ser., 16, 2017, 265-288.
  6. F. James, N. Vauchelet, One-dimensional aggregation equation after blow up: existence, uniqueness and numerical simulation, Netw. Heterog. Media, Special Issue on contemporary topics in conservation laws, Vol 11 no 1 (2016), 163-180.
  7. M. Kolwalczyk, B. Perthame, N. Vauchelet, Transversal instability for the thermodiffusive reaction-diffusion system, Proceeding of the International Conference on Nonlinear and Multiscale Partial Differential Equations : Theory, Numerics and Applications, Chin. Ann. Math. B 36 (2015), no 5, 871-882.
  8. F. James, N. Vauchelet, Numerical simulation of a hyperbolic model for chemotaxis after blow up, Proceedings of 14th Conference on Hyperbolic Problems, Padova, Italy (2012), F. Ancona, A. Bressan, P. Marcati, A. Marson Eds., AIMS on Applied Mathematics, 8 (2014), 693-700.
  9. N. Ben Abdallah, C. Jourdana, P. Pietra, N. Vauchelet, A hybrid classical-quantum approach for ultra-scaled confined nanostructures : modeling and simulation, ESAIM Proc., Vol. 35 (2012), 239-244.
  10. F. Charles, N. Vauchelet, C. Besse, T. Goudon, I. Lacroix-Violet, J.-P. Dudon, L. Navoret, Numerical approximation of Knudsen layer for Euler-Poisson system, ESAIM Proc., Vol 32 (2011), 177-194.
  11. F. James, N. Vauchelet, On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis, Riv. Mat. Univ. Parma., Vol. 3 (2012), 91-113.
  12. N. Ben Abdallah, F. Méhats, P. Pietra, N. Vauchelet, A drift-diffusion subband model for the simulation of the Double-Gate MOSFET, IEEE-NANO 2005, 5th Conference on Nanotechnology, (2005) vol 2, 519-522.



Habilitation : le 8 décembre 2014 au Laboratoire Jacques-Louis Lions, UPMC. (version pdf)


Thèse : soutenue le 24 novembre 2006 à l'Université Paul Sabatier, Toulouse III.
Sujet de thèse : Modélisation mathématique du transport diffusif de charges partiellement quantiques. (version pdf)
Directeurs de thèse : Naoufel Ben Abdallah et Florian Méhats.