Home page of Laurent Di Menza

Selected publications:

  1. G. Decocq, P. Regnault, J. Lenoir, F. Paccaut, L. Di Menza, G. Delvoye, E. Janvresse, D. Closset-Kopp, O. Goubet
    Modelling plant community dynamics in changing forest ecosystems: a review
    Botany Letters, https://doi.org/10.1080/23818107.2023.2231045 (2023)
  2. L. Di Menza, O. Goubet, E. Hamraoui
    Numerical study of quintic NLS equation with defect
    North Western European Journal of Mathematics , vol. 9, pp. 55-75 (2023)
  3. L. Di Menza, V. Joanne-Fabre
    An age group model for the study of a population of trees
    Disc. Cont. Dyn. Syst., Ser S, doi: 10.3934/dcdss.2020464 (2020)
  4. L. Di Menza, J.-P. Nicolas, M. Pellen
    A new type of charged black hole bomb
    Gener. Relat. Gravit., n. 1, vol. 52, pp. 1-43 (2020)
  5. L. Di Menza, C. Michaut, O. Saincir
    Diffusion approximation in a radiative transfer model for astrophysical flows
    ESAIM Proc. Surveys, n. 64, pp. 78-92 (2018)
  6. L. Di Menza, O. Goubet, E. Hamraoui
    Numerical study of quintic NLS equation with defect
    Accepted in North Western European Journal of Mathematics (2017)
  7. L. Di Menza, C. Michaut, H.-C. Nguyen, S. Bouquet
    HADES : A New Tool for the Numerical Simulation of High-Mach Number Astrophysical Radiative Jets
    High Energy Density Physics, vol. 22, pp. 77-89 (2017)
  8. L. Di Menza, O. Goubet
    Stabilizing blow-up solutions to nonlinear Schrödinger equation
    Communications in Pure and Applied Analysis, vol. 16, n. 3, pp. 1059-1082 (2017).
  9. L. Di Menza, O. Goubet, E. Hamraoui, E. Zahrouni
    Calcul numérique de solutions de l'équation de Schrödinger non linéaire faiblement amortie avec défaut
    13th Africain Conference on Research in Computer Science and Applied Mathematics (CARI' 2016) proceedings, pp. 43-53 (2016)
  10. M. Colin, L. Di Menza, J.-C. Saut
    Solitons in quadratic media
    Nonlinearity, vol. 29, 3, pp. 1000-1035 (2016)
  11. L. Di Menza, J.-P. Nicolas
    Superradiance for the Reissner-Nordstrom metric
    Classical and Quantum Gravity, vol. 32, 15, 145013 (2015)
  12. Michaut C., Nguyen C., Di Menza L.
    Computation radiation hydrodynamics
    Astrophys. Space Sci, vol. 366, pp. 175-181 (2011)
  13. Cavet C., Nguyen H.-C., Michaut C., Falize E., Bouquet S., Di Menza L.
    Theoretical and Numerical Studies of the Vishniac Instability in Supernova Remnants
    Astrophys. Space Sci, vol. 322, 1-4, pp. 91-95 (2009)
  14. Di Menza L.
    Numerical computations of solitons in optical systems
    M2AN, vol. 3, n. 1, pp. 173-208 (2009)
  15. Di Menza L., Gallo C.
    The black solitons of one-dimensional NLS equations
    Nonlinearity, vol. 20, pp. 461-496 (2007)
  16. Barton-Smith M., Debussche A., Di Menza L.
    Numerical Study of two-dimensional stochastic NLS Equations
    Num. Meth. for PDE's, vol. 21, n. 4, pp. 810-842 (2005)
  17. Di Menza L., Lehner T.
    The Chaotic Mixmaster and the suppression of Chaos in Scalar-Tensor Cosmology
    Gener. Relat. Gravit., vol. 36, n. 12, pp. 2635-2672 (2004)
  18. Di Menza L., Lehner T.
    Revisitation of Chaos in Bianchi IX Universe and in generalized scalar-tensor cosmologies
    Chaos, Solitons and Fractals, vol. 16, n. 4, pp. 597-611 (2003)
  19. Le Berre M., Ressayre E., Tallet A., Pomeau Y., Di Menza L.
    Example of a chaotic crystal: the Labyrinth
    Phys. Rev. E, vol. 66, 026203 (2002)
  20. Debussche A., Di Menza L.
    Numerical resolution of stochastic focusing NLS equation
    Phys.~D, vol. 162, n. 3-4, pp. 131-154 (2002)
  21. Messaoudi K., Huntz A.-M., Di Menza L.
    Residual stresses in the Aluminia scale, Experiments, modelling and stress relaxation phenomena
    Ox. Met., vol. 53, n. 1-2, pp. 49-75 (2000).
  22. Tlidi M., Le Berre M., Ressayre E., Tallet A., Di Menza L.
    High intensity localized structures in the DOPO : comparison between the propagation and the mean-field models
    Phys. Rev. A, vol. 61, n. 4, pp. 428-445 (2000)
  23. Di Menza L.
    Numerical simulations with finite differences of wave propagation in diffractive quadratic media
    J. Opt. B: Quant. Semicl. Opt., n. 1, pp. 19-24 (1999)
  24. Bruneau C.-H., Lehner T., Di Menza L.
    Numerical resolution of some nonlinear Schrödinger equations in plasmas
    Num. Meth. for PDE's, vol. 15, n. 6, pp. 672-696 (1999)
  25. Di Menza L.
    Transparent and artificial boundary conditions for the linear Schrödinger equation
    Numer. Funct. Anal. Opt., vol. 18, n. 7-8, pp. 759-776 (1997)
  26. Di Menza L.
    Absorbing boundary conditions on a hypersurface for the linear Schrödinger equation
    Appl. Math. Lett., vol. 9, n. 4, pp. 55-59 (1996)

Books:

  1. L. Di Menza
    Analyse Numérique des Equations aux Dérivées Partielles
    Editions Cassini, ISBN 2842250737, 229 p., septembre 2009
  2. L. Di Menza
    Equations dispersives : aspects théoriques et numériques
    Coming soon

Book chapter:

  1. L. Di Menza
    Some Aspects concerning the Numerical Computation of Solitons,
    pp. 48-60, in Solitary waves in fluid media, C. David and Z. Feng, ISBN: 978-1-60805-702-3, 2010

Scientific diffusion:

  1. L. Di Menza
    Comment modéliser l'impact du réchauffement climatique sur un écosystème,
    Le journal du CNRS, November 2017

Preprints:

  1. L. Di Menza, O. Goubet, E. Hamraoui
    Numerical study of the two-dimensional NLS cubic equation with a line defect
  2. L. Di Menza
    Local transparent conditions for the linear Schrödinger equation
  3. L. Di Menza
    Revisited transparent conditions for the wave equation
  4. L. Di Menza, T. Lehner
    Influence of quantum potential on structure formation by the Schrödinger-Newton equation

Scientific events:

  1. Member of the Organization Commitee of the Online Conference ROND 2024, Reims-Osaka-Nagoya days, december 17-18 2024
  2. Member of the Organization Commitee of the Conference GO 2024, en l'honneur des 60 ans d'Olivier Goubet, Lille, november 4-6 2024
  3. Member of the Organization Commitee of the Conference Analyse Appliquée et Modélisation, à la mémoire d'Ezzeddine Zahrouni, Monastir, november 14-16, 2023
  4. Member of the Organization Commitee of the Workshop PROPAL: wave propagation in random media, Reims, june 3-4, 2019
  5. Member of the Organization Commitee of the Workshop Problèmes inverses, Aspects numériques et théoriques, Reims, december 17-19, 2018
  6. Organizer of the last Journée de la Fédération F-ARC, Reims, october 17, 2017
  7. Member of the Organization and the Scientific Commitee of the 8ème biénnale des Mathématiques Appliquées et Industrielles SMAI 2017, Ronce-les-Bains, june 5-9, 2017
  8. Organizer of the Conference Modélisation des Systèmes Economiques et Sociaux, Reims, december 9, 2015
  9. Organizer of the Workshop Autour des équations de Schrödinger et des modèles dispersifs, Reims, december 17-18, 2013
  10. Co-organizer of the 3rd Conference Modélisation et Calcul, Reims, march 21-22, 2013
  11. Co-organizer of the Conference Aspects numériques des équations de Gross-Pitaevskii, Reims, december 13-14, 2012
  12. Co-organizer of the 2nd Conference Modélisation et Calcul, Reims, 13 december 13, 2011
  13. Co-organizer of the 1st Conference Modélisation et Calcul, Reims, december 14-15, 2010

Workgroup on dispersive PDEs:

In 2022, this workgroup aimed to focus on a few aspects concerning the modeling, the mathematical study, the search of explicit represenation formulas as well as computational aspects for dispersives equations. A Masterclass course initiated this workgroup.

Workgroup on Inverse Problems:

In 2014, we organized a workgroup on theoretical and merical aspects of inverse problems. The goal is to implement numerical algorithms for both academic and realistic examples.

Workgroup on SPDEs:

In 2012, we organized a workgroup on stochastic partial differential equations (SPDEs), in order to address the question of how stochastic terms can influence the time dynamics of solutions of deterministic models in simple cases. It requires to introduce probabilistic tools such as Itö integral or white-noise and to combine these notions to usual analysis frameork for the study of these problems.

Responsabilities:

Research groups:

  • 1999-2002: Action Concertée Incitative ``Blanche'' (Young Researchers): Influence of stochastic terms on nonlinear dispersive wave propagation. Head member : A. Debussche
  • 2010-2011: SAKURA Project (JSPS-EGIDE): Theoretical and numerical analysis of models for Bose-Einstein condensation. Head member: A. De Bouard
  • 2009-2013: Member of ANR ArDyPiTeq. Lead member : P. Gravejat
  • 2009-2013: Member of ANR Microwave. Lead member : X. Antoine
  • 2015-2016: Lead member of PEPS MoMIS ARDIHES (Le massif des Ardennes)
  • 2019-2021 : Member of the Project 80 Prime MONACAL (MOdéliser la dyNAmique Complexe en environnement ALéatoire: réponse des forêts aux changements globaux)

PhD students :

  • 2007-2010 : Fouad Hadj Selem, Étude théorique et numérique des états stationnaires localisés pour l'équation de Schrödinger non linéaire avec potentiel quadratique
  • 2007-2011 : Hung Chinh Nguyen, Simulation de modèles hydrodynamiques et de transfert radiatif intervenant dans la description d'écoulements astrophysiques, coadvisor: Claire Michaut (Observatoire Paris-Meudon)
  • 2013-2017 : Emna Hamraoui, Étude théorique et numérique de solutions de l'équation de Schrödinger non linéaire avec défauts surfaciques, coadvisors: Olivier Goubet (Picardie University) and Ezzeddine Zahrouni (Carthage University)
  • 2015-2019 : Océane Saincir, Approximation numérique de modèles d'hydrodynamique radiative et applications à la physique stellaire, coadvisor: Claire Michaut (Observatoire Paris-Meudon)
  • 2021-2025 : Jade Le Quentrec, Étude théorique et numérique d'équations de Schrödinger non linéaires avec termes de défauts, coadvisor: Olivier Goubet (Lille)
  • 2024- : Alexandre Delorme, Convergence faible et incertitude de modèles, coadvisor: Laurence Carassus (CentreleSupélec)