• Research topic : Nonlinear Network Wave Equations: periodic solutions and graph characterizations.
  • PhD : From October 2015 to september 2018.
  • Funding : XTerM project co-financed by the European Union with the European regional development fund and by the Normandie Regional Council.
  • Advisors : Jean Guy CAPUTO, Arnaud KNIPPEL.
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RESEARCH INTERESTS

  • Complex Systems.
  • Nonlinear Dynamical Systems on Networks.
  • Dynamical Flux on Networks.
  • Nonlinear Waves and Localization in Networks.
  • Graph Theory and Applications to Network Dynamics.
  • Numerical Methods for Partial Differential Equations.

PAPERS

  1. J-G. Caputo, I. Khames, A. Knippel and P. Panayotaros. «Periodic orbits in nonlinear wave equations on networks»,  J. Phys. A: Math. Theor. 50,  375101 (2017).
  2. J-G. Caputo, I. Khames, A. Knippel and A.B. Aceves, « Localized solutions of nonlinear wave equations on networks », submitted (2018). https://arxiv.org/abs/1804.07628
  3. J-G. Caputo, I. Khames and A. Knippel, « On graph Laplacians eigenvectors with components in {+1,-1,0} », submitted (2018). http://arxiv.org/abs/1806.00072
  4. [Before the PhD thesis] F. Hubert, M. Jedouaa, I. Khames, J. Olivier, O. Theodoly and A. Trescases. «Cell motility in   confinement: A computational model for the shape of the cell» ESAIM: PROCEEDINGS AND SURVEYS, CEMRACS 2015: Coupling multi-physics models involving fluids, Vol. 55, p. 148-166 (2016).

COMMUNICATIONS:

  1. Conference on Complex Systems CCS 2016 , 19-22 september 2016, Amsterdam, The Netherlands. Oral presentation in the satellite session of Dynamic Networks and Smart Territory Simulation, control and self-Organization « Mode coupling in a nonlinear network ». Oral presentation in Foundations parallel session « Nonlinear resonances for discrete graphs ».
  2. La 8ème Journée de la Fédération Normandie-Mathématiques , 6 october 2016, Laboratoire de Mathématiques de l’INSA de Rouen. Poster « Mode Coupling in a nonlinear network ».
  3. Seminar IIMAS, Universidad Nacional Autónoma de México , 17 october 2016. Oral presentation « Mode coupling in a nonlinear network ».
  4. Rencontres Rouennaises d’EDP 2016 , 3-4 november 2016, LMRS Université de Rouen. Poster « Mode Coupling in a nonlinear network ».
  5. La 9ème Journée de la Fédération Normandie-Mathématiques , 13 june 2017, LMRS Université de Rouen. Poster « Periodic orbits in nonlinear wave equations on networks ».
  6. La 9ème édition des Journées Des Doctorants JDD 2017 , 13-14 june 2017, Université de Rouen. Oral presentation « Periodic orbits in nonlinear wave equations on networks ».
  7. La 10ème édition des Journées Polyèdres et Optimisation Combinatoire JPOC10 , 14-16 june 2017, Villetaneuse, Paris. Oral presentation « Graphes bivalents et trivalents ».
  8. Workshop on Advance in Nonlinear Complex Systems and Applications , Normandie University, 4-5 jully 2017, Le Havre, France. Oral presentation « Periodic orbits in nonlinear wave equations on networks ». Abstract in Proceeding of Wancsa 2017, p.28.
  9. Conference on Complex Systems CCS 2017 , 17-22 september 2017, Cancun, México. Oral presentation in the parallel session Complexity in Physics and Chemistry - Nonlinear dynamics « Periodic orbits in nonlinear wave equations on networks ».
  10. La 10ème journée d’Automne d’Optimisation dans les Réseaux , 17 november 2017, INSA de Rouen. Oral presentation « Graphes bivalents et trivalents ».
  11. Seminar PhD students , 23 november 2017, Le Havre, France. Oral presentation « Orbites périodiques dans l’équation d’ondes nonlinéaire sur graphes ».
  12. Workshop on Graph Spectra Combinatorics and Optimization , 25-27 January 2018, Aveiro, Portugal. Oral presentation « On bivalent and trivalent graphs ».
  13. Conference on Nonlinear Localization in Lattices, 18-22 June 2018, Spetses, Greece. Oral presentation « Localized solutions of nonlinear network wave equation ».
  14. La 10ème journée de la Fédération Normandie Mathématiques, Caen (LMNO), 28 juin 2018. Oral presentation « Solutions  localisées de l’équation d’onde non-linéaire sur graphes ».
  15. The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 5-9 July 2018, Taipei, Taiwan. Oral presentation « Periodic orbits in nonlinear wave equations on networks ».

 INTERNATIONAL COOPERATIONS

  • Prof. Alejandro B. ACEVES (Department of Mathematics, Southern Methodist University, USA).
  • Prof. Panayotis PANAYOTAROS (Depto. Matemáticas y Mecánica, IIMAS, Universidad Nacional Autónoma de México, MEXICO). 

RESEARCH VISITS

  1. IIMAS Universidad Nacional Autonoma de México, MEXICO (October 2016) with Panayotis PANAYOTAROS (financial support from the French-Mexican bilateral grant SEP-CONACYT-ANUIES-ECOS Nord M15M01).
  2. IIMAS Universidad Nacional Autonoma de México, MEXICO (14 september-14 october 2017) with Panayotis PANAYOTAROS (financial support from the French-Mexican bilateral grant SEP-CONACYT-ANUIES-ECOS Nord M15M01).

EDUCATION

  • 2014 - 2015 : Master 2 in Pure and Applied Mathematics. Université de Nice Sophia Antipolis, FRANCE.
  • 2013 - 2014 : Master 1 in Mathematical Analysis and Applications. Université des sciences et de la technologie d'Oran, ALGERIA.
  • 2010 - 2013 : License in Mathematics. Université des sciences et de la technologie d'Oran, ALGERIA.

INTERNSHIPS

  • License Thesis (2013): « The Zeta function and Riemann hypothesis ». Advisor: Prof. Samir BEKKARA. Département de Mathématiques, Université des Sciences et de la Technologie d’Oran, ALGERIA.
  • Master’s Thesis (2015): « Global regularity for a logarithmically supercritical hyperdissipative dyadic equation and Navier-Stokes equations ». Advisor: Prof. Cédric BERNARDIN. Département de Mathématiques, Université de Nice Sophia Antipolis, FRANCE.
  • CEMRACS 2015 (SMAI) on Coupling Multi-Physics Models involving Fluids, 20 July-28 August 2015, CIRM, Marseille, FRANCE.
  • Parallel Computing in CRIANN (Centre Régional Informatique et d’Applications Numériques de Normandie), 18-20 november 2015, Rouen.

AWARDS AND FELLOWSHIPS

  • Master 2 scholarship for the 2014-2015 academic year offered by the J.A. Dieudonné Laboratory University of Nice Sophia Antipolis with the support of the Euro-Maghreb Laboratory of Mathematics and Its Interactions.
  • PhD scholarship 01/10/2015 - 30/09/2018, funded by the XTerM project.