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Bibliography

Major publications by the team in recent years
  • 1R. Alicandro, M. Cicalese, A. Gloria.

    Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity, in: Arch. Ration. Mech. Anal., 2011, vol. 200, no 3, pp. 881–943.
  • 2A. Gloria.

    Reduction of the resonance error - Part 1: Approximation of homogenized coefficients, in: Math. Models Methods Appl. Sci., 2011, vol. 21, no 8, pp. 1601–1630.
  • 3A. Gloria.

    Numerical homogenization: survey, new results, and perspectives, in: Esaim. Proc., 2012, vol. 37, Mathematical and numerical approaches for multiscale problem.
  • 4A. Gloria, F. Otto.

    An optimal variance estimate in stochastic homogenization of discrete elliptic equations, in: Ann. Probab., 2011, vol. 39, no 3, pp. 779–856.
  • 5A. Gloria, F. Otto.

    An optimal error estimate in stochastic homogenization of discrete elliptic equations, in: Ann. Appl. Probab., 2012, vol. 22, no 1, pp. 1–28.
  • 6A. Gloria, M. Penrose.

    Random parking, Euclidean functionals, and rubber elasticity, in: Comm. Math. Physics, 2013, vol. 321, no 1, pp. 1–31.
Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 8D. Bonheure, E. Moreira dos Santos, M. Ramos, H. Tavares.

    Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems, in: Journal de Mathématiques Pures et Appliquées, 2015, vol. 104, no 6, pp. 1075–1107. [ DOI : 10.1016/j.matpur.2015.07.005 ]

    https://hal.archives-ouvertes.fr/hal-01182582
  • 9C. Cancès, T. Gallouët, L. Monsaingeon.

    The gradient flow structure for incompressible immiscible two-phase flows in porous media, in: Comptes rendus de l'académie des sciences, Mathématiques, 2015, vol. 353, pp. 985-989.

    https://hal.archives-ouvertes.fr/hal-01122770
  • 10M. De Buhan, A. Gloria, P. Le Tallec, M. Vidrascu.

    Reconstruction of a constitutive law for rubber from in silico experiments using Ogden's laws, in: International Journal of Solids and Structures, 2015, 16 p. [ DOI : 10.1016/j.ijsolstr.2015.02.026 ]

    https://hal.inria.fr/hal-00933240
  • 11G. Dujardin, P. Lafitte.

    Asymptotic behavior of splitting schemes involving time-subcycling techniques, in: IMA Journal of Numerical Analysis, October 2015.

    https://hal.archives-ouvertes.fr/hal-00751217
  • 12A. Gloria, M. Duerinckx.

    Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas, in: Archive for Rational Mechanics and Analysis, 2015, 39 p.

    https://hal.inria.fr/hal-01138797
  • 13A. Gloria, Z. Habibi.

    Reduction of the resonance error in numerical homogenisation II: correctors and extrapolation, in: Foundations of Computational Mathematics, 2015, 67 p. [ DOI : 10.1007/s10208-015-9246-z ]

    https://hal.inria.fr/hal-00933234
  • 14A. Gloria, D. Marahrens.

    Annealed estimates on the Green functions and uncertainty quantification, in: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 2015, 43 p, 43 pages.

    https://hal.archives-ouvertes.fr/hal-01093386
  • 15A. Gloria, S. Neukamm, F. Otto.

    Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics, in: Inventiones Mathematicae, 2015, 61 p. [ DOI : 10.1007/s00222-014-0518-z ]

    https://hal.archives-ouvertes.fr/hal-01093405
  • 16A. Gloria, J. Nolen.

    A quantitative central limit theorem for the effective conductance on the discrete torus, in: Communications on Pure and Applied Mathematics, 2015, 38 p.

    https://hal.archives-ouvertes.fr/hal-01093352
  • 17A. Gloria, F. Otto.

    Quantitative results on the corrector equation in stochastic homogenization, in: Journal of the European Mathematical Society, 2015, 57 p, 57 pages, 1 figure.

    https://hal.archives-ouvertes.fr/hal-01093381
  • 18S. R. Nodari, M. Conforti, G. Dujardin, A. Kudlinski, A. Mussot, S. Trillo, S. De Bièvre.

    Modulational instability in dispersion-kicked optical fibers, in: Physical Review A, July 2015, vol. 92, no 1. [ DOI : 10.1103/PhysRevA.92.013810 ]

    https://hal.inria.fr/hal-01250315
  • 19E. Soret, S. De Bièvre.

    Stochastic acceleration in a random time-dependent potential, in: Stochastic Processes and their Applications, July 2015, vol. 125, pp. 2752–2785.

    https://hal.archives-ouvertes.fr/hal-01061294
  • 20G. Thiofack, S. Coulibaly, M. Taki, S. De Bievre, G. Dujardin.

    Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schrödinger equations, in: Physical Review A, October 2015, vol. 92, no 4.

    https://hal.archives-ouvertes.fr/hal-01202842

Scientific Books (or Scientific Book chapters)

  • 21D. Bonheure, R. Nascimento.

    Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion, in: Contributions to Nonlinear Elliptic Equations and Systems, Progress in Nonlinear Differential Equations and Their Applications, Springer, 2015, vol. 86. [ DOI : 10.1007/978-3-319-19902-3_4 ]

    https://hal.archives-ouvertes.fr/hal-01182833
  • 22S. De Bievre, F. Genoud, S. R. Nodari.

    Orbital stability: analysis meets geometry, in: Nonlinear Optical and Atomic Systems, Lecture Notes in Mathematics, 2015, vol. 2146, pp. 147-273. [ DOI : 10.1007/978-3-319-19015-0_3 ]

    https://hal.archives-ouvertes.fr/hal-01028168

Other Publications

References in notes
  • 36G. Agrawal.

    Nonlinear fiber optics, Academic Press, 2006.
  • 37B. Aguer, S. De Bièvre, P. Lafitte, P. E. Parris.

    Classical motion in force fields with short range correlations, in: J. Stat. Phys., 2010, vol. 138, no 4-5, pp. 780 – 814.
  • 38A. Anantharaman, C. Le Bris.

    A numerical approach related to defect-type theories for some weakly random problems in homogenization, in: Multiscale Model. Simul., 2011, vol. 9, no 2, pp. 513–544.

    http://dx.doi.org/10.1137/10079639X
  • 39A. Anantharaman, C. Le Bris.

    Elements of mathematical foundations for numerical approaches for weakly random homogenization problems, in: Commun. Comput. Phys., 2012, vol. 11, no 4, pp. 1103–1143.

    http://dx.doi.org/10.4208/cicp.030610.010411s
  • 40T. Arbogast.

    Numerical subgrid upscaling of two-phase flow in porous media, in: Numerical treatment of multiphase flows in porous media (Beijing, 1999), Berlin, Lecture Notes in Phys., Springer, 2000, vol. 552, pp. 35–49.
  • 41S. N. Armstrong, Z. Shen.

    Lipschitz estimates in almost-periodic homogenization, in: Commun. Pure Appl. Mathematics, September 2015.
  • 42S. N. Armstrong, C. K. Smart.

    Quantitative stochastic homogenization of convex integral functionals, in: Ann. Scientifiques de l'ENS, 2015.
  • 43M. Avellaneda, F.-H. Lin.

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    http://dx.doi.org/10.1002/cpa.3160400607
  • 44J. M. Ball.

    Some open problems in elasticity, in: Geometry, mechanics, and dynamics, New York, Springer, 2002, pp. 3–59.
  • 45A. Benoit.

    Geometric optics expansions for hyperbolic corner problems, selfinteraction phenomenon., Preprint https://hal.archives-ouvertes.fr/hal-01196341/document .
  • 46A. Braides.

    Homogenization of some almost periodic functionals, in: Rend. Accad. Naz. Sci. XL, 1985, vol. 103, pp. 261–281.
  • 47G. Dal Maso, L. Modica.

    Nonlinear stochastic homogenization and ergodic theory, in: J. Reine Angew. Math., 1986, vol. 368, pp. 28–42.
  • 48S. De Bièvre, F. Genoud, S. Rota Nodari.

    Orbital Stability: Analysis Meets Geometry, in: Nonlinear Optical and Atomic Systems, C. Besse, J.-C. Garreau (editors), Lecture Notes in Mathematics, Springer International Publishing, 2015, vol. 2146, pp. 147-273.
  • 49S. De Bièvre, C. Mejia-Monasterio, E. P. Parris.

    Preprint, 2016.
  • 50S. De Bièvre, P. Parris.

    Equilibration, generalized equipartition and diffusion in dynamical Lorentz gases, in: J. Stat. Phys., 2011, vol. 142, pp. 356–385.
  • 51S. De Bièvre, G. Forni.

    Transport properties of kicked and quasiperiodic Hamiltonians, in: J. Statist. Phys., 2010, vol. 90, no 5-6, pp. 1201–1223.
  • 52M. Disertori, W. Kirsch, A. Klein, F. Klopp, V. Rivasseau.

    Random Schrödinger operators, Panoramas et Synthèses, Société Mathématique de France, Paris, 2008, no 25.
  • 53M. Duerinckx.

    Mean-field limits for some Riesz interaction gradient flows, January 2016, working paper or preprint.

    https://hal.archives-ouvertes.fr/hal-01252661
  • 54Y. Efendiev, T. Hou.

    Multiscale finite element methods, Surveys and Tutorials in the Applied Mathematical Sciences, Springer, New York, 2009, vol. 4, Theory and applications.
  • 55P. Flory.

    Statistical mechanics of chain molecules, Interscience Publishers, New York, 1969.
  • 56J.-C. Garreau, B. Vermersch.

    Spectral description of the dynamics of ultracold interacting bosons in disordered lattices, in: New. J. Phys., 2013, vol. 15, 045030.
  • 57A. Gloria, P. Le Tallec, M. Vidrascu.

    Foundation, analysis, and numerical investigation of a variational network-based model for rubber, in: Continuum Mech. Thermodyn..
  • 58A. Gloria, S. Neukamm, F. Otto.

    A regularity theory for random elliptic operators and homogenization, September 2014, working paper or preprint.

    https://hal.archives-ouvertes.fr/hal-01093368
  • 59T. Hou, X. Wu.

    A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, in: J. Comput. Phys., 1997, vol. 134, pp. 169–189.
  • 60S. M. Kozlov.

    Averaging of differential operators with almost periodic rapidly oscillating coefficients, in: Mat. Sb. (N.S.), 1978, vol. 107(149), no 2, pp. 199–217, 317.
  • 61S. Kozlov.

    The averaging of random operators, in: Mat. Sb. (N.S.), 1979, vol. 109(151), no 2, pp. 188–202, 327.
  • 62F. Legoll, W. Minvielle.

    A control variate approach based on a defect-type theory for variance reduction in stochastic homogenization, in: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2015, vol. 13, no 2, pp. 519-550.

    https://hal.archives-ouvertes.fr/hal-01053459
  • 63S. Müller.

    Homogenization of nonconvex integral functionals and cellular elastic materials, in: Arch. Rat. Mech. Anal., 1987, vol. 99, pp. 189–212.
  • 64A. Naddaf, T. Spencer.

    Estimates on the variance of some homogenization problems, Preprint, 1998.
  • 65G. Papanicolaou, S. Varadhan.

    Boundary value problems with rapidly oscillating random coefficients, in: Random fields, Vol. I, II (Esztergom, 1979), Amsterdam, Colloq. Math. Soc. János Bolyai, North-Holland, 1981, vol. 27, pp. 835–873.
  • 66S. Serfaty.

    Mean Field Limits of the Gross-Pitaevskii and Parabolic Ginzburg-Landau Equations, in: ArXiv e-prints, July 2015.
  • 67E. Soret, S. D. Bièvre.

    Stochastic acceleration in a random time-dependent potential, in: Stochastic Processes and their Applications, 2015, vol. 125, no 7, pp. 2752 – 2785.
  • 68C. Sulem, P.-L. Sulem.

    The nonlinear Schrödinger equation, Springer-Verlag, New-York, 1999.
  • 69L. Treloar.

    The Physics of Rubber Elasticity, Oxford at the Clarendon Press, Oxford, 1949.
  • 70E. Weinan.

    Principles of multiscale modeling, Cambridge University Press, Cambridge, 2011, xviii+466 p.


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