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, n^o 3, pp. 881–943.
• 2A. Gloria.
  Numerical homogenization: survey, new results, and perspectives, in: Esaim. Proc., 2012, vol. 37, Mathematical and numerical approaches for multiscale problem.
• 3A. Gloria, F. Otto.
  An optimal variance estimate in stochastic homogenization of discrete elliptic equations, in: Ann. Probab., 2011, vol. 39, n^o 3, pp. 779–856.
• 4A. Gloria, F. Otto.
  An optimal error estimate in stochastic homogenization of discrete elliptic equations, in: Ann. Appl. Probab., 2012, vol. 22, n^o 1, pp. 1–28.
• 5A. Gloria, M. Penrose.
  Random parking, Euclidean functionals, and rubber elasticity, in: Comm. Math. Physics, 2013, vol. 321, n^o 1, pp. 1–31.

Publications of the year

Articles in International Peer-Reviewed Journals

• 6S. N. Armstrong, A. Gloria, T. Kuusi.
  Bounded correctors in almost periodic homogenization, in: Archive for Rational Mechanics and Analysis, 2016, vol. 222, n^o 1, pp. 393–426. [ DOI : 10.1007/s00205-016-1004-0 ]
  https://hal.inria.fr/hal-01230991
• 7O. Blondel, P. Gonçalves, M. Simon.
  Convergence to the Stochastic Burgers Equation from a degenerate microscopic dynamics, in: Electronic Journal of Probability, December 2016, vol. 21, n^o 69, 25 p. [ DOI : 10.1214/16-EJP15 ]
  https://hal.archives-ouvertes.fr/hal-01295541
• 8D. Bonheure, J.-B. Casteras, B. Noris.
  Layered solutions with unbounded mass for the Keller–Segel equation, in: Journal of Fixed Point Theory and Applications, 2016. [ DOI : 10.1007/s11784-016-0364-2 ]
  https://hal.archives-ouvertes.fr/hal-01398930
• 9D. Bonheure, S. Cingolani, M. Nys.
  Nonlinear Schrödinger equation: concentration on circles driven by an external magnetic field, in: Calculus of Variations and Partial Differential Equations, 2016, vol. 55. [ DOI : 10.1007/s00526-016-1013-8 ]
  https://hal.archives-ouvertes.fr/hal-01182834
• 10D. Bonheure, P. D 'avenia, A. Pomponio.
  On the electrostatic Born-Infeld equation with extended charges, in: Communications in Mathematical Physics, 2016. [ DOI : 10.1007/s00220-016-2586-y ]
  https://hal.archives-ouvertes.fr/hal-01182830
• 11D. Bonheure, M. Grossi, B. Noris, S. Terracini.
  Multi-layer radial solutions for a supercritical Neumann problem, in: Journal of Differential Equations, 2016, vol. 261. [ DOI : 10.1016/j.jde.2016.03.016 ]
  https://hal.archives-ouvertes.fr/hal-01182832
• 12D. Bonheure, C. Grumiau, C. Troestler.
  Multiple radial positive solutions of semilinear elliptic problems with Neumann boundary conditions, in: Nonlinear Analysis: Theory, Methods and Applications, 2016, vol. 147, pp. 236-273. [ DOI : 10.1016/j.na.2016.09.010 ]
  https://hal.archives-ouvertes.fr/hal-01408548
• 13D. Bonheure, F. Hamel.
  One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R${}^N$, in: Chinese Annals of Mathematics - Series B, 2016, 25 p.
  https://hal.archives-ouvertes.fr/hal-01182688
• 14D. Bonheure, F. Juraj, S. Alberto.
  Qualitative properties of solutions to mixed-diffusion bistable equations, in: Calculus of Variations and Partial Differential Equations, May 2016, vol. 55. [ DOI : 10.1007/s00526-016-0987-6 ]
  https://hal.archives-ouvertes.fr/hal-01203710
• 15D. Bonheure, J. D. Rossi, N. Saintier.
  The limit as p→∞ in the eigenvalue problem for a system of p-Laplacians, in: Annali di Matematica Pura ed Applicata, 2016, vol. 195, n^o 5, pp. 1771–1785. [ DOI : 10.1007/s10231-015-0547-2 ]
  https://hal.archives-ouvertes.fr/hal-01408551
• 16J.-B. Casteras, E. Heinonen, I. Holopainen.
  Solvability of Minimal Graph Equation Under Pointwise Pinching Condition for Sectional Curvatures, in: The Journal of Geometric Analysis, 2016. [ DOI : 10.1007/s12220-016-9712-0 ]
  https://hal.archives-ouvertes.fr/hal-01398918
• 17J.-B. Casteras, J. B. Ripoll.
  On asymptotic plateau’s problem for CMC hypersurfaces on rank 1 symmetric spaces of noncompact type, in: Asian Journal of Mathematics, 2016, vol. 20, n^o 4, pp. 695 - 708. [ DOI : 10.4310/AJM.2016.v20.n4.a5 ]
  https://hal.archives-ouvertes.fr/hal-01398916
• 18C. Chainais-Hillairet, T. Gallouët.
  Study of a pseudo-stationary state for a corrosion model: existence and numerical approximation, in: Nonlinear Analysis: Real World Applications, 2016.
  https://hal.inria.fr/hal-01147621
• 19M. Conforti, A. Mussot, A. Kudlinski, S. Rota Nodari, G. Dujardin, S. De Bièvre, A. Armaroli, S. Trillo.
  Heteroclinic Structure of Parametric Resonance in the Nonlinear Schrödinger Equation, in: Physical Review Letters, June 2016, vol. 117, n^o 1. [ DOI : 10.1103/PhysRevLett.117.013901 ]
  https://hal.archives-ouvertes.fr/hal-01333882
• 20S. De Bièvre, A. Vavasseur, T. Goudon.
  Particles interacting with a vibrating medium: existence of solutions and convergence to the Vlasov–Poisson system, in: SIAM Journal on Mathematical Analysis, 2016, vol. 48, n^o 6, pp. 3984–4020.
  https://hal.archives-ouvertes.fr/hal-01286519
• 21M. Duerinckx.
  Mean-field limits for some Riesz interaction gradient flows, in: SIAM Journal on Mathematical Analysis, 2016, vol. 48, n^o 3, pp. 2269-2300.
  https://hal.archives-ouvertes.fr/hal-01252661
• 22M. Duerinckx, A. Gloria.
  Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas, in: Archive for Rational Mechanics and Analysis, 2016, vol. 220, n^o 1, pp. 297–361. [ DOI : 10.1007/s00205-015-0933-3 ]
  https://hal.inria.fr/hal-01138797
• 23M. Duerinckx, A. Gloria.
  Stochastic homogenization of nonconvex unbounded integral functionals with convex growth, in: Archive for Rational Mechanics and Analysis, 2016, vol. 221, n^o 3, pp. 1511–1584. [ DOI : 10.1007/s00205-016-0992-0 ]
  https://hal.inria.fr/hal-01192752
• 24G. A. Francfort, A. Gloria.
  Isotropy prohibits the loss of strong ellipticity through homogenization in linear elasticity, in: Comptes Rendus Mathématique, 2016, vol. 354, pp. 1139 - 1144. [ DOI : 10.1016/j.crma.2016.09.014 ]
  https://hal.inria.fr/hal-01398518
• 25A. Gloria, Z. Habibi.
  Reduction of the resonance error in numerical homogenisation II: correctors and extrapolation, in: Foundations of Computational Mathematics, 2016, vol. 16, n^o 1, pp. 217–296. [ DOI : 10.1007/s10208-015-9246-z ]
  https://hal.inria.fr/hal-00933234
• 26A. Gloria, D. Marahrens.
  Annealed estimates on the Green functions and uncertainty quantification, in: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 2016, vol. 33, n^o 6, pp. 1153–1197, 43 pages. [ DOI : 10.1016/j.anihpc.2015.04.001 ]
  https://hal.archives-ouvertes.fr/hal-01093386
• 27A. Gloria, J. Nolen.
  A quantitative central limit theorem for the effective conductance on the discrete torus, in: Communications on Pure and Applied Mathematics, 2016, vol. 69, n^o 12, pp. 2304–2348. [ DOI : 10.1002/cpa.21614 ]
  https://hal.archives-ouvertes.fr/hal-01093352
• 28M. Simon, P. Goncalves, T. Franco.
  Crossover to the stochastic Burgers equation for the WASEP with a slow bond, in: Communications in Mathematical Physics, 2016. [ DOI : 10.1007/s00220-016-2607-x ]
  https://hal.inria.fr/hal-01355447
• 29M. Simon, P. Gonçalves, M. Jara.
  Second order Boltzmann-Gibbs principle for polynomial functions and applications, in: Journal of Statistical Physics, December 2016. [ DOI : 10.1007/s10955-016-1686-6 ]
  https://hal.inria.fr/hal-01381009

Other Publications

• 30A. Benoit.
  Geometric optics expansions for hyperbolic corner problems II : from weak stability to violent instability, October 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01242899
• 31A. Benoit.
  Semi-group stability of finite difference schemes in corner domains, December 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01417105
• 32C. Bernardin, P. Gonçalves, M. Jara, M. Simon.
  Interpolation process between standard diffusion and fractional diffusion, July 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01348503
• 33D. Bonheure, J.-B. Casteras, B. Noris.
  Multiple positive solutions of the stationary Keller-Segel system, November 2016, 33 pages.
  https://hal.archives-ouvertes.fr/hal-01398922
• 34D. Bonheure, S. Cingolani, J. Van Schaftingen.
  The logarithmic Choquard equation : sharp asymptotics and nondegeneracy of the groundstate, December 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01414010
• 35J.-B. Casteras, E. Heinonen, I. Holopainen.
  Dirichlet problem for $f$-minimal graphs, November 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01398920
• 36D. Cohen, G. Dujardin.
  Exponential integrators for nonlinear Schrödinger equations with white noise dispersion, November 2016, working paper or preprint.
  https://hal.inria.fr/hal-01403036
• 37S. De Bievre, S. Rota Nodari.
  Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups, May 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01312534
• 38M. Duerinckx.
  Well-posedness for mean-field evolutions arising in superconductivity, October 2016, working paper or preprint.
  https://hal.inria.fr/hal-01389812
• 39M. Duerinckx, A. Gloria, F. Otto.
  The structure of fluctuations in stochastic homogenization, February 2016, working paper or preprint.
  https://hal.inria.fr/hal-01398515
• 40A. Gloria, F. Otto.
  The corrector in stochastic homogenization: optimal rates, stochastic integrability, and fluctuations, May 2016, working paper or preprint.
  https://hal.inria.fr/hal-01230985
• 41T. Komorowski, S. Olla, M. Simon.
  Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities, August 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01358979
• 42G. G. L. Tiofack, S. Coulibaly, M. Taki, S. De Bièvre, G. Dujardin.
  Periodic modulations controlling Kuznetsov-Ma soliton formation in nonlinear Schrödinger equations, July 2016, working paper or preprint.
  https://hal.inria.fr/hal-01403028

References in notes

• 43G. Agrawal.
  Nonlinear fiber optics, Academic Press, 2006.
• 44B. 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, n^o 4-5, pp. 780 – 814.
• 45A. 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, n^o 2, pp. 513–544.
  http://dx.doi.org/10.1137/10079639X
• 46A. Anantharaman, C. Le Bris.
  Elements of mathematical foundations for numerical approaches for weakly random homogenization problems, in: Commun. Comput. Phys., 2012, vol. 11, n^o 4, pp. 1103–1143.
  http://dx.doi.org/10.4208/cicp.030610.010411s
• 47T. 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.
• 48S. N. Armstrong, Z. Shen.
  Lipschitz estimates in almost-periodic homogenization, in: Commun. Pure Appl. Mathematics, September 2015.
• 49S. N. Armstrong, C. K. Smart.
  Quantitative stochastic homogenization of convex integral functionals, in: Ann. Scientifiques de l'ENS, 2015.
• 50J. M. Ball.
  Some open problems in elasticity, in: Geometry, mechanics, and dynamics, New York, Springer, 2002, pp. 3–59.
• 51G. Basile, C. Bernardin, S. Olla.
  Thermal conductivity for a momentum conservative model, in: Comm. Math. Phys., 2009, vol. 287, n^o 1, pp. 67–98.
  http://dx.doi.org/10.1007/s00220-008-0662-7
• 52C. Bernardin, P. Gonçalves, M. Jara.
  3/4-fractional superdiffusion in a system of harmonic oscillators perturbed by a conservative noise, in: Arch. Ration. Mech. Anal., 2016, vol. 220, n^o 2, pp. 505–542.
  http://dx.doi.org/10.1007/s00205-015-0936-0
• 53C. Bernardin, P. Gonçalves, M. Jara, M. Sasada, M. Simon.
  From normal diffusion to superdiffusion of energy in the evanescent flip noise limit, in: J. Stat. Phys., 2015, vol. 159, n^o 6, pp. 1327–1368.
  http://dx.doi.org/10.1007/s10955-015-1235-8
• 54D. Bonheure, J.-B. Casteras, R. Nascimento.
  Orbitally stable standing waves of a mixed dispersion nonlinear Schrödinger equation, in: Preprint, 2016.
• 55A. Braides.
  Homogenization of some almost periodic functionals, in: Rend. Accad. Naz. Sci. XL, 1985, vol. 103, pp. 261–281.
• 56G. Dal Maso, L. Modica.
  Nonlinear stochastic homogenization and ergodic theory, in: J. Reine Angew. Math., 1986, vol. 368, pp. 28–42.
• 57S. De Bièvre, C. Mejia-Monasterio, E. P. Parris.
  Preprint, 2016.
• 58S. De Bièvre, P. Parris.
  Equilibration, generalized equipartition and diffusion in dynamical Lorentz gases, in: J. Stat. Phys., 2011, vol. 142, pp. 356–385.
• 59S. De Bièvre, J. Faupin, B. Schubnel.
  Spectral analysis of a model for quantum friction, December 2015, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01246914
• 60S. De Bièvre, G. Forni.
  Transport properties of kicked and quasiperiodic Hamiltonians, in: J. Statist. Phys., 2010, vol. 90, n^o 5-6, pp. 1201–1223.
• 61M. Disertori, W. Kirsch, A. Klein, F. Klopp, V. Rivasseau.
  Random Schrödinger operators, Panoramas et Synthèses, Société Mathématique de France, Paris, 2008, n^o 25.
• 62Y. Efendiev, T. Hou.
  Multiscale finite element methods, Surveys and Tutorials in the Applied Mathematical Sciences, Springer, New York, 2009, vol. 4, Theory and applications.
• 63P. Flory.
  Statistical mechanics of chain molecules, Interscience Publishers, New York, 1969.
• 64J.-C. Garreau, B. Vermersch.
  Spectral description of the dynamics of ultracold interacting bosons in disordered lattices, in: New. J. Phys., 2013, vol. 15, 045030.
• 65A. Gloria, P. Le Tallec, M. Vidrascu.
  Foundation, analysis, and numerical investigation of a variational network-based model for rubber, in: Continuum Mech. Thermodyn..
• 66P. Gonçalves, M. Jara.
  Nonlinear fluctuations of weakly asymmetric interacting particle systems, in: Arch. Ration. Mech. Anal., 2014, vol. 212, n^o 2, pp. 597–644.
  http://dx.doi.org/10.1007/s00205-013-0693-x
• 67D. Horoshko, S. De Bièvre, M. I. Kolobov, G. Patera.
  Entanglement of quantum circular states of light, in: Phys.Rev.A, June 2016. [ DOI : 10.1103/PhysRevA.93.062323 ]
  https://hal.inria.fr/hal-01408553
• 68T. 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.
• 69M. Jara, T. Komorowski, S. Olla.
  Limit theorems for additive functionals of a Markov chain, in: Ann. Appl. Probab., 2009, vol. 19, n^o 6, pp. 2270–2300.
  http://dx.doi.org/10.1214/09-AAP610
• 70S. M. Kozlov.
  Averaging of differential operators with almost periodic rapidly oscillating coefficients, in: Mat. Sb. (N.S.), 1978, vol. 107(149), n^o 2, pp. 199–217, 317.
• 71S. Kozlov.
  The averaging of random operators, in: Mat. Sb. (N.S.), 1979, vol. 109(151), n^o 2, pp. 188–202, 327.
• 72F. 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, n^o 2, pp. 519-550.
  https://hal.archives-ouvertes.fr/hal-01053459
• 73S. Müller.
  Homogenization of nonconvex integral functionals and cellular elastic materials, in: Arch. Rat. Mech. Anal., 1987, vol. 99, pp. 189–212.
• 74A. Naddaf, T. Spencer.
  Estimates on the variance of some homogenization problems, Preprint, 1998.
• 75G. 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.
• 76C. Sulem, P.-L. Sulem.
  The nonlinear Schrödinger equation, Springer-Verlag, New-York, 1999.
• 77L. Treloar.
  The Physics of Rubber Elasticity, Oxford at the Clarendon Press, Oxford, 1949.
• 78E. Weinan.
  Principles of multiscale modeling, Cambridge University Press, Cambridge, 2011, xviii+466 p.