Antoine Gloria
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Research

Publications and Preprints

Cours

ERC QUANTHOM






New:
  • Linear waves in disordered media
    • (with A. Benoit) Long-time homogenization and asymptotic ballistic transport of classical waves (preprint), Ann. Scientifiques de l'ENS.
    • (with M. Duerinckx and C. Shirley) Approximate normal forms via Floquet-Bloch theory. Part 1: Nehorosev stability for linear waves in disordered media, in preparation.

  • Homogenization and linear elasticity
    • (with M. Ruf) Loss of strong ellipticity through homogenization in 2D linear elasticity: A phase diagram (preprint), Arch. Ration. Mech. Anal.

  • Thermodynamic limit of free energies on random lattices
    • (with M. Cicalese and M. Ruf) From statistical polymer physics to nonlinear elasticity (preprint).

  • Quantitative theory of stochastic homogenization for uncorrelated and correlated coefficient fields: weighted functional inequalities, large-scale regularity, quantitative estimates (optimal scalings and nearly-optimal stochastic integrability), and theory of fluctuations
    • (with M. Duerinckx) Weighted functional inequalities: Concentration properties (preprint).
    • (with M. Duerinckx) Weighted functional inequalities: Constructive approach (preprint).
    • (with M. Duerinckx) Weighted second-order Poincaré inequalities: Application to RSA models (preprint).
    • (with S. Neukamm and F. Otto) A regularity theory for random elliptic operators (preprint).
    • (with S. Neukamm and F. Otto) Quantitative stochastic homogenization for correlated coefficient fields (preprint).
    • (with M. Duerinckx and F. Otto) The structure of fluctuations in stochastic homogenization (preprint).
    • (with M. Duerinckx and F. Otto) Robustness of the pathwise structure of fluctuations in stochastic homogenization, in preparation.
    • (with M. Duerinckx and J. Fischer) Scaling limit of the homogenization commutator for correlated Gaussian coefficient fields, in preparation.
    • (with F. Otto) The corrector in stochastic homogenization: optimal rates, stochastic integrability, and fluctuations (preprint).





Publications:

Qualitative homogenization of discrete elliptic equations and applications
  • (with A. Braides) Exact Bounds on the Effective Behavior of a Conducting Discrete Polycrystal, SIAM MMS, 6 (2008), No. 4, pp 1198-1216 (pdf).

  • (with R. Alicandro and M. Cicalese) Variational description of bulk energies for bounded and unbounded spin systems, Nonlinearity, 21 (2008), pp 1881-1910 (pdf).

  • (with R. Alicandro and M. Cicalese) Mathematical derivation of a rubber-like stored energy functional, C. R. Acad. Sci. Paris, Série I, 345 (2007), No. 8, pp 479-482 (pdf).

  • (with R. Alicandro and M. Cicalese) Convergence analysis of the Bol-Reese model for rubber, Proceedings of CMDS 11, Presse des Mines de Paris, 2008, pp 137-142 (pdf).

  • (with R. Alicandro and M. Cicalese) Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity, Arch. Ration. Mech. Anal., 200 (2011), No 3, pp 881-943 (pdf).

Quantitative stochastic homogenization of discrete elliptic equations
  • (with F. Otto) An optimal variance estimate in stochastic homogenization of discrete elliptic equations, Ann. of Probab., 39 (2011), No 3, pp 779-856 (pdf).

  • (with F. Otto) An optimal error estimate in stochastic homogenization of discrete elliptic equations, Ann. Appl. Probab., 22 (2012), No 1, pp 1-28 (pdf).

  • (with J.-C. Mourrat) Spectral measure and approximation of homogenized coefficients, Probab. Theory Related Fields, 154 (2012), No. 1, pp 287-326, (pdf).

  • (with J.-C. Mourrat) Quantitative version of the Kipnis-Varadhan theorem and Monte-Carlo approximation of homogenized coefficients, Ann. Appl. Probab., 23 (2013), No. 4, pp 1544-1583 (pdf).

  • (with S. Neukamm and F. Otto) Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics, Inventiones Mathematicae, 199 (2015), No. 2, pp 455-515 (long version, short version).

  • (with S. Neukamm and F. Otto) A quantitative two-scale expansion in stochastic homogenization of discrete linear elliptic equations, M2AN Modél. Math. Anal. Numér, special issue 2014: Multiscale problems and techniques (pdf).

  • (with J. Nolen) A quantitative central limit theorem for the effective conductance on the discrete torus, Commun. Pure and Appl. Math. (pdf)

  • (with M. Duerinckx and F. Otto) The structure of fluctuations in stochastic homogenization (pdf).

Qualitative homogenization of elliptic PDEs and integral functionals
  • Stochastic diffeomorphisms and homogenization of multiple integrals, AMRX, Vol. 2008, Article ID abn001 (pdf).

  • (with M. Barchiesi) New counterexamples to the cell formula in nonconvex homogenization, Arch. Ration. Mech. Anal., 195 (2010), No 3, pp 991-1024 (pdf).

  • (with S. Neukamm) Commutability of homogenization and linearization at identity in finite elasticity and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire, 28 (2011), No 6, pp 941-964 (pdf).

  • (with M. Duerinckx) Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas, Arch. Ration. Mech. Anal. (pdf).

  • (with M. Duerinckx) Stochastic homogenization of nonconvex unbounded integral functionals with convex growth, Arch. Ration. Mech. Anal. (pdf).

  • (with G. A. Francfort) Isotropy prohibits the loss of strong ellipticity through homogenization in linear elasticity (pdf), CRAS.

Quantitative stochastic homogenization of elliptic PDEs
  • Fluctuation of solutions to linear elliptic equations with noisy diffusion coefficients, Comm. Partial Differential Equations, 38 (2013), No 2, pp 304-338 (pdf).

  • (with F. Otto) Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization, Esaim Proc (pdf).

  • (with F. Otto) Quantitative results on the corrector equation in stochastic homogenization, J. Eur. Math. Soc. (pdf).

  • (with D. Marahrens) Annealed estimates on the Green functions and uncertainty quantification, Ann. Inst. H. Poincaré Anal. Non Linéaire (pdf).

  • (with S. Armstrong and T. Kuusi) Bounded correctors in almost periodic homogenization, Arch. Ration. Mech. Anal. (pdf).

Numerical analysis for homogenization problems
  • A direct approach to numerical homogenization in nonlinear elasticity, NHM, 1 (2006), No.1, pp 109-141 (pdf).

  • Analytical framework for the numerical homogenization of elliptic monotone operators and quasiconvex energies, SIAM MMS, 5 (2006), No. 3, pp 996-1043 (pdf).

  • Analytical framework for numerical homogenization. Part 2: Windowing and oversampling, SIAM MMS, 7 (2008), No. 1, pp 274-293 (pdf).

  • Reduction of the resonance error. Part 1: Approximation of homogenized coefficients, Math. Models Methods Appl. Sci. (M3AS), 21 (2011), No. 3, pp 1601-1630 (abstract, pdf).

  • Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations, M2AN Modél. Math. Anal. Numér, 46 (2012), No. 1, pp 1-38 (pdf).

  • (with T. Goudon and S. Krell) Numerical homogenization of a nonlinearly coupled elliptic-parabolic system, reduced basis method, and application to nuclear waste storage, Math. Models Methods Appl. Sci. (M3AS), 23 (2013), No. 13, pp 2523-2560 (pdf).

  • Numerical homogenization: survey, new results, and perspectives, ESAIM: Proc. Volume 37, September 2012, Mathematical and numerical approaches for multiscale problem (pdf).

  • (with A.-C. Egloffe, J.-C. Mourrat, and T. N. Nguyen) Random walk in random environment, corrector equation, and homogenized coefficients: from theory to numerics, back and forth, IMA J. Num. Anal. (pdf).

  • (with Z. Habibi) Reduction of the resonance error in numerical homogenization II: correctors and extrapolation, Foundations of Computational Mathematics (pdf).

Multiscale modelling in rubber elasticity
  • (with P. Le Tallec and M. Vidrascu) Foundation, analysis, and numerical investigation of a variational network-based model for rubber, Cont. Mech. Thermodynamics, 26 (2014), No 1, pp 1-31 (pdf).

  • (with M. de Buhan, P. Le Tallec, and M. Vidrascu) Reconstruction of a constitutive law for rubber from in silico experiments using Ogden's laws, Int. Journal of Solids and Structures, 62 (2015), pp 158–173 (pdf).

Stochastic geometry and applications
  • (with M. D. Penrose) Random parking, Euclidean functionals, and rubber elasticity, Commun. Math. Phys., 321 (2013), No. 1, pp 1-31 (pdf).

  • When are increment-stationary random point sets stationary?, Electron. Commun. Probab. 19 (2014), no. 30, 1–14 (pdf).

Numerical analysis for hyperbolic problems
  • (with J.-F. Coulombel) Semigroup stability of finite difference schemes for multidimensional hyperbolic initial boundary value problems (pdf), Math. Comp., 80 (2011), pp 165-203.

Fluid-structure interaction problems
  • (with M.-A. Fernandez, J.-F. Gerbeau and M. Vidrascu) Domain decomposition based Newton methods for fluid-structure interaction problems, ESAIM: Proceedings, special volume CANUM 2006, 22 (2007), pp 67-82 (pdf)

  • (with M.-A. Fernandez, J.-F. Gerbeau and M. Vidrascu) A partitioned Newton method for the interaction of a fluid and a 3D shell structure (pdf), Eur. J. Comp. Mech., 19 (2010), 5-7, pp.479-512